Scippy

SCIP

Solving Constraint Integer Programs

sepa_rlt.c
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4 /* SCIP --- Solving Constraint Integer Programs */
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24 
25 /**@file sepa_rlt.c
26  * @ingroup DEFPLUGINS_SEPA
27  * @brief separator for cuts generated by Reformulation-Linearization-Technique (RLT)
28  * @author Fabian Wegscheider
29  * @author Ksenia Bestuzheva
30  *
31  * @todo implement the possibility to add extra auxiliary variables for RLT (like in DOI 10.1080/10556788.2014.916287)
32  * @todo add RLT cuts for the product of equality constraints
33  * @todo implement dynamic addition of RLT cuts during branching (see DOI 10.1007/s10898-012-9874-7)
34  * @todo use SCIPvarIsBinary instead of SCIPvarGetType() == SCIP_VARTYPE_BINARY ?
35  * @todo parameter maxusedvars seems arbitrary (too large for small problems; too small for large problems); something more adaptive we can do? (e.g., all variables with priority >= x% of highest prio)
36  */
37 
38 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
39 
40 #include <assert.h>
41 #include <string.h>
42 
43 #include "scip/sepa_rlt.h"
44 #include "scip/cons_nonlinear.h"
45 #include "scip/pub_lp.h"
46 #include "scip/expr_pow.h"
47 #include "scip/nlhdlr_bilinear.h"
48 #include "scip/cutsel_hybrid.h"
49 
50 
51 #define SEPA_NAME "rlt"
52 #define SEPA_DESC "reformulation-linearization-technique separator"
53 #define SEPA_PRIORITY 10 /**< priority for separation */
54 #define SEPA_FREQ 0 /**< frequency for separating cuts; zero means to separate only in the root node */
55 #define SEPA_MAXBOUNDDIST 1.0 /**< maximal relative distance from the current node's dual bound to primal bound
56  * compared to best node's dual bound for applying separation.*/
57 #define SEPA_USESSUBSCIP FALSE /**< does the separator use a secondary SCIP instance? */
58 #define SEPA_DELAY FALSE /**< should separation method be delayed, if other separators found cuts? */
59 
60 #define DEFAULT_MAXUNKNOWNTERMS 0 /**< maximum number of unknown bilinear terms a row can have to be used */
61 #define DEFAULT_MAXUSEDVARS 100 /**< maximum number of variables that will be used to compute rlt cuts */
62 #define DEFAULT_MAXNCUTS -1 /**< maximum number of cuts that will be added per round */
63 #define DEFAULT_MAXROUNDS 1 /**< maximum number of separation rounds per node (-1: unlimited) */
64 #define DEFAULT_MAXROUNDSROOT 10 /**< maximum number of separation rounds in the root node (-1: unlimited) */
65 #define DEFAULT_ONLYEQROWS FALSE /**< whether only equality rows should be used for rlt cuts */
66 #define DEFAULT_ONLYCONTROWS FALSE /**< whether only continuous rows should be used for rlt cuts */
67 #define DEFAULT_ONLYORIGINAL TRUE /**< whether only original variables and rows should be used for rlt cuts */
68 #define DEFAULT_USEINSUBSCIP FALSE /**< whether the separator should also be used in sub-scips */
69 #define DEFAULT_USEPROJECTION FALSE /**< whether the separator should first check projected rows */
70 #define DEFAULT_DETECTHIDDEN FALSE /**< whether implicit products should be detected and separated by McCormick */
71 #define DEFAULT_HIDDENRLT FALSE /**< whether RLT cuts should be added for hidden products */
72 #define DEFAULT_ADDTOPOOL TRUE /**< whether globally valid RLT cuts are added to the global cut pool */
73 
74 #define DEFAULT_GOODSCORE 1.0 /**< threshold for score of cut relative to best score to be considered good,
75  * so that less strict filtering is applied */
76 #define DEFAULT_BADSCORE 0.5 /**< threshold for score of cut relative to best score to be discarded */
77 #define DEFAULT_OBJPARALWEIGHT 0.0 /**< weight of objective parallelism in cut score calculation */
78 #define DEFAULT_EFFICACYWEIGHT 1.0 /**< weight of efficacy in cut score calculation */
79 #define DEFAULT_DIRCUTOFFDISTWEIGHT 0.0 /**< weight of directed cutoff distance in cut score calculation */
80 #define DEFAULT_GOODMAXPARALL 0.1 /**< maximum parallelism for good cuts */
81 #define DEFAULT_MAXPARALL 0.1 /**< maximum parallelism for non-good cuts */
82 
83 #define MAXVARBOUND 1e+5 /**< maximum allowed variable bound for computing an RLT-cut */
84 
85 /*
86  * Data structures
87  */
88 
89 /** data object for pairs and triples of variables */
90 struct HashData
91 {
92  SCIP_VAR* vars[3]; /**< variables in the pair or triple, used for hash comparison */
93  int nvars; /**< number of variables */
94  int nrows; /**< number of rows */
95  int firstrow; /**< beginning of the corresponding row linked list */
96 };
97 typedef struct HashData HASHDATA;
98 
99 /** data structure representing an array of variables together with number of elements and size;
100  * used for storing variables that are in some sense adjacent to a given variable
101  */
102 struct AdjacentVarData
103 {
104  SCIP_VAR** adjacentvars; /**< adjacent vars */
105  int nadjacentvars; /**< number of vars in adjacentvars */
106  int sadjacentvars; /**< size of adjacentvars */
107 };
109 
110 /** separator data */
111 struct SCIP_SepaData
112 {
113  SCIP_CONSHDLR* conshdlr; /**< nonlinear constraint handler */
114  SCIP_Bool iscreated; /**< indicates whether the sepadata has been initialized yet */
115  SCIP_Bool isinitialround; /**< indicates that this is the first round and original rows are used */
116 
117  /* bilinear variables */
118  SCIP_VAR** varssorted; /**< variables that occur in bilinear terms sorted by priority */
119  SCIP_HASHMAP* bilinvardatamap; /**< maps each bilinear var to ADJACENTVARDATA containing vars appearing
120  together with it in bilinear products */
121  int* varpriorities; /**< priorities of variables */
122  int nbilinvars; /**< total number of variables occurring in bilinear terms */
123  int sbilinvars; /**< size of arrays for variables occurring in bilinear terms */
124 
125  /* information about bilinear terms */
126  int* eqauxexpr; /**< position of the auxexpr that is equal to the product (-1 if none) */
127  int nbilinterms; /**< total number of bilinear terms */
128 
129  /* parameters */
130  int maxunknownterms; /**< maximum number of unknown bilinear terms a row can have to be used (-1: unlimited) */
131  int maxusedvars; /**< maximum number of variables that will be used to compute rlt cuts (-1: unlimited) */
132  int maxncuts; /**< maximum number of cuts that will be added per round (-1: unlimited) */
133  int maxrounds; /**< maximum number of separation rounds per node (-1: unlimited) */
134  int maxroundsroot; /**< maximum number of separation rounds in the root node (-1: unlimited) */
135  SCIP_Bool onlyeqrows; /**< whether only equality rows should be used for rlt cuts */
136  SCIP_Bool onlycontrows; /**< whether only continuous rows should be used for rlt cuts */
137  SCIP_Bool onlyoriginal; /**< whether only original rows and variables should be used for rlt cuts */
138  SCIP_Bool useinsubscip; /**< whether the separator should also be used in sub-scips */
139  SCIP_Bool useprojection; /**< whether the separator should first check projected rows */
140  SCIP_Bool detecthidden; /**< whether implicit products should be detected and separated by McCormick */
141  SCIP_Bool hiddenrlt; /**< whether RLT cuts should be added for hidden products */
142  SCIP_Bool addtopool; /**< whether globally valid RLT cuts are added to the global cut pool */
143 
144  /* cut selection parameters */
145  SCIP_Real goodscore; /**< threshold for score of cut relative to best score to be considered good,
146  * so that less strict filtering is applied */
147  SCIP_Real badscore; /**< threshold for score of cut relative to best score to be discarded */
148  SCIP_Real objparalweight; /**< weight of objective parallelism in cut score calculation */
149  SCIP_Real efficacyweight; /**< weight of efficacy in cut score calculation */
150  SCIP_Real dircutoffdistweight;/**< weight of directed cutoff distance in cut score calculation */
151  SCIP_Real goodmaxparall; /**< maximum parallelism for good cuts */
152  SCIP_Real maxparall; /**< maximum parallelism for non-good cuts */
153 };
154 
155 /* a simplified representation of an LP row */
156 struct RLT_SimpleRow
157 {
158  const char* name; /**< name of the row */
159  SCIP_Real* coefs; /**< coefficients */
160  SCIP_VAR** vars; /**< variables */
161  SCIP_Real rhs; /**< right hand side */
162  SCIP_Real lhs; /**< left hand side */
163  SCIP_Real cst; /**< constant */
164  int nnonz; /**< number of nonzeroes */
165  int size; /**< size of the coefs and vars arrays */
166 };
168 
169 /*
170  * Local methods
171  */
172 
173 /** returns TRUE iff both keys are equal
174  *
175  * two variable pairs/triples are equal if the variables are equal
176  */
177 static
178 SCIP_DECL_HASHKEYEQ(hashdataKeyEqConss)
179 { /*lint --e{715}*/
180  HASHDATA* hashdata1;
181  HASHDATA* hashdata2;
182  int v;
183 
184  hashdata1 = (HASHDATA*)key1;
185  hashdata2 = (HASHDATA*)key2;
186 
187  /* check data structure */
188  assert(hashdata1->nvars == hashdata2->nvars);
189  assert(hashdata1->firstrow != -1 || hashdata2->firstrow != -1);
190 
191  for( v = hashdata1->nvars-1; v >= 0; --v )
192  {
193  /* tests if variables are equal */
194  if( hashdata1->vars[v] != hashdata2->vars[v] )
195  return FALSE;
196 
197  assert(SCIPvarCompare(hashdata1->vars[v], hashdata2->vars[v]) == 0);
198  }
199 
200  /* if two hashdata objects have the same variables, then either one of them doesn't have a row list yet
201  * (firstrow == -1) or they both point to the same row list
202  */
203  assert(hashdata1->firstrow == -1 || hashdata2->firstrow == -1 || hashdata1->firstrow == hashdata2->firstrow);
204 
205  return TRUE;
206 }
207 
208 /** returns the hash value of the key */
209 static
210 SCIP_DECL_HASHKEYVAL(hashdataKeyValConss)
211 { /*lint --e{715}*/
212  HASHDATA* hashdata;
213  int minidx;
214  int mididx;
215  int maxidx;
216  int idx[3];
217 
218  hashdata = (HASHDATA*)key;
219  assert(hashdata != NULL);
220  assert(hashdata->nvars == 3 || hashdata->nvars == 2);
221 
222  idx[0] = SCIPvarGetIndex(hashdata->vars[0]);
223  idx[1] = SCIPvarGetIndex(hashdata->vars[1]);
224  idx[2] = SCIPvarGetIndex(hashdata->vars[hashdata->nvars - 1]);
225 
226  minidx = MIN3(idx[0], idx[1], idx[2]);
227  maxidx = MAX3(idx[0], idx[1], idx[2]);
228  if( idx[0] == maxidx )
229  mididx = MAX(idx[1], idx[2]);
230  else
231  mididx = MAX(idx[0], MIN(idx[1], idx[2]));
232 
233  /* vars should already be sorted by index */
234  assert(minidx <= mididx && mididx <= maxidx);
235 
236  return SCIPhashFour(hashdata->nvars, minidx, mididx, maxidx);
237 }
238 
239 /** store a pair of adjacent variables */
240 static
242  SCIP* scip, /**< SCIP data structure */
243  SCIP_HASHMAP* adjvarmap, /**< hashmap mapping variables to their ADJACENTVARDATAs */
244  SCIP_VAR** vars /**< variable pair to be stored */
245  )
246 {
247  int v1;
248  int v2;
249  int i;
250  ADJACENTVARDATA* adjacentvardata;
251 
252  assert(adjvarmap != NULL);
253 
254  /* repeat for each variable of the new pair */
255  for( v1 = 0; v1 < 2; ++v1 )
256  {
257  v2 = 1 - v1;
258 
259  /* look for data of the first variable */
260  adjacentvardata = (ADJACENTVARDATA*) SCIPhashmapGetImage(adjvarmap, (void*)(size_t) SCIPvarGetIndex(vars[v1]));
261 
262  /* if the first variable has not been added to adjvarmap yet, add it here */
263  if( adjacentvardata == NULL )
264  {
265  SCIP_CALL( SCIPallocClearBlockMemory(scip, &adjacentvardata) );
266  SCIP_CALL( SCIPhashmapInsert(adjvarmap, (void*)(size_t) SCIPvarGetIndex(vars[v1]), adjacentvardata) );
267  }
268 
269  assert(adjacentvardata != NULL);
270 
271  /* look for second variable in adjacentvars of the first variable */
272  if( adjacentvardata->adjacentvars == NULL )
273  {
274  /* we don't know how many adjacent vars there will be - take a guess */
275  SCIP_CALL( SCIPallocBlockMemoryArray(scip, &adjacentvardata->adjacentvars, 4) );
276  adjacentvardata->adjacentvars[0] = vars[v2];
277  ++adjacentvardata->nadjacentvars;
278  adjacentvardata->sadjacentvars = 4;
279  }
280  else
281  {
282  SCIP_Bool found;
283  int pos2;
284 
285  found = SCIPsortedvecFindPtr((void**) adjacentvardata->adjacentvars, SCIPvarComp, vars[v2],
286  adjacentvardata->nadjacentvars, &pos2);
287 
288  /* add second var to adjacentvardata->adjacentvars, if not already added */
289  if( !found )
290  {
291  /* ensure size of adjacentvardata->adjacentvars */
292  SCIP_CALL( SCIPensureBlockMemoryArray(scip, &adjacentvardata->adjacentvars, &adjacentvardata->sadjacentvars,
293  adjacentvardata->nadjacentvars + 1) );
294 
295  /* insert second var at the correct position */
296  for( i = adjacentvardata->nadjacentvars; i > pos2; --i )
297  {
298  adjacentvardata->adjacentvars[i] = adjacentvardata->adjacentvars[i-1];
299  }
300  adjacentvardata->adjacentvars[pos2] = vars[v2];
301  ++adjacentvardata->nadjacentvars;
302  }
303  }
304 
305  /* if this is a self-adjacent var, only need to add the connection once */
306  if( vars[v1] == vars[v2] )
307  break;
308  }
309 
310  return SCIP_OKAY;
311 }
312 
313 /** returns the array of adjacent variables for a given variable */
314 static
316  SCIP_HASHMAP* adjvarmap, /**< hashmap mapping variables to their ADJACENTVARDATAs */
317  SCIP_VAR* var, /**< variable */
318  int* nadjacentvars /**< buffer to store the number of variables in the returned array */
319  )
320 {
321  ADJACENTVARDATA* adjacentvardata;
322 
323  assert(adjvarmap != NULL);
324 
325  *nadjacentvars = 0;
326  adjacentvardata = (ADJACENTVARDATA*) SCIPhashmapGetImage(adjvarmap, (void*)(size_t) SCIPvarGetIndex(var));
327 
328  if( adjacentvardata == NULL )
329  return NULL;
330 
331  *nadjacentvars = adjacentvardata->nadjacentvars;
332 
333  return adjacentvardata->adjacentvars;
334 }
335 
336 /** frees all ADJACENTVARDATAs stored in a hashmap */
337 static
338 void clearVarAdjacency(
339  SCIP* scip, /**< SCIP data structure */
340  SCIP_HASHMAP* adjvarmap /**< hashmap mapping variables to their ADJACENTVARDATAs */
341  )
342 {
343  int i;
344  SCIP_HASHMAPENTRY* entry;
345  ADJACENTVARDATA* adjacentvardata;
346 
347  assert(adjvarmap != NULL);
348 
349  for( i = 0; i < SCIPhashmapGetNEntries(adjvarmap); ++i )
350  {
351  entry = SCIPhashmapGetEntry(adjvarmap, i);
352 
353  if( entry == NULL )
354  continue;
355 
356  adjacentvardata = (ADJACENTVARDATA*) SCIPhashmapEntryGetImage(entry);
357 
358  /* if adjacentvardata has been added to the hashmap, it can't be empty */
359  assert(adjacentvardata->adjacentvars != NULL);
360 
361  SCIPfreeBlockMemoryArray(scip, &adjacentvardata->adjacentvars, adjacentvardata->sadjacentvars);
362  SCIPfreeBlockMemory(scip, &adjacentvardata);
363  }
364 }
365 
366 /** free separator data */
367 static
369  SCIP* scip, /**< SCIP data structure */
370  SCIP_SEPADATA* sepadata /**< separation data */
371  )
372 { /*lint --e{715}*/
373  int i;
374 
375  assert(sepadata->iscreated);
376 
377  if( sepadata->nbilinvars != 0 )
378  {
379  /* release bilinvars that were captured for rlt and free all related arrays */
380 
381  /* if there are bilinear vars, some of them must also participate in the same product */
382  assert(sepadata->bilinvardatamap != NULL);
383 
384  clearVarAdjacency(scip, sepadata->bilinvardatamap);
385 
386  for( i = 0; i < sepadata->nbilinvars; ++i )
387  {
388  assert(sepadata->varssorted[i] != NULL);
389  SCIP_CALL( SCIPreleaseVar(scip, &(sepadata->varssorted[i])) );
390  }
391 
392  SCIPhashmapFree(&sepadata->bilinvardatamap);
393  SCIPfreeBlockMemoryArray(scip, &sepadata->varssorted, sepadata->sbilinvars);
394  SCIPfreeBlockMemoryArray(scip, &sepadata->varpriorities, sepadata->sbilinvars);
395  sepadata->nbilinvars = 0;
396  sepadata->sbilinvars = 0;
397  }
398 
399  /* free the remaining array */
400  if( sepadata->nbilinterms > 0 )
401  {
402  SCIPfreeBlockMemoryArray(scip, &sepadata->eqauxexpr, sepadata->nbilinterms);
403  }
404 
405  sepadata->iscreated = FALSE;
406 
407  return SCIP_OKAY;
408 }
409 
410 /** creates and returns rows of original linear constraints */
411 static
413  SCIP* scip, /**< SCIP data structure */
414  SCIP_ROW*** rows, /**< buffer to store the rows */
415  int* nrows /**< buffer to store the number of linear rows */
416  )
417 {
418  SCIP_CONS** conss;
419  int nconss;
420  int i;
421 
422  assert(rows != NULL);
423  assert(nrows != NULL);
424 
425  conss = SCIPgetConss(scip);
426  nconss = SCIPgetNConss(scip);
427  *nrows = 0;
428 
429  SCIP_CALL( SCIPallocBufferArray(scip, rows, nconss) );
430 
431  for( i = 0; i < nconss; ++i )
432  {
433  SCIP_ROW *row;
434 
435  row = SCIPconsGetRow(scip, conss[i]);
436 
437  if( row != NULL )
438  {
439  (*rows)[*nrows] = row;
440  ++*nrows;
441  }
442  }
443 
444  return SCIP_OKAY;
445 }
446 
447 /** fills an array of rows suitable for RLT cut generation */
448 static
450  SCIP* scip, /**< SCIP data structure */
451  SCIP_SEPA* sepa, /**< separator */
452  SCIP_SEPADATA* sepadata, /**< separator data */
453  SCIP_ROW** prob_rows, /**< problem rows */
454  SCIP_ROW** rows, /**< an array to be filled with suitable rows */
455  int* nrows, /**< buffer to store the number of suitable rows */
456  SCIP_HASHMAP* row_to_pos, /**< hashmap linking row indices to positions in rows */
457  SCIP_Bool allowlocal /**< are local rows allowed? */
458  )
459 {
460  int new_nrows;
461  int r;
462  int j;
463  SCIP_Bool iseqrow;
464  SCIP_COL** cols;
465  SCIP_Bool iscontrow;
466 
467  new_nrows = 0;
468 
469  for( r = 0; r < *nrows; ++r )
470  {
471  iseqrow = SCIPisEQ(scip, SCIProwGetLhs(prob_rows[r]), SCIProwGetRhs(prob_rows[r]));
472 
473  /* if equality rows are requested, only those can be used */
474  if( sepadata->onlyeqrows && !iseqrow )
475  continue;
476 
477  /* if global cuts are requested, only globally valid rows can be used */
478  if( !allowlocal && SCIProwIsLocal(prob_rows[r]) )
479  continue;
480 
481  /* if continuous rows are requested, only those can be used */
482  if( sepadata->onlycontrows )
483  {
484  cols = SCIProwGetCols(prob_rows[r]);
485  iscontrow = TRUE;
486 
487  /* check row for integral variables */
488  for( j = 0; j < SCIProwGetNNonz(prob_rows[r]); ++j )
489  {
490  if( SCIPcolIsIntegral(cols[j]) )
491  {
492  iscontrow = FALSE;
493  break;
494  }
495  }
496 
497  if( !iscontrow )
498  continue;
499  }
500 
501  /* don't try to use rows that have been generated by the RLT separator */
502  if( SCIProwGetOriginSepa(prob_rows[r]) == sepa )
503  continue;
504 
505  /* if we are here, the row has passed all checks and should be added to rows */
506  rows[new_nrows] = prob_rows[r];
507  SCIP_CALL( SCIPhashmapSetImageInt(row_to_pos, (void*)(size_t)SCIProwGetIndex(prob_rows[r]), new_nrows) ); /*lint !e571 */
508  ++new_nrows;
509  }
510 
511  *nrows = new_nrows;
512 
513  return SCIP_OKAY;
514 }
515 
516 /** make sure that the arrays in sepadata are large enough to store information on n variables */
517 static
519  SCIP* scip, /**< SCIP data structure */
520  SCIP_SEPADATA* sepadata, /**< separator data */
521  int n /**< number of variables that we need to store */
522  )
523 {
524  int newsize;
525 
526  /* check whether array is large enough */
527  if( n <= sepadata->sbilinvars )
528  return SCIP_OKAY;
529 
530  /* compute new size */
531  newsize = SCIPcalcMemGrowSize(scip, n);
532  assert(n <= newsize);
533 
534  /* realloc arrays */
535  SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &sepadata->varssorted, sepadata->sbilinvars, newsize) );
536  SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &sepadata->varpriorities, sepadata->sbilinvars, newsize) );
537 
538  sepadata->sbilinvars = newsize;
539 
540  return SCIP_OKAY;
541 }
542 
543 /** saves variables x and y to separator data and stores information about their connection
544  *
545  * variables must be captured separately
546  */
547 static
549  SCIP* scip, /**< SCIP data structure */
550  SCIP_SEPADATA* sepadata, /**< separator data */
551  SCIP_VAR* x, /**< x variable */
552  SCIP_VAR* y, /**< y variable */
553  SCIP_HASHMAP* varmap, /**< hashmap linking var index to position */
554  int nlocks /**< number of locks */
555  )
556 {
557  int xpos;
558  int ypos;
559  int xidx;
560  int yidx;
561  SCIP_VAR* vars[2];
562 
563  if( sepadata->bilinvardatamap == NULL )
564  {
565  int varmapsize;
566  int nvars;
567 
568  /* the number of variables participating in bilinear products cannot exceed twice the number of bilinear terms;
569  * however, if we detect hidden products, the number of terms is yet unknown, so use the number of variables
570  */
571  nvars = SCIPgetNVars(scip);
572  varmapsize = sepadata->detecthidden ? nvars : MIN(nvars, sepadata->nbilinterms * 2);
573 
574  SCIP_CALL( SCIPhashmapCreate(&sepadata->bilinvardatamap, SCIPblkmem(scip), varmapsize) );
575  }
576 
577  xidx = SCIPvarGetIndex(x);
578  yidx = SCIPvarGetIndex(y);
579 
580  xpos = SCIPhashmapGetImageInt(varmap, (void*)(size_t) xidx); /*lint !e571 */
581 
582  if( xpos == INT_MAX )
583  {
584  /* add x to sepadata and initialise its priority */
585  SCIP_CALL( SCIPhashmapInsertInt(varmap, (void*)(size_t) xidx, sepadata->nbilinvars) ); /*lint !e571*/
586  SCIP_CALL( ensureVarsSize(scip, sepadata, sepadata->nbilinvars + 1) );
587  sepadata->varssorted[sepadata->nbilinvars] = x;
588  sepadata->varpriorities[sepadata->nbilinvars] = 0;
589  xpos = sepadata->nbilinvars;
590  ++sepadata->nbilinvars;
591  }
592 
593  assert(xpos >= 0 && xpos < sepadata->nbilinvars );
594  assert(xpos == SCIPhashmapGetImageInt(varmap, (void*)(size_t) xidx)); /*lint !e571 */
595 
596  /* add locks to priority of x */
597  sepadata->varpriorities[xpos] += nlocks;
598 
599  if( xidx != yidx )
600  {
601  ypos = SCIPhashmapGetImageInt(varmap, (void*)(size_t) yidx); /*lint !e571 */
602 
603  if( ypos == INT_MAX )
604  {
605  /* add y to sepadata and initialise its priority */
606  SCIP_CALL( SCIPhashmapInsertInt(varmap, (void*)(size_t) yidx, sepadata->nbilinvars) ); /*lint !e571*/
607  SCIP_CALL( ensureVarsSize(scip, sepadata, sepadata->nbilinvars + 1) );
608  sepadata->varssorted[sepadata->nbilinvars] = y;
609  sepadata->varpriorities[sepadata->nbilinvars] = 0;
610  ypos = sepadata->nbilinvars;
611  ++sepadata->nbilinvars;
612  }
613 
614  assert(ypos >= 0 && ypos < sepadata->nbilinvars);
615  assert(ypos == SCIPhashmapGetImageInt(varmap, (void*)(size_t) yidx)); /*lint !e571 */
616 
617  /* add locks to priority of y */
618  sepadata->varpriorities[ypos] += nlocks;
619  }
620 
621  /* remember the connection between x and y */
622  vars[0] = x;
623  vars[1] = y;
624  SCIP_CALL( addAdjacentVars(scip, sepadata->bilinvardatamap, vars) );
625 
626  return SCIP_OKAY;
627 }
628 
629 /** extract a bilinear product from two linear relations, if possible
630  *
631  * First, the two given rows are brought to the form:
632  * \f[
633  * a_1x + b_1w + c_1y \leq/\geq d_1,\\
634  * a_2x + b_2w + c_2y \leq/\geq d_2,
635  * \f]
636  * where \f$ a_1a_2 \leq 0 \f$ and the first implied relation is enabled when \f$ x = 1 \f$
637  * and the second when \f$ x = 0 \f$, and \f$ b_1, b_2 > 0 \f$, the product relation can be written as:
638  * \f[
639  * \frac{b_1b_2w + (b_2(a_1 - d_1) + b_1d_2)x + b_1c_2y - b_1d_2}{b_1c_2 - c_1b_2} \leq/\geq xy.
640  * \f]
641  * The inequality sign in the product relation is similar to that in the given linear relations if
642  * \f$ b_1c_2 - c_1b_2 > 0 \f$ and opposite if \f$ b_1c_2 - c_1b_2 > 0 \f$.
643  *
644  * To obtain this formula, the given relations are first multiplied by scaling factors \f$ \alpha \f$
645  * and \f$ \beta \f$, which is necessary in order for the solution to always exist, and written as
646  * implications:
647  * \f{align}{
648  * x = 1 & ~\Rightarrow~ \alpha b_1w + \alpha c_1y \leq/\geq \alpha(d_1 - a_1), \\
649  * x = 0 & ~\Rightarrow~ \beta b_2w + \beta c_2y \leq/\geq \beta d_2.
650  * \f}
651  * Then a linear system is solved which ensures that the coefficients of the two implications of the product
652  * relation are equal to the corresponding coefficients in the linear relations.
653  * If the product relation is written as:
654  * \f[
655  * Ax + Bw + Cy + D \leq/\geq xy,
656  * \f]
657  * then the system is
658  * \f[
659  * B = \alpha b_1, ~C - 1 = \alpha c_1, ~D+A = \alpha(a_1-d_1),\\
660  * B = \beta b_2, ~C = \beta c_2, ~D = -\beta d_2.
661  * \f]
662  */
663 static
665  SCIP* scip, /**< SCIP data structure */
666  SCIP_SEPADATA* sepadata, /**< separator data */
667  SCIP_VAR** vars_xwy, /**< 3 variables involved in the inequalities in the order x,w,y */
668  SCIP_Real* coefs1, /**< coefficients of the first inequality (always implied, i.e. has x) */
669  SCIP_Real* coefs2, /**< coefficients of the second inequality (can be unconditional) */
670  SCIP_Real d1, /**< side of the first inequality */
671  SCIP_Real d2, /**< side of the second inequality */
672  SCIP_SIDETYPE sidetype1, /**< side type (lhs or rls) in the first inequality */
673  SCIP_SIDETYPE sidetype2, /**< side type (lhs or rhs) in the second inequality */
674  SCIP_HASHMAP* varmap, /**< variable map */
675  SCIP_Bool f /**< the first relation is an implication x == f */
676  )
677 {
678  SCIP_Real mult;
679 
680  /* coefficients and constant of the auxexpr */
681  SCIP_Real A; /* coefficient of x */
682  SCIP_Real B; /* coefficient of w */
683  SCIP_Real C; /* coefficient of y */
684  SCIP_Real D; /* constant */
685 
686  /* variables */
687  SCIP_VAR* w;
688  SCIP_VAR* x;
689  SCIP_VAR* y;
690 
691  /* does auxexpr overestimate the product? */
692  SCIP_Bool overestimate;
693 
694  /* coefficients in given relations: a for x, b for w, c for y; 1 and 2 for 1st and 2nd relation, respectively */
695  SCIP_Real a1 = coefs1[0];
696  SCIP_Real b1 = coefs1[1];
697  SCIP_Real c1 = coefs1[2];
698  SCIP_Real a2 = coefs2[0];
699  SCIP_Real b2 = coefs2[1];
700  SCIP_Real c2 = coefs2[2];
701 
702  x = vars_xwy[0];
703  w = vars_xwy[1];
704  y = vars_xwy[2];
705 
706  /* check given linear relations and decide if to continue */
707 
708  assert(SCIPvarGetType(x) == SCIP_VARTYPE_BINARY); /* x must be binary */
709  assert(a1 != 0.0); /* the first relation is always conditional */
710  assert(b1 != 0.0 || b2 != 0.0); /* at least one w coefficient must be nonzero */
711 
712  SCIPdebugMsg(scip, "Extracting product from two implied relations:\n");
713  SCIPdebugMsg(scip, "Relation 1: <%s> == %u => %g<%s> + %g<%s> %s %g\n", SCIPvarGetName(x), f, b1,
714  SCIPvarGetName(w), c1, SCIPvarGetName(y), sidetype1 == SCIP_SIDETYPE_LEFT ? ">=" : "<=",
715  f ? d1 - a1 : d1);
716  SCIPdebugMsg(scip, "Relation 2: <%s> == %d => %g<%s> + %g<%s> %s %g\n", SCIPvarGetName(x), !f, b2,
717  SCIPvarGetName(w), c2, SCIPvarGetName(y), sidetype2 == SCIP_SIDETYPE_LEFT ? ">=" : "<=",
718  f ? d2 : d2 - a2);
719 
720  /* cannot use a global bound on x to detect a product */
721  if( (b1 == 0.0 && c1 == 0.0) || (b2 == 0.0 && c2 == 0.0) )
722  return SCIP_OKAY;
723 
724  /* cannot use a global bound on y to detect a non-redundant product relation */
725  if( a2 == 0.0 && b2 == 0.0 ) /* only check the 2nd relation because the 1st at least has x */
726  {
727  SCIPdebugMsg(scip, "Ignoring a global bound on y\n");
728  return SCIP_OKAY;
729  }
730 
731  SCIPdebugMsg(scip, "binary var = <%s>, product of its coefs: %g\n", SCIPvarGetName(x), a1*a2);
732 
733  /* rewrite the linear relations in a standard form:
734  * a1x + b1w + c1y <=/>= d1,
735  * a2x + b2w + c2y <=/>= d2,
736  * where b1 > 0, b2 > 0 and first implied relation is activated when x == 1
737  */
738 
739  /* if needed, multiply the rows by -1 so that coefs of w are positive */
740  if( b1 < 0 )
741  {
742  a1 *= -1.0;
743  b1 *= -1.0;
744  c1 *= -1.0;
745  d1 *= -1.0;
746  sidetype1 = sidetype1 == SCIP_SIDETYPE_LEFT ? SCIP_SIDETYPE_RIGHT : SCIP_SIDETYPE_LEFT;
747  }
748  if( b2 < 0 )
749  {
750  a2 *= -1.0;
751  b2 *= -1.0;
752  c2 *= -1.0;
753  d2 *= -1.0;
754  sidetype2 = sidetype2 == SCIP_SIDETYPE_LEFT ? SCIP_SIDETYPE_RIGHT : SCIP_SIDETYPE_LEFT;
755  }
756 
757  /* the linear relations imply a product only if the inequality signs are similar */
758  if( sidetype1 != sidetype2 )
759  return SCIP_OKAY;
760 
761  /* when b1c2 = b2c1, the linear relations do not imply a product relation */
762  if( SCIPisRelEQ(scip, b2*c1, c2*b1) )
763  {
764  SCIPdebugMsg(scip, "Ignoring a pair of linear relations because b1c2 = b2c1\n");
765  return SCIP_OKAY;
766  }
767 
768  if( !f )
769  {
770  /* swap the linear relations so that the relation implied by x == TRUE goes first */
771  SCIPswapReals(&a1, &a2);
772  SCIPswapReals(&b1, &b2);
773  SCIPswapReals(&c1, &c2);
774  SCIPswapReals(&d1, &d2);
775  }
776 
777  /* all conditions satisfied, we can extract the product and write it as:
778  * (1/(b1c2 - c1b2))*(b1b2w + (b2(a1 - d1) + b1d2)x + b1c2y - b1d2) >=/<= xy,
779  * where the inequality sign in the product relation is similar to that in the given linear relations
780  * if b1c2 - c1b2 > 0 and opposite if b1c2 - c1b2 > 0
781  */
782 
783  /* compute the multiplier */
784  mult = 1/(b1*c2 - c1*b2);
785 
786  /* determine the inequality sign; only check sidetype1 because sidetype2 is equal to it */
787  overestimate = (sidetype1 == SCIP_SIDETYPE_LEFT && mult > 0.0) || (sidetype1 == SCIP_SIDETYPE_RIGHT && mult < 0.0);
788 
789  SCIPdebugMsg(scip, "found suitable implied rels (w,x,y): %g<%s> + %g<%s> + %g<%s> <= %g\n", a1,
790  SCIPvarGetName(x), b1, SCIPvarGetName(w), c1, SCIPvarGetName(y), d1);
791  SCIPdebugMsg(scip, " and %g<%s> + %g<%s> + %g<%s> <= %g\n", a2, SCIPvarGetName(x),
792  b2, SCIPvarGetName(w), c2, SCIPvarGetName(y), d2);
793 
794  /* compute the coefficients for x, w and y and the constant in auxexpr */
795  A = (b2*a1 - d1*b2 + d2*b1)*mult;
796  B = b1*b2*mult;
797  C = b1*c2*mult;
798  D = -b1*d2*mult;
799 
800  SCIPdebugMsg(scip, "product: <%s><%s> %s %g<%s> + %g<%s> + %g<%s> + %g\n", SCIPvarGetName(x), SCIPvarGetName(y),
801  overestimate ? "<=" : ">=", A, SCIPvarGetName(x), B, SCIPvarGetName(w), C, SCIPvarGetName(y), D);
802 
803  SCIP_CALL( addProductVars(scip, sepadata, x, y, varmap, 1) );
804  SCIP_CALL( SCIPinsertBilinearTermImplicitNonlinear(scip, sepadata->conshdlr, x, y, w, A, C, B, D, overestimate) );
805 
806  return SCIP_OKAY;
807 }
808 
809 /** convert an implied bound: `binvar` = `binval` &rArr; `implvar` &le;/&ge; `implbnd` into a big-M constraint */
810 static
811 void implBndToBigM(
812  SCIP* scip, /**< SCIP data structure */
813  SCIP_VAR** vars_xwy, /**< variables in order x,w,y */
814  int binvarpos, /**< position of binvar in vars_xwy */
815  int implvarpos, /**< position of implvar in vars_xwy */
816  SCIP_BOUNDTYPE bndtype, /**< type of implied bound */
817  SCIP_Bool binval, /**< value of binvar which implies the bound */
818  SCIP_Real implbnd, /**< value of the implied bound */
819  SCIP_Real* coefs, /**< coefficients of the big-M constraint */
820  SCIP_Real* side /**< side of the big-M constraint */
821  )
822 {
823  SCIP_VAR* implvar;
824  SCIP_Real globbnd;
825 
826  assert(vars_xwy != NULL);
827  assert(coefs != NULL);
828  assert(side != NULL);
829  assert(binvarpos != implvarpos);
830 
831  implvar = vars_xwy[implvarpos];
832  globbnd = bndtype == SCIP_BOUNDTYPE_LOWER ? SCIPvarGetLbGlobal(implvar) : SCIPvarGetUbGlobal(implvar);
833 
834  /* Depending on the bound type and binval, there are four possibilities:
835  * binvar == 1 => implvar >= implbnd <=> (implvar^l - implbnd)binvar + implvar >= implvar^l;
836  * binvar == 0 => implvar >= implbnd <=> (implbnd - implvar^l)binvar + implvar >= implbnd;
837  * binvar == 1 => implvar <= implbnd <=> (implvar^u - implbnd)binvar + implvar <= implvar^u;
838  * binvar == 0 => implvar <= implbnd <=> (implbnd - implvar^u)binvar + implvar <= implbnd.
839  */
840 
841  coefs[0] = 0.0;
842  coefs[1] = 0.0;
843  coefs[2] = 0.0;
844  coefs[binvarpos] = binval ? globbnd - implbnd : implbnd - globbnd;
845  coefs[implvarpos] = 1.0;
846  *side = binval ? globbnd : implbnd;
847 
848  SCIPdebugMsg(scip, "Got an implied relation with binpos = %d, implpos = %d, implbnd = %g, "
849  "bnd type = %s, binval = %u, glbbnd = %g\n", binvarpos, implvarpos, implbnd,
850  bndtype == SCIP_BOUNDTYPE_LOWER ? "lower" : "upper", binval, globbnd);
851  SCIPdebugMsg(scip, "Constructed big-M: %g*bvar + implvar %s %g\n", coefs[binvarpos],
852  bndtype == SCIP_BOUNDTYPE_LOWER ? ">=" : "<=", *side);
853 }
854 
855 /** extract products from a relation given by coefs1, vars, side1 and sidetype1 and
856  * implied bounds of the form `binvar` = `!f` &rArr; `implvar` &ge;/&le; `implbnd`
857  */
858 static
860  SCIP* scip, /**< SCIP data structure */
861  SCIP_SEPADATA* sepadata, /**< separator data */
862  SCIP_Real* coefs1, /**< coefficients of the first linear relation */
863  SCIP_VAR** vars_xwy, /**< variables in the order x, w, y */
864  SCIP_Real side1, /**< side of the first relation */
865  SCIP_SIDETYPE sidetype1, /**< is the left or right hand side given for the first relation? */
866  int binvarpos, /**< position of the indicator variable in the vars_xwy array */
867  int implvarpos, /**< position of the variable that is bounded */
868  SCIP_HASHMAP* varmap, /**< variable map */
869  SCIP_Bool f /**< the value of x that activates the first relation */
870  )
871 {
872  SCIP_Real coefs2[3] = { 0., 0., 0. };
873  SCIP_Real impllb;
874  SCIP_Real implub;
875  SCIP_VAR* binvar;
876  SCIP_VAR* implvar;
877  SCIP_Real side2;
878  int i;
879  SCIP_Bool binvals[2] = {!f, f};
880 
881  assert(binvarpos != implvarpos);
882  assert(implvarpos != 0); /* implied variable must be continuous, therefore it can't be x */
883 
884  binvar = vars_xwy[binvarpos];
885  implvar = vars_xwy[implvarpos];
886 
887  assert(SCIPvarGetType(binvar) == SCIP_VARTYPE_BINARY);
888  assert(SCIPvarGetType(implvar) != SCIP_VARTYPE_BINARY);
889 
890  /* loop over binvals; if binvar is x (case binvarpos == 0), then we want to use only implications from
891  * binvar == !f (which is the option complementing the first relation, which is implied from f); if
892  * binvar is not x, this doesn't matter since the implbnd doesn't depend on x, therefore try both !f and f
893  */
894  for( i = 0; i < (binvarpos == 0 ? 1 : 2); ++i )
895  {
896  /* get implications binvar == binval => implvar <=/>= implbnd */
897  SCIPvarGetImplicVarBounds(binvar, binvals[i], implvar, &impllb, &implub);
898 
899  if( impllb != SCIP_INVALID ) /*lint !e777*/
900  {
901  /* write the implied bound as a big-M constraint */
902  implBndToBigM(scip, vars_xwy, binvarpos, implvarpos, SCIP_BOUNDTYPE_LOWER, binvals[i], impllb, coefs2, &side2);
903 
904  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1, side2, sidetype1,
905  SCIP_SIDETYPE_LEFT, varmap, f) );
906  }
907 
908  if( implub != SCIP_INVALID ) /*lint !e777*/
909  {
910  /* write the implied bound as a big-M constraint */
911  implBndToBigM(scip, vars_xwy, binvarpos, implvarpos, SCIP_BOUNDTYPE_UPPER, binvals[i], implub, coefs2, &side2);
912 
913  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1, side2, sidetype1,
914  SCIP_SIDETYPE_RIGHT, varmap, f) );
915  }
916  }
917 
918  return SCIP_OKAY;
919 }
920 
921 /** extract products from a relation given by `coefs1`, `vars_xwy`, `side1` and `sidetype1` and
922  * cliques containing `vars_xwy[varpos1]` and `vars_xwy[varpos2]`
923  */
924 static
926  SCIP* scip, /**< SCIP data structure */
927  SCIP_SEPADATA* sepadata, /**< separator data */
928  SCIP_Real* coefs1, /**< coefficients of the first linear relation */
929  SCIP_VAR** vars_xwy, /**< variables of the first relation in the order x, w, y */
930  SCIP_Real side1, /**< side of the first relation */
931  SCIP_SIDETYPE sidetype1, /**< is the left or right hand side given for the first relation? */
932  int varpos1, /**< position of the first variable in the vars_xwy array */
933  int varpos2, /**< position of the second variable in the vars_xwy array */
934  SCIP_HASHMAP* varmap, /**< variable map */
935  SCIP_Bool f /**< the value of x that activates the first relation */
936  )
937 {
938  SCIP_Real coefs2[3] = { 0., 0., 0. };
939  SCIP_VAR* var1;
940  SCIP_VAR* var2;
941  SCIP_Real side2;
942  int i;
943  int imax;
944  SCIP_Bool binvals[2] = {!f, f};
945 
946  var1 = vars_xwy[varpos1];
947  var2 = vars_xwy[varpos2];
948 
949  /* this decides whether we do one or two iterations of the loop for binvals: if var1
950  * or var2 is x, we only want cliques with x = !f (which is the option complementing
951  * the first relation, which is implied from f); otherwise this doesn't matter since
952  * the clique doesn't depend on x, therefore try both !f and f
953  */
954  imax = (varpos1 == 0 || varpos2 == 0) ? 1 : 2;
955 
956  assert(SCIPvarGetType(var1) == SCIP_VARTYPE_BINARY);
957  assert(SCIPvarGetType(var2) == SCIP_VARTYPE_BINARY);
958 
959  for( i = 0; i < imax; ++i )
960  {
961  /* if var1=TRUE and var2=TRUE are in a clique (binvals[i] == TRUE), the relation var1 + var2 <= 1 is implied
962  * if var1=FALSE and var2=TRUE are in a clique (binvals[i] == FALSE), the relation (1 - var1) + var2 <= 1 is implied
963  */
964  if( SCIPvarsHaveCommonClique(var1, binvals[i], var2, TRUE, TRUE) )
965  {
966  SCIPdebugMsg(scip, "vars %s<%s> and <%s> are in a clique\n", binvals[i] ? "" : "!", SCIPvarGetName(var1), SCIPvarGetName(var2));
967  coefs2[varpos1] = binvals[i] ? 1.0 : -1.0;
968  coefs2[varpos2] = 1.0;
969  side2 = binvals[i] ? 1.0 : 0.0;
970 
971  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1, side2, sidetype1,
972  SCIP_SIDETYPE_RIGHT, varmap, f) );
973  }
974 
975  /* if var1=TRUE and var2=FALSE are in the same clique, the relation var1 + (1-var2) <= 1 is implied
976  * if var1=FALSE and var2=FALSE are in the same clique, the relation (1-var1) + (1-var2) <= 1 is implied
977  */
978  if( SCIPvarsHaveCommonClique(var1, binvals[i], var2, FALSE, TRUE) )
979  {
980  SCIPdebugMsg(scip, "vars %s<%s> and !<%s> are in a clique\n", binvals[i] ? "" : "!", SCIPvarGetName(var1), SCIPvarGetName(var2));
981  coefs2[varpos1] = binvals[i] ? 1.0 : -1.0;
982  coefs2[varpos2] = -1.0;
983  side2 = binvals[i] ? 0.0 : -1.0;
984 
985  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1, side2, sidetype1,
986  SCIP_SIDETYPE_RIGHT, varmap, f) );
987  }
988  }
989 
990  return SCIP_OKAY;
991 }
992 
993 
994 /** extract products from a relation given by `coefs1`, `vars`, `side1` and `sidetype1` and unconditional relations
995  * (inequalities with 2 nonzeros) containing `vars[varpos1]` and `vars[varpos2]`
996  */
997 static
999  SCIP* scip, /**< SCIP data structure */
1000  SCIP_SEPADATA* sepadata, /**< separator data */
1001  SCIP_ROW** rows, /**< problem rows */
1002  int* row_list, /**< linked list of rows corresponding to 2 or 3 var sets */
1003  SCIP_HASHTABLE* hashtable, /**< hashtable storing unconditional relations */
1004  SCIP_Real* coefs1, /**< coefficients of the first linear relation */
1005  SCIP_VAR** vars_xwy, /**< variables of the first relation in the order x, w, y */
1006  SCIP_Real side1, /**< side of the first relation */
1007  SCIP_SIDETYPE sidetype1, /**< is the left or right hand side given for the first relation? */
1008  int varpos1, /**< position of the first unconditional variable in the vars_xwy array */
1009  int varpos2, /**< position of the second unconditional variable in the vars_xwy array */
1010  SCIP_HASHMAP* varmap, /**< variable map */
1011  SCIP_Bool f /**< the value of x that activates the first relation */
1012  )
1013 {
1014  HASHDATA hashdata;
1015  HASHDATA* foundhashdata;
1016  SCIP_ROW* row2;
1017  int r2;
1018  int pos1;
1019  int pos2;
1020  SCIP_Real coefs2[3] = { 0., 0., 0. };
1021  SCIP_VAR* var1;
1022  SCIP_VAR* var2;
1023 
1024  /* always unconditional, therefore x must not be one of the two variables */
1025  assert(varpos1 != 0);
1026  assert(varpos2 != 0);
1027 
1028  var1 = vars_xwy[varpos1];
1029  var2 = vars_xwy[varpos2];
1030 
1031  hashdata.nvars = 2;
1032  hashdata.firstrow = -1;
1033  if( SCIPvarGetIndex(var1) < SCIPvarGetIndex(var2) )
1034  {
1035  pos1 = 0;
1036  pos2 = 1;
1037  }
1038  else
1039  {
1040  pos1 = 1;
1041  pos2 = 0;
1042  }
1043 
1044  hashdata.vars[pos1] = var1;
1045  hashdata.vars[pos2] = var2;
1046 
1047  foundhashdata = (HASHDATA*)SCIPhashtableRetrieve(hashtable, &hashdata);
1048 
1049  if( foundhashdata != NULL )
1050  {
1051  /* if the var pair exists, use all corresponding rows */
1052  r2 = foundhashdata->firstrow;
1053 
1054  while( r2 != -1 )
1055  {
1056  row2 = rows[r2];
1057  assert(SCIProwGetNNonz(row2) == 2);
1058  assert(var1 == SCIPcolGetVar(SCIProwGetCols(row2)[pos1]));
1059  assert(var2 == SCIPcolGetVar(SCIProwGetCols(row2)[pos2]));
1060 
1061  coefs2[varpos1] = SCIProwGetVals(row2)[pos1];
1062  coefs2[varpos2] = SCIProwGetVals(row2)[pos2];
1063 
1064  SCIPdebugMsg(scip, "Unconditional:\n");
1065  if( !SCIPisInfinity(scip, -SCIProwGetLhs(row2)) )
1066  {
1067  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1068  SCIProwGetLhs(row2) - SCIProwGetConstant(row2), sidetype1, SCIP_SIDETYPE_LEFT, varmap, f) );
1069  }
1070  if( !SCIPisInfinity(scip, SCIProwGetRhs(row2)) )
1071  {
1072  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1073  SCIProwGetRhs(row2) - SCIProwGetConstant(row2), sidetype1, SCIP_SIDETYPE_RIGHT, varmap, f) );
1074  }
1075 
1076  r2 = row_list[r2];
1077  }
1078  }
1079 
1080  return SCIP_OKAY;
1081 }
1082 
1083 /** finds and stores implied relations (x = f &rArr; ay + bw &le; c, f can be 0 or 1) and 2-variable relations
1084  *
1085  * Fills the following:
1086  *
1087  * - An array of variables that participate in two variable relations; for each such variable, ADJACENTVARDATA
1088  * containing an array of variables that participate in two variable relations together with it; and a hashmap
1089  * mapping variables to ADJACENTVARDATAs.
1090  *
1091  * - Hashtables storing hashdata objects with the two or three variables and the position of the first row in the
1092  * `prob_rows` array, which in combination with the linked list (described below) will allow access to all rows that
1093  * depend only on the corresponding variables.
1094  *
1095  * - Linked lists of row indices. Each list corresponds to a pair or triple of variables and contains positions of rows
1096  * which depend only on those variables. All lists are stored in `row_list`, an array of length `nrows`, which is
1097  * possible because each row belongs to at most one list. The array indices of `row_list` represent the positions of
1098  * rows in `prob_rows`, and a value in the `row_list` array represents the next index in the list (-1 if there is no next
1099  * list element). The first index of each list is stored in one of the hashdata objects as firstrow.
1100  */
1101 static
1103  SCIP* scip, /**< SCIP data structure */
1104  SCIP_ROW** prob_rows, /**< linear rows of the problem */
1105  int nrows, /**< number of rows */
1106  SCIP_HASHTABLE* hashtable2, /**< hashtable to store 2-variable relations */
1107  SCIP_HASHTABLE* hashtable3, /**< hashtable to store implied relations */
1108  SCIP_HASHMAP* vars_in_2rels, /**< connections between variables that appear in 2-variable relations */
1109  int* row_list /**< linked lists of row positions for each 2 or 3 variable set */
1110  )
1111 {
1112  int r;
1113  SCIP_COL** cols;
1114  HASHDATA searchhashdata;
1115  HASHDATA* elementhashdata;
1116 
1117  assert(prob_rows != NULL);
1118  assert(nrows > 0);
1119  assert(hashtable2 != NULL);
1120  assert(hashtable3 != NULL);
1121  assert(vars_in_2rels != NULL);
1122  assert(row_list != NULL);
1123 
1124  for( r = 0; r < nrows; ++r )
1125  {
1126  assert(prob_rows[r] != NULL);
1127 
1128  cols = SCIProwGetCols(prob_rows[r]);
1129  assert(cols != NULL);
1130 
1131  /* initialise with the "end of list" value */
1132  row_list[r] = -1;
1133 
1134  /* look for unconditional relations with 2 variables */
1135  if( SCIProwGetNNonz(prob_rows[r]) == 2 )
1136  {
1137  /* if at least one of the variables is binary, this is either an implied bound
1138  * or a clique; these are covered separately */
1141  {
1142  SCIPdebugMsg(scip, "ignoring relation <%s> because a var is binary\n", SCIProwGetName(prob_rows[r]));
1143  continue;
1144  }
1145 
1146  /* fill in searchhashdata so that to search for the two variables in hashtable2 */
1147  searchhashdata.nvars = 2;
1148  searchhashdata.firstrow = -1;
1149  searchhashdata.vars[0] = SCIPcolGetVar(cols[0]);
1150  searchhashdata.vars[1] = SCIPcolGetVar(cols[1]);
1151 
1152  /* get the element corresponding to the two variables */
1153  elementhashdata = (HASHDATA*)SCIPhashtableRetrieve(hashtable2, &searchhashdata);
1154 
1155  if( elementhashdata != NULL )
1156  {
1157  /* if element exists, update it by adding the row */
1158  row_list[r] = elementhashdata->firstrow;
1159  elementhashdata->firstrow = r;
1160  ++elementhashdata->nrows;
1161  }
1162  else
1163  {
1164  /* create an element for the combination of two variables */
1165  SCIP_CALL( SCIPallocBuffer(scip, &elementhashdata) );
1166 
1167  elementhashdata->nvars = 2;
1168  elementhashdata->nrows = 1;
1169  elementhashdata->vars[0] = searchhashdata.vars[0];
1170  elementhashdata->vars[1] = searchhashdata.vars[1];
1171  elementhashdata->firstrow = r;
1172 
1173  SCIP_CALL( SCIPhashtableInsert(hashtable2, (void*)elementhashdata) );
1174 
1175  /* hashdata.vars are two variables participating together in a two variable relation, therefore update
1176  * these variables' adjacency data
1177  */
1178  SCIP_CALL( addAdjacentVars(scip, vars_in_2rels, searchhashdata.vars) );
1179  }
1180  }
1181 
1182  /* look for implied relations (three variables, at least one binary variable) */
1183  if( SCIProwGetNNonz(prob_rows[r]) == 3 )
1184  {
1185  /* an implied relation contains at least one binary variable */
1189  continue;
1190 
1191  /* fill in hashdata so that to search for the three variables in hashtable3 */
1192  searchhashdata.nvars = 3;
1193  searchhashdata.firstrow = -1;
1194  searchhashdata.vars[0] = SCIPcolGetVar(cols[0]);
1195  searchhashdata.vars[1] = SCIPcolGetVar(cols[1]);
1196  searchhashdata.vars[2] = SCIPcolGetVar(cols[2]);
1197 
1198  /* get the element corresponding to the three variables */
1199  elementhashdata = (HASHDATA*)SCIPhashtableRetrieve(hashtable3, &searchhashdata);
1200 
1201  if( elementhashdata != NULL )
1202  {
1203  /* if element exists, update it by adding the row */
1204  row_list[r] = elementhashdata->firstrow;
1205  elementhashdata->firstrow = r;
1206  ++elementhashdata->nrows;
1207  }
1208  else
1209  {
1210  /* create an element for the combination of three variables */
1211  SCIP_CALL( SCIPallocBuffer(scip, &elementhashdata) );
1212 
1213  elementhashdata->nvars = 3;
1214  elementhashdata->nrows = 1;
1215  elementhashdata->vars[0] = searchhashdata.vars[0];
1216  elementhashdata->vars[1] = searchhashdata.vars[1];
1217  elementhashdata->vars[2] = searchhashdata.vars[2];
1218  elementhashdata->firstrow = r;
1219 
1220  SCIP_CALL( SCIPhashtableInsert(hashtable3, (void*)elementhashdata) );
1221  }
1222  }
1223  }
1224 
1225  return SCIP_OKAY;
1226 }
1227 
1228 /** detect bilinear products encoded in linear constraints */
1229 static
1231  SCIP* scip, /**< SCIP data structure */
1232  SCIP_SEPADATA* sepadata, /**< separation data */
1233  SCIP_HASHMAP* varmap /**< variable map */
1234  )
1235 {
1236  int r1; /* first relation index */
1237  int r2; /* second relation index */
1238  int i; /* outer loop counter */
1239  int permwy; /* index for permuting w and y */
1240  int nrows;
1241  SCIP_ROW** prob_rows;
1242  SCIP_HASHTABLE* hashtable3;
1243  SCIP_HASHTABLE* hashtable2;
1244  HASHDATA* foundhashdata;
1245  SCIP_VAR* vars_xwy[3];
1246  SCIP_Real coefs1[3];
1247  SCIP_Real coefs2[3];
1248  SCIP_ROW* row1;
1249  SCIP_ROW* row2;
1250  int xpos;
1251  int ypos;
1252  int wpos;
1253  int f; /* value of the binary variable */
1254  SCIP_VAR** relatedvars;
1255  int nrelatedvars;
1256  SCIP_Bool xfixing;
1257  SCIP_SIDETYPE sidetype1;
1258  SCIP_SIDETYPE sidetype2;
1259  SCIP_Real side1;
1260  SCIP_Real side2;
1261  int* row_list;
1262  SCIP_HASHMAP* vars_in_2rels;
1263  int nvars;
1264 
1265  /* get the (original) rows */
1266  SCIP_CALL( getOriginalRows(scip, &prob_rows, &nrows) );
1267 
1268  if( nrows == 0 )
1269  {
1270  SCIPfreeBufferArray(scip, &prob_rows);
1271  return SCIP_OKAY;
1272  }
1273 
1274  /* create tables of implied and unconditional relations */
1275  SCIP_CALL( SCIPhashtableCreate(&hashtable3, SCIPblkmem(scip), nrows, SCIPhashGetKeyStandard,
1276  hashdataKeyEqConss, hashdataKeyValConss, NULL) );
1277  SCIP_CALL( SCIPhashtableCreate(&hashtable2, SCIPblkmem(scip), nrows, SCIPhashGetKeyStandard,
1278  hashdataKeyEqConss, hashdataKeyValConss, NULL) );
1279  SCIP_CALL( SCIPallocBufferArray(scip, &row_list, nrows) );
1280 
1281  /* allocate the adjacency data map for variables that appear in 2-var relations */
1282  nvars = SCIPgetNVars(scip);
1283  SCIP_CALL( SCIPhashmapCreate(&vars_in_2rels, SCIPblkmem(scip), MIN(nvars, nrows * 2)) );
1284 
1285  /* fill the data structures that will be used for product detection: hashtables and linked lists allowing to access
1286  * two and three variable relations by the variables; and the hashmap for accessing variables participating in two
1287  * variable relations with each given variable */
1288  SCIP_CALL( fillRelationTables(scip, prob_rows, nrows, hashtable2, hashtable3, vars_in_2rels, row_list) );
1289 
1290  /* start actually looking for products */
1291  /* go through all sets of three variables */
1292  for( i = 0; i < SCIPhashtableGetNEntries(hashtable3); ++i )
1293  {
1294  foundhashdata = (HASHDATA*)SCIPhashtableGetEntry(hashtable3, i);
1295  if( foundhashdata == NULL )
1296  continue;
1297 
1298  SCIPdebugMsg(scip, "(<%s>, <%s>, <%s>): ", SCIPvarGetName(foundhashdata->vars[0]),
1299  SCIPvarGetName(foundhashdata->vars[1]), SCIPvarGetName(foundhashdata->vars[2]));
1300 
1301  /* An implied relation has the form: x == f => l(w,y) <=/>= side (f is 0 or 1, l is a linear function). Given
1302  * a linear relation with three variables, any binary var can be x: we try them all here because this can
1303  * produce different products.
1304  */
1305  for( xpos = 0; xpos < 3; ++xpos )
1306  {
1307  /* in vars_xwy, the order of variables is always as in the name: x, w, y */
1308  vars_xwy[0] = foundhashdata->vars[xpos];
1309 
1310  /* x must be binary */
1311  if( SCIPvarGetType(vars_xwy[0]) != SCIP_VARTYPE_BINARY )
1312  continue;
1313 
1314  /* the first row might be an implication from f == 0 or f == 1: try both */
1315  for( f = 0; f <= 1; ++f )
1316  {
1317  xfixing = f == 1;
1318 
1319  /* go through implied relations for the corresponding three variables */
1320  for( r1 = foundhashdata->firstrow; r1 != -1; r1 = row_list[r1] )
1321  {
1322  /* get the implied relation */
1323  row1 = prob_rows[r1];
1324 
1325  assert(SCIProwGetNNonz(row1) == 3);
1326  /* the order of variables in all rows should be the same, and similar to the order in hashdata->vars,
1327  * therefore the x variable from vars_xwy should be similar to the column variable at xpos
1328  */
1329  assert(vars_xwy[0] == SCIPcolGetVar(SCIProwGetCols(row1)[xpos]));
1330 
1331  coefs1[0] = SCIProwGetVals(row1)[xpos];
1332 
1333  /* use the side for which the inequality becomes tighter when x == xfixing than when x == !xfixing */
1334  if( (!xfixing && coefs1[0] > 0.0) || (xfixing && coefs1[0] < 0.0) )
1335  {
1336  sidetype1 = SCIP_SIDETYPE_LEFT;
1337  side1 = SCIProwGetLhs(row1);
1338  }
1339  else
1340  {
1341  sidetype1 = SCIP_SIDETYPE_RIGHT;
1342  side1 = SCIProwGetRhs(row1);
1343  }
1344 
1345  if( SCIPisInfinity(scip, REALABS(side1)) )
1346  continue;
1347 
1348  side1 -= SCIProwGetConstant(row1);
1349 
1350  /* permute w and y */
1351  for( permwy = 1; permwy <= 2; ++permwy )
1352  {
1353  wpos = (xpos + permwy) % 3;
1354  ypos = (xpos - permwy + 3) % 3;
1355  vars_xwy[1] = foundhashdata->vars[wpos];
1356  vars_xwy[2] = foundhashdata->vars[ypos];
1357 
1358  assert(vars_xwy[1] == SCIPcolGetVar(SCIProwGetCols(row1)[wpos]));
1359  assert(vars_xwy[2] == SCIPcolGetVar(SCIProwGetCols(row1)[ypos]));
1360 
1361  coefs1[1] = SCIProwGetVals(row1)[wpos];
1362  coefs1[2] = SCIProwGetVals(row1)[ypos];
1363 
1364  /* look for the second relation: it should be tighter when x == !xfixing than when x == xfixing
1365  * and can be either another implied relation or one of several types of two and one variable
1366  * relations
1367  */
1368 
1369  /* go through the remaining rows (implied relations) for these three variables */
1370  for( r2 = row_list[r1]; r2 != -1; r2 = row_list[r2] )
1371  {
1372  /* get the second implied relation */
1373  row2 = prob_rows[r2];
1374 
1375  assert(SCIProwGetNNonz(row2) == 3);
1376  assert(vars_xwy[0] == SCIPcolGetVar(SCIProwGetCols(row2)[xpos]));
1377  assert(vars_xwy[1] == SCIPcolGetVar(SCIProwGetCols(row2)[wpos]));
1378  assert(vars_xwy[2] == SCIPcolGetVar(SCIProwGetCols(row2)[ypos]));
1379 
1380  coefs2[0] = SCIProwGetVals(row2)[xpos];
1381  coefs2[1] = SCIProwGetVals(row2)[wpos];
1382  coefs2[2] = SCIProwGetVals(row2)[ypos];
1383 
1384  /* use the side for which the inequality becomes tighter when x == !xfixing than when x == xfixing */
1385  if( (!xfixing && coefs2[0] > 0.0) || (xfixing && coefs2[0] < 0.0) )
1386  {
1387  sidetype2 = SCIP_SIDETYPE_RIGHT;
1388  side2 = SCIProwGetRhs(row2);
1389  }
1390  else
1391  {
1392  sidetype2 = SCIP_SIDETYPE_LEFT;
1393  side2 = SCIProwGetLhs(row2);
1394  }
1395 
1396  if( SCIPisInfinity(scip, REALABS(side2)) )
1397  continue;
1398 
1399  side2 -= SCIProwGetConstant(row2);
1400 
1401  SCIPdebugMsg(scip, "Two implied relations:\n");
1402  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1, side2, sidetype1,
1403  sidetype2, varmap, xfixing) );
1404  }
1405 
1406  /* use global bounds on w */
1407  coefs2[0] = 0.0;
1408  coefs2[1] = 1.0;
1409  coefs2[2] = 0.0;
1410  SCIPdebugMsg(scip, "w global bounds:\n");
1411  if( !SCIPisInfinity(scip, -SCIPvarGetLbGlobal(vars_xwy[1])) )
1412  {
1413  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1414  SCIPvarGetLbGlobal(vars_xwy[1]), sidetype1, SCIP_SIDETYPE_LEFT, varmap, xfixing) );
1415  }
1416 
1417  if( !SCIPisInfinity(scip, SCIPvarGetUbGlobal(vars_xwy[1])) )
1418  {
1419  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1420  SCIPvarGetUbGlobal(vars_xwy[1]), sidetype1, SCIP_SIDETYPE_RIGHT, varmap, xfixing) );
1421  }
1422 
1423  /* use implied bounds and cliques with w */
1424  if( SCIPvarGetType(vars_xwy[1]) != SCIP_VARTYPE_BINARY )
1425  {
1426  /* w is non-binary - look for implied bounds x == !f => w >=/<= bound */
1427  SCIPdebugMsg(scip, "Implied relation + implied bounds on w:\n");
1428  SCIP_CALL( detectProductsImplbnd(scip, sepadata, coefs1, vars_xwy, side1, sidetype1, 0, 1,
1429  varmap, xfixing) );
1430  }
1431  else
1432  {
1433  /* w is binary - look for cliques containing x and w */
1434  SCIPdebugMsg(scip, "Implied relation + cliques with x and w:\n");
1435  SCIP_CALL( detectProductsClique(scip, sepadata, coefs1, vars_xwy, side1, sidetype1, 0, 1,
1436  varmap, xfixing) );
1437  }
1438 
1439  /* use unconditional relations (i.e. relations of w and y) */
1440 
1441  /* implied bound w == 0/1 => y >=/<= bound */
1442  if( SCIPvarGetType(vars_xwy[1]) == SCIP_VARTYPE_BINARY && SCIPvarGetType(vars_xwy[2]) != SCIP_VARTYPE_BINARY )
1443  {
1444  SCIPdebugMsg(scip, "Implied relation + implied bounds with w and y:\n");
1445  SCIP_CALL( detectProductsImplbnd(scip, sepadata, coefs1, vars_xwy, side1, sidetype1, 1, 2, varmap, xfixing) );
1446  }
1447 
1448  /* implied bound y == 0/1 => w >=/<= bound */
1449  if( SCIPvarGetType(vars_xwy[2]) == SCIP_VARTYPE_BINARY && SCIPvarGetType(vars_xwy[1]) != SCIP_VARTYPE_BINARY )
1450  {
1451  SCIPdebugMsg(scip, "Implied relation + implied bounds with y and w:\n");
1452  SCIP_CALL( detectProductsImplbnd(scip, sepadata, coefs1, vars_xwy, side1, sidetype1, 2, 1, varmap, xfixing) );
1453  }
1454 
1455  /* cliques containing w and y */
1456  if( SCIPvarGetType(vars_xwy[1]) == SCIP_VARTYPE_BINARY && SCIPvarGetType(vars_xwy[2]) == SCIP_VARTYPE_BINARY )
1457  {
1458  SCIPdebugMsg(scip, "Implied relation + cliques with w and y:\n");
1459  SCIP_CALL( detectProductsClique(scip, sepadata, coefs1, vars_xwy, side1, sidetype1, 1, 2, varmap, xfixing) );
1460  }
1461 
1462  /* inequalities containing w and y */
1463  if( SCIPvarGetType(vars_xwy[1]) != SCIP_VARTYPE_BINARY && SCIPvarGetType(vars_xwy[2]) != SCIP_VARTYPE_BINARY )
1464  {
1465  SCIPdebugMsg(scip, "Implied relation + unconditional with w and y:\n");
1466  SCIP_CALL( detectProductsUnconditional(scip, sepadata, prob_rows, row_list, hashtable2, coefs1,
1467  vars_xwy, side1, sidetype1, 1, 2, varmap, xfixing) );
1468  }
1469  }
1470  }
1471  }
1472  }
1473  SCIPfreeBuffer(scip, &foundhashdata);
1474  }
1475 
1476  /* also loop through implied bounds to look for products */
1477  for( i = 0; i < SCIPgetNBinVars(scip); ++i )
1478  {
1479  /* first choose the x variable: it can be any binary variable in the problem */
1480  vars_xwy[0] = SCIPgetVars(scip)[i];
1481 
1482  assert(SCIPvarGetType(vars_xwy[0]) == SCIP_VARTYPE_BINARY);
1483 
1484  /* consider both possible values of x */
1485  for( f = 0; f <= 1; ++f )
1486  {
1487  xfixing = f == 1;
1488 
1489  /* go through implications of x */
1490  for( r1 = 0; r1 < SCIPvarGetNImpls(vars_xwy[0], xfixing); ++r1 )
1491  {
1492  /* w is the implication var */
1493  vars_xwy[1] = SCIPvarGetImplVars(vars_xwy[0], xfixing)[r1];
1494  assert(SCIPvarGetType(vars_xwy[1]) != SCIP_VARTYPE_BINARY);
1495 
1496  /* write the implication as a big-M constraint */
1497  implBndToBigM(scip, vars_xwy, 0, 1, SCIPvarGetImplTypes(vars_xwy[0], xfixing)[r1], xfixing,
1498  SCIPvarGetImplBounds(vars_xwy[0], xfixing)[r1], coefs1, &side1);
1499  sidetype1 = SCIPvarGetImplTypes(vars_xwy[0], xfixing)[r1] == SCIP_BOUNDTYPE_LOWER ?
1501 
1502  /* if the global bound is equal to the implied bound, there is nothing to do */
1503  if( SCIPisZero(scip, coefs1[0]) )
1504  continue;
1505 
1506  SCIPdebugMsg(scip, "Implication %s == %u => %s %s %g\n", SCIPvarGetName(vars_xwy[0]), xfixing,
1507  SCIPvarGetName(vars_xwy[1]), sidetype1 == SCIP_SIDETYPE_LEFT ? ">=" : "<=",
1508  SCIPvarGetImplBounds(vars_xwy[0], xfixing)[r1]);
1509  SCIPdebugMsg(scip, "Written as big-M: %g%s + %s %s %g\n", coefs1[0], SCIPvarGetName(vars_xwy[0]),
1510  SCIPvarGetName(vars_xwy[1]), sidetype1 == SCIP_SIDETYPE_LEFT ? ">=" : "<=", side1);
1511 
1512  /* the second relation is in w and y (y could be anything, but must be in relation with w) */
1513 
1514  /* x does not participate in the second relation, so we immediately set its coefficient to 0.0 */
1515  coefs2[0] = 0.0;
1516 
1517  SCIPdebugMsg(scip, "Implic of x = <%s> + implied lb on w = <%s>:\n", SCIPvarGetName(vars_xwy[0]), SCIPvarGetName(vars_xwy[1]));
1518 
1519  /* use implied lower bounds on w: w >= b*y + d */
1520  for( r2 = 0; r2 < SCIPvarGetNVlbs(vars_xwy[1]); ++r2 )
1521  {
1522  vars_xwy[2] = SCIPvarGetVlbVars(vars_xwy[1])[r2];
1523  if( vars_xwy[2] == vars_xwy[0] )
1524  continue;
1525 
1526  coefs2[1] = 1.0;
1527  coefs2[2] = -SCIPvarGetVlbCoefs(vars_xwy[1])[r2];
1528 
1529  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1530  SCIPvarGetVlbConstants(vars_xwy[1])[r2], sidetype1, SCIP_SIDETYPE_LEFT, varmap, xfixing) );
1531  }
1532 
1533  SCIPdebugMsg(scip, "Implic of x = <%s> + implied ub on w = <%s>:\n", SCIPvarGetName(vars_xwy[0]), SCIPvarGetName(vars_xwy[1]));
1534 
1535  /* use implied upper bounds on w: w <= b*y + d */
1536  for( r2 = 0; r2 < SCIPvarGetNVubs(vars_xwy[1]); ++r2 )
1537  {
1538  vars_xwy[2] = SCIPvarGetVubVars(vars_xwy[1])[r2];
1539  if( vars_xwy[2] == vars_xwy[0] )
1540  continue;
1541 
1542  coefs2[1] = 1.0;
1543  coefs2[2] = -SCIPvarGetVubCoefs(vars_xwy[1])[r2];
1544 
1545  SCIP_CALL( extractProducts(scip, sepadata, vars_xwy, coefs1, coefs2, side1,
1546  SCIPvarGetVubConstants(vars_xwy[1])[r2], sidetype1, SCIP_SIDETYPE_RIGHT, varmap, xfixing) );
1547  }
1548 
1549  /* use unconditional relations containing w */
1550  relatedvars = getAdjacentVars(vars_in_2rels, vars_xwy[1], &nrelatedvars);
1551  if( relatedvars == NULL )
1552  continue;
1553 
1554  for( r2 = 0; r2 < nrelatedvars; ++r2 )
1555  {
1556  vars_xwy[2] = relatedvars[r2];
1557  SCIPdebugMsg(scip, "Implied bound + unconditional with w and y:\n");
1558  SCIP_CALL( detectProductsUnconditional(scip, sepadata, prob_rows, row_list, hashtable2, coefs1,
1559  vars_xwy, side1, sidetype1, 1, 2, varmap, xfixing) );
1560  }
1561  }
1562  }
1563  }
1564 
1565  /* free memory */
1566  clearVarAdjacency(scip, vars_in_2rels);
1567  SCIPhashmapFree(&vars_in_2rels);
1568 
1569  SCIPdebugMsg(scip, "Unconditional relations table:\n");
1570  for( i = 0; i < SCIPhashtableGetNEntries(hashtable2); ++i )
1571  {
1572  foundhashdata = (HASHDATA*)SCIPhashtableGetEntry(hashtable2, i);
1573  if( foundhashdata == NULL )
1574  continue;
1575 
1576  SCIPdebugMsg(scip, "(%s, %s): ", SCIPvarGetName(foundhashdata->vars[0]),
1577  SCIPvarGetName(foundhashdata->vars[1]));
1578 
1579  SCIPfreeBuffer(scip, &foundhashdata);
1580  }
1581 
1582  SCIPfreeBufferArray(scip, &row_list);
1583 
1584  SCIPhashtableFree(&hashtable2);
1585  SCIPhashtableFree(&hashtable3);
1586 
1587  SCIPfreeBufferArray(scip, &prob_rows);
1588 
1589  return SCIP_OKAY;
1590 }
1591 
1592 /** helper method to create separation data */
1593 static
1595  SCIP* scip, /**< SCIP data structure */
1596  SCIP_SEPADATA* sepadata /**< separation data */
1597  )
1598 {
1599  SCIP_HASHMAP* varmap;
1600  int i;
1601  SCIP_CONSNONLINEAR_BILINTERM* bilinterms;
1602  int varmapsize;
1603  int nvars;
1604 
1605  assert(sepadata != NULL);
1606 
1607  /* initialize some fields of sepadata */
1608  sepadata->varssorted = NULL;
1609  sepadata->varpriorities = NULL;
1610  sepadata->bilinvardatamap = NULL;
1611  sepadata->eqauxexpr = NULL;
1612  sepadata->nbilinvars = 0;
1613  sepadata->sbilinvars = 0;
1614 
1615  /* get total number of bilinear terms */
1616  sepadata->nbilinterms = SCIPgetNBilinTermsNonlinear(sepadata->conshdlr);
1617 
1618  /* skip if there are no bilinear terms and implicit product detection is off */
1619  if( sepadata->nbilinterms == 0 && !sepadata->detecthidden )
1620  return SCIP_OKAY;
1621 
1622  /* the number of variables participating in bilinear products cannot exceed twice the number of bilinear terms;
1623  * however, if we detect hidden products, the number of terms is yet unknown, so use the number of variables
1624  */
1625  nvars = SCIPgetNVars(scip);
1626  varmapsize = sepadata->detecthidden ? nvars : MIN(nvars, sepadata->nbilinterms * 2);
1627 
1628  /* create variable map */
1629  SCIP_CALL( SCIPhashmapCreate(&varmap, SCIPblkmem(scip), varmapsize) );
1630 
1631  /* get all bilinear terms from the nonlinear constraint handler */
1632  bilinterms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
1633 
1634  /* store the information of all variables that appear bilinearly */
1635  for( i = 0; i < sepadata->nbilinterms; ++i )
1636  {
1637  assert(bilinterms[i].x != NULL);
1638  assert(bilinterms[i].y != NULL);
1639  assert(bilinterms[i].nlockspos + bilinterms[i].nlocksneg > 0);
1640 
1641  /* skip bilinear term if it does not have an auxiliary variable */
1642  if( bilinterms[i].aux.var == NULL )
1643  continue;
1644 
1645  /* if only original variables should be used, skip products that contain at least one auxiliary variable */
1646  if( sepadata->onlyoriginal && (SCIPvarIsRelaxationOnly(bilinterms[i].x) ||
1647  SCIPvarIsRelaxationOnly(bilinterms[i].y)) )
1648  continue;
1649 
1650  /* coverity[forward_null] */
1651  SCIP_CALL( addProductVars(scip, sepadata, bilinterms[i].x, bilinterms[i].y, varmap,
1652  bilinterms[i].nlockspos + bilinterms[i].nlocksneg) );
1653  }
1654 
1655  if( sepadata->detecthidden )
1656  {
1657  int oldnterms = sepadata->nbilinterms;
1658 
1659  /* coverity[forward_null] */
1660  SCIP_CALL( detectHiddenProducts(scip, sepadata, varmap) );
1661 
1662  /* update nbilinterms and bilinterms, as detectHiddenProducts might have found new terms */
1663  sepadata->nbilinterms = SCIPgetNBilinTermsNonlinear(sepadata->conshdlr);
1664  bilinterms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
1665 
1666  if( sepadata->nbilinterms > oldnterms )
1667  {
1668  SCIPstatisticMessage(" Number of hidden products: %d\n", sepadata->nbilinterms - oldnterms);
1669  }
1670  }
1671 
1672  SCIPhashmapFree(&varmap);
1673 
1674  if( sepadata->nbilinterms == 0 )
1675  {
1676  return SCIP_OKAY;
1677  }
1678 
1679  /* mark positions of aux.exprs that must be equal to the product */
1680  SCIP_CALL( SCIPallocBlockMemoryArray(scip, &sepadata->eqauxexpr, sepadata->nbilinterms) );
1681 
1682  for( i = 0; i < sepadata->nbilinterms; ++i )
1683  {
1684  int j;
1685 
1686  sepadata->eqauxexpr[i] = -1;
1687  for( j = 0; j < bilinterms[i].nauxexprs; ++j )
1688  {
1689  assert(bilinterms[i].aux.exprs[j] != NULL);
1690 
1691  if( bilinterms[i].aux.exprs[j]->underestimate && bilinterms[i].aux.exprs[j]->overestimate )
1692  {
1693  sepadata->eqauxexpr[i] = j;
1694  break;
1695  }
1696  }
1697  }
1698 
1699  /* find maxnumber of variables that occur most often and sort them by number of occurrences
1700  * (same as normal sort, except that entries at positions maxusedvars..nbilinvars may be unsorted at end)
1701  */
1702  SCIPselectDownIntPtr(sepadata->varpriorities, (void**) sepadata->varssorted, MIN(sepadata->maxusedvars,sepadata->nbilinvars-1),
1703  sepadata->nbilinvars);
1704 
1705  /* capture all variables */
1706  for( i = 0; i < sepadata->nbilinvars; ++i )
1707  {
1708  assert(sepadata->varssorted[i] != NULL);
1709  SCIP_CALL( SCIPcaptureVar(scip, sepadata->varssorted[i]) );
1710  }
1711 
1712  /* mark that separation data has been created */
1713  sepadata->iscreated = TRUE;
1714  sepadata->isinitialround = TRUE;
1715 
1716  if( SCIPgetNBilinTermsNonlinear(sepadata->conshdlr) > 0 )
1717  SCIPstatisticMessage(" Found bilinear terms\n");
1718  else
1719  SCIPstatisticMessage(" No bilinear terms\n");
1720 
1721  return SCIP_OKAY;
1722 }
1723 
1724 /** get the positions of the most violated auxiliary under- and overestimators for each product
1725  *
1726  * -1 means no relation with given product is violated
1727  */
1728 static
1729 void getBestEstimators(
1730  SCIP* scip, /**< SCIP data structure */
1731  SCIP_SEPADATA* sepadata, /**< separator data */
1732  SCIP_SOL* sol, /**< solution at which to evaluate the expressions */
1733  int* bestunderestimators,/**< array of indices of best underestimators for each term */
1734  int* bestoverestimators /**< array of indices of best overestimators for each term */
1735  )
1736 {
1737  SCIP_Real prodval;
1738  SCIP_Real auxval;
1739  SCIP_Real prodviol;
1740  SCIP_Real viol_below;
1741  SCIP_Real viol_above;
1742  int i;
1743  int j;
1745 
1746  assert(bestunderestimators != NULL);
1747  assert(bestoverestimators != NULL);
1748 
1749  terms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
1750 
1751  for( j = 0; j < SCIPgetNBilinTermsNonlinear(sepadata->conshdlr); ++j )
1752  {
1753  viol_below = 0.0;
1754  viol_above = 0.0;
1755 
1756  /* evaluate the product expression */
1757  prodval = SCIPgetSolVal(scip, sol, terms[j].x) * SCIPgetSolVal(scip, sol, terms[j].y);
1758 
1759  bestunderestimators[j] = -1;
1760  bestoverestimators[j] = -1;
1761 
1762  /* if there are any auxexprs, look there */
1763  for( i = 0; i < terms[j].nauxexprs; ++i )
1764  {
1765  auxval = SCIPevalBilinAuxExprNonlinear(scip, terms[j].x, terms[j].y, terms[j].aux.exprs[i], sol);
1766  prodviol = auxval - prodval;
1767 
1768  if( terms[j].aux.exprs[i]->underestimate && SCIPisFeasGT(scip, auxval, prodval) && prodviol > viol_below )
1769  {
1770  viol_below = prodviol;
1771  bestunderestimators[j] = i;
1772  }
1773  if( terms[j].aux.exprs[i]->overestimate && SCIPisFeasGT(scip, prodval, auxval) && -prodviol > viol_above )
1774  {
1775  viol_above = -prodviol;
1776  bestoverestimators[j] = i;
1777  }
1778  }
1779 
1780  /* if the term has a plain auxvar, it will be treated differently - do nothing here */
1781  }
1782 }
1783 
1784 /** tests if a row contains too many unknown bilinear terms w.r.t. the parameters */
1785 static
1787  SCIP_SEPADATA* sepadata, /**< separation data */
1788  SCIP_ROW* row, /**< the row to be tested */
1789  SCIP_VAR* var, /**< the variable that is to be multiplied with row */
1790  int* currentnunknown, /**< buffer to store number of unknown terms in current row if acceptable */
1791  SCIP_Bool* acceptable /**< buffer to store the result */
1792  )
1793 {
1794  int i;
1795  int idx;
1797 
1798  assert(row != NULL);
1799  assert(var != NULL);
1800 
1801  *currentnunknown = 0;
1802  terms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
1803 
1804  for( i = 0; (i < SCIProwGetNNonz(row)) && (sepadata->maxunknownterms < 0 || *currentnunknown <= sepadata->maxunknownterms); ++i )
1805  {
1806  idx = SCIPgetBilinTermIdxNonlinear(sepadata->conshdlr, var, SCIPcolGetVar(SCIProwGetCols(row)[i]));
1807 
1808  /* if the product hasn't been found, no auxiliary expressions for it are known */
1809  if( idx < 0 )
1810  {
1811  ++(*currentnunknown);
1812  continue;
1813  }
1814 
1815  /* known terms are only those that have an aux.var or equality estimators */
1816  if( sepadata->eqauxexpr[idx] == -1 && !(terms[idx].nauxexprs == 0 && terms[idx].aux.var != NULL) )
1817  {
1818  ++(*currentnunknown);
1819  }
1820  }
1821 
1822  *acceptable = sepadata->maxunknownterms < 0 || *currentnunknown <= sepadata->maxunknownterms;
1823 
1824  return SCIP_OKAY;
1825 }
1826 
1827 /** adds coefficients and constant of an auxiliary expression
1828  *
1829  * the variables the pointers are pointing to must already be initialized
1830  */
1831 static
1832 void addAuxexprCoefs(
1833  SCIP_VAR* var1, /**< first product variable */
1834  SCIP_VAR* var2, /**< second product variable */
1835  SCIP_CONSNONLINEAR_AUXEXPR* auxexpr, /**< auxiliary expression to be added */
1836  SCIP_Real coef, /**< coefficient of the auxiliary expression */
1837  SCIP_Real* coefaux, /**< pointer to add the coefficient of the auxiliary variable */
1838  SCIP_Real* coef1, /**< pointer to add the coefficient of the first variable */
1839  SCIP_Real* coef2, /**< pointer to add the coefficient of the second variable */
1840  SCIP_Real* cst /**< pointer to add the constant */
1841  )
1842 {
1843  assert(auxexpr != NULL);
1844  assert(auxexpr->auxvar != NULL);
1845  assert(coefaux != NULL);
1846  assert(coef1 != NULL);
1847  assert(coef2 != NULL);
1848  assert(cst != NULL);
1849 
1850  *coefaux += auxexpr->coefs[0] * coef;
1851 
1852  /* in auxexpr, x goes before y and has the smaller index,
1853  * so compare vars to figure out which one is x and which is y
1854  */
1855  if( SCIPvarCompare(var1, var2) < 1 )
1856  {
1857  *coef1 += auxexpr->coefs[1] * coef;
1858  *coef2 += auxexpr->coefs[2] * coef;
1859  }
1860  else
1861  {
1862  *coef1 += auxexpr->coefs[2] * coef;
1863  *coef2 += auxexpr->coefs[1] * coef;
1864  }
1865  *cst += coef * auxexpr->cst;
1866 }
1867 
1868 /** add a linear term `coef`*`colvar` multiplied by a bound factor (var - lb(var)) or (ub(var) - var)
1869  *
1870  * adds the linear term with `colvar` to `cut` and updates `coefvar` and `cst`
1871  */
1872 static
1874  SCIP* scip, /**< SCIP data structure */
1875  SCIP_SEPADATA* sepadata, /**< separator data */
1876  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
1877  int* bestunderest, /**< positions of most violated underestimators for each product term */
1878  int* bestoverest, /**< positions of most violated overestimators for each product term */
1879  SCIP_ROW* cut, /**< cut to which the term is to be added */
1880  SCIP_VAR* var, /**< multiplier variable */
1881  SCIP_VAR* colvar, /**< row variable to be multiplied */
1882  SCIP_Real coef, /**< coefficient of the bilinear term */
1883  SCIP_Bool uselb, /**< whether we multiply with (var - lb) or (ub - var) */
1884  SCIP_Bool uselhs, /**< whether to create a cut for the lhs or rhs */
1885  SCIP_Bool local, /**< whether local or global cuts should be computed */
1886  SCIP_Bool computeEqCut, /**< whether conditions are fulfilled to compute equality cuts */
1887  SCIP_Real* coefvar, /**< coefficient of var */
1888  SCIP_Real* cst, /**< buffer to store the constant part of the cut */
1889  SCIP_Bool* success /**< buffer to store whether cut was updated successfully */
1890  )
1891 {
1892  SCIP_Real lbvar;
1893  SCIP_Real ubvar;
1894  SCIP_Real refpointvar;
1895  SCIP_Real signfactor;
1896  SCIP_Real boundfactor;
1897  SCIP_Real coefauxvar;
1898  SCIP_Real coefcolvar;
1899  SCIP_Real coefterm;
1900  int auxpos;
1901  int idx;
1903  SCIP_VAR* auxvar;
1904 
1905  terms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
1906 
1907  if( computeEqCut )
1908  {
1909  lbvar = 0.0;
1910  ubvar = 0.0;
1911  }
1912  else
1913  {
1914  lbvar = local ? SCIPvarGetLbLocal(var) : SCIPvarGetLbGlobal(var);
1915  ubvar = local ? SCIPvarGetUbLocal(var) : SCIPvarGetUbGlobal(var);
1916  }
1917 
1918  refpointvar = MAX(lbvar, MIN(ubvar, SCIPgetSolVal(scip, sol, var))); /*lint !e666*/
1919 
1920  signfactor = (uselb ? 1.0 : -1.0);
1921  boundfactor = (uselb ? -lbvar : ubvar);
1922 
1923  coefterm = coef * signfactor; /* coefficient of the bilinear term */
1924  coefcolvar = coef * boundfactor; /* coefficient of the linear term */
1925  coefauxvar = 0.0; /* coefficient of the auxiliary variable corresponding to the bilinear term */
1926  auxvar = NULL;
1927 
1928  assert(!SCIPisInfinity(scip, REALABS(coefterm)));
1929 
1930  /* first, add the linearisation of the bilinear term */
1931 
1932  idx = SCIPgetBilinTermIdxNonlinear(sepadata->conshdlr, var, colvar);
1933  auxpos = -1;
1934 
1935  /* for an implicit term, get the position of the best estimator */
1936  if( idx >= 0 && terms[idx].nauxexprs > 0 )
1937  {
1938  if( computeEqCut )
1939  {
1940  /* use an equality auxiliary expression (which should exist for computeEqCut to be TRUE) */
1941  assert(sepadata->eqauxexpr[idx] >= 0);
1942  auxpos = sepadata->eqauxexpr[idx];
1943  }
1944  else if( (uselhs && coefterm > 0.0) || (!uselhs && coefterm < 0.0) )
1945  {
1946  /* use an overestimator */
1947  auxpos = bestoverest[idx];
1948  }
1949  else
1950  {
1951  /* use an underestimator */
1952  auxpos = bestunderest[idx];
1953  }
1954  }
1955 
1956  /* if the term is implicit and a suitable auxiliary expression for var*colvar exists, add the coefficients
1957  * of the auxiliary expression for coefterm*var*colvar to coefauxvar, coefcolvar, coefvar and cst
1958  */
1959  if( auxpos >= 0 )
1960  {
1961  SCIPdebugMsg(scip, "auxiliary expression for <%s> and <%s> found, will be added to cut:\n",
1962  SCIPvarGetName(colvar), SCIPvarGetName(var));
1963  addAuxexprCoefs(var, colvar, terms[idx].aux.exprs[auxpos], coefterm, &coefauxvar, coefvar, &coefcolvar, cst);
1964  auxvar = terms[idx].aux.exprs[auxpos]->auxvar;
1965  }
1966  /* for an existing term, use the auxvar if there is one */
1967  else if( idx >= 0 && terms[idx].nauxexprs == 0 && terms[idx].aux.var != NULL )
1968  {
1969  SCIPdebugMsg(scip, "auxvar for <%s> and <%s> found, will be added to cut:\n",
1970  SCIPvarGetName(colvar), SCIPvarGetName(var));
1971  coefauxvar += coefterm;
1972  auxvar = terms[idx].aux.var;
1973  }
1974 
1975  /* otherwise, use clique information or the McCormick estimator in place of the bilinear term */
1976  else if( colvar != var )
1977  {
1978  SCIP_Bool found_clique = FALSE;
1979  SCIP_Real lbcolvar = local ? SCIPvarGetLbLocal(colvar) : SCIPvarGetLbGlobal(colvar);
1980  SCIP_Real ubcolvar = local ? SCIPvarGetUbLocal(colvar) : SCIPvarGetUbGlobal(colvar);
1981  SCIP_Real refpointcolvar = MAX(lbcolvar, MIN(ubcolvar, SCIPgetSolVal(scip, sol, colvar))); /*lint !e666*/
1982 
1983  assert(!computeEqCut);
1984 
1985  if( REALABS(lbcolvar) > MAXVARBOUND || REALABS(ubcolvar) > MAXVARBOUND )
1986  {
1987  *success = FALSE;
1988  return SCIP_OKAY;
1989  }
1990 
1991  SCIPdebugMsg(scip, "auxvar for <%s> and <%s> not found, will linearize the product\n", SCIPvarGetName(colvar), SCIPvarGetName(var));
1992 
1993  /* if both variables are binary, check if they are contained together in some clique */
1995  {
1996  int c;
1997  SCIP_CLIQUE** varcliques;
1998 
1999  varcliques = SCIPvarGetCliques(var, TRUE);
2000 
2001  /* look through cliques containing var */
2002  for( c = 0; c < SCIPvarGetNCliques(var, TRUE); ++c )
2003  {
2004  if( SCIPcliqueHasVar(varcliques[c], colvar, TRUE) ) /* var + colvar <= 1 => var*colvar = 0 */
2005  {
2006  /* product is zero, add nothing */
2007  found_clique = TRUE;
2008  break;
2009  }
2010 
2011  if( SCIPcliqueHasVar(varcliques[c], colvar, FALSE) ) /* var + (1-colvar) <= 1 => var*colvar = var */
2012  {
2013  *coefvar += coefterm;
2014  found_clique = TRUE;
2015  break;
2016  }
2017  }
2018 
2019  if( !found_clique )
2020  {
2021  varcliques = SCIPvarGetCliques(var, FALSE);
2022 
2023  /* look through cliques containing complement of var */
2024  for( c = 0; c < SCIPvarGetNCliques(var, FALSE); ++c )
2025  {
2026  if( SCIPcliqueHasVar(varcliques[c], colvar, TRUE) ) /* (1-var) + colvar <= 1 => var*colvar = colvar */
2027  {
2028  coefcolvar += coefterm;
2029  found_clique = TRUE;
2030  break;
2031  }
2032 
2033  if( SCIPcliqueHasVar(varcliques[c], colvar, FALSE) ) /* (1-var) + (1-colvar) <= 1 => var*colvar = var + colvar - 1 */
2034  {
2035  *coefvar += coefterm;
2036  coefcolvar += coefterm;
2037  *cst -= coefterm;
2038  found_clique = TRUE;
2039  break;
2040  }
2041  }
2042  }
2043  }
2044 
2045  if( !found_clique )
2046  {
2047  SCIPdebugMsg(scip, "clique for <%s> and <%s> not found or at least one of them is not binary, will use McCormick\n", SCIPvarGetName(colvar), SCIPvarGetName(var));
2048  SCIPaddBilinMcCormick(scip, coefterm, lbvar, ubvar, refpointvar, lbcolvar,
2049  ubcolvar, refpointcolvar, uselhs, coefvar, &coefcolvar, cst, success);
2050  if( !*success )
2051  return SCIP_OKAY;
2052  }
2053  }
2054 
2055  /* or, if it's a quadratic term, use a secant for overestimation and a gradient for underestimation */
2056  else
2057  {
2058  SCIPdebugMsg(scip, "auxvar for <%s>^2 not found, will use gradient and secant estimators\n", SCIPvarGetName(colvar));
2059 
2060  assert(!computeEqCut);
2061 
2062  /* for a binary var, var^2 = var */
2063  if( SCIPvarGetType(var) == SCIP_VARTYPE_BINARY )
2064  {
2065  *coefvar += coefterm;
2066  }
2067  else
2068  {
2069  /* depending on over-/underestimation and the sign of the column variable, compute secant or tangent */
2070  if( (uselhs && coefterm > 0.0) || (!uselhs && coefterm < 0.0) )
2071  SCIPaddSquareSecant(scip, coefterm, lbvar, ubvar, coefvar, cst, success);
2072  else
2073  SCIPaddSquareLinearization(scip, coefterm, refpointvar, SCIPvarIsIntegral(var), coefvar, cst, success);
2074 
2075  if( !*success )
2076  return SCIP_OKAY;
2077  }
2078  }
2079 
2080  /* add the auxiliary variable if its coefficient is nonzero */
2081  if( !SCIPisZero(scip, coefauxvar) )
2082  {
2083  assert(auxvar != NULL);
2084  SCIP_CALL( SCIPaddVarToRow(scip, cut, auxvar, coefauxvar) );
2085  }
2086 
2087  /* we are done with the product linearisation, now add the term which comes from multiplying
2088  * coef*colvar by the constant part of the bound factor
2089  */
2090 
2091  if( colvar != var )
2092  {
2093  assert(!SCIPisInfinity(scip, REALABS(coefcolvar)));
2094  SCIP_CALL( SCIPaddVarToRow(scip, cut, colvar, coefcolvar) );
2095  }
2096  else
2097  *coefvar += coefcolvar;
2098 
2099  return SCIP_OKAY;
2100 }
2101 
2102 /** creates the RLT cut formed by multiplying a given row with (x - lb) or (ub - x)
2103  *
2104  * In detail:
2105  * - The row is multiplied either with (x - lb(x)) or with (ub(x) - x), depending on parameter `uselb`, or by x if
2106  * this is an equality cut
2107  * - The (inequality) cut is computed either for lhs or rhs, depending on parameter `uselhs`.
2108  * - Terms for which no auxiliary variable and no clique relation exists are replaced by either McCormick, secants,
2109  * or gradient linearization cuts.
2110  */
2111 static
2113  SCIP* scip, /**< SCIP data structure */
2114  SCIP_SEPA* sepa, /**< separator */
2115  SCIP_SEPADATA* sepadata, /**< separation data */
2116  SCIP_ROW** cut, /**< buffer to store the cut */
2117  SCIP_ROW* row, /**< the row that is used for the rlt cut (NULL if using projected row) */
2118  RLT_SIMPLEROW* projrow, /**< projected row that is used for the rlt cut (NULL if using row) */
2119  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
2120  int* bestunderest, /**< positions of most violated underestimators for each product term */
2121  int* bestoverest, /**< positions of most violated overestimators for each product term */
2122  SCIP_VAR* var, /**< the variable that is used for the rlt cuts */
2123  SCIP_Bool* success, /**< buffer to store whether cut was created successfully */
2124  SCIP_Bool uselb, /**< whether we multiply with (var - lb) or (ub - var) */
2125  SCIP_Bool uselhs, /**< whether to create a cut for the lhs or rhs */
2126  SCIP_Bool local, /**< whether local or global cuts should be computed */
2127  SCIP_Bool computeEqCut, /**< whether conditions are fulfilled to compute equality cuts */
2128  SCIP_Bool useprojrow /**< whether to use projected row instead of normal row */
2129  )
2130 { /*lint --e{413}*/
2131  SCIP_Real signfactor;
2132  SCIP_Real boundfactor;
2133  SCIP_Real lbvar;
2134  SCIP_Real ubvar;
2135  SCIP_Real coefvar;
2136  SCIP_Real consside;
2137  SCIP_Real finalside;
2138  SCIP_Real cstterm;
2139  SCIP_Real lhs;
2140  SCIP_Real rhs;
2141  SCIP_Real rowcst;
2142  int i;
2143  const char* rowname;
2144  char cutname[SCIP_MAXSTRLEN];
2145 
2146  assert(sepadata != NULL);
2147  assert(cut != NULL);
2148  assert(useprojrow || row != NULL);
2149  assert(!useprojrow || projrow != NULL);
2150  assert(var != NULL);
2151  assert(success != NULL);
2152 
2153  lhs = useprojrow ? projrow->lhs : SCIProwGetLhs(row);
2154  rhs = useprojrow ? projrow->rhs : SCIProwGetRhs(row);
2155  rowname = useprojrow ? projrow->name : SCIProwGetName(row);
2156  rowcst = useprojrow ? projrow ->cst : SCIProwGetConstant(row);
2157 
2158  assert(!computeEqCut || SCIPisEQ(scip, lhs, rhs));
2159 
2160  *cut = NULL;
2161 
2162  /* get data for given variable */
2163  if( computeEqCut )
2164  {
2165  lbvar = 0.0;
2166  ubvar = 0.0;
2167  }
2168  else
2169  {
2170  lbvar = local ? SCIPvarGetLbLocal(var) : SCIPvarGetLbGlobal(var);
2171  ubvar = local ? SCIPvarGetUbLocal(var) : SCIPvarGetUbGlobal(var);
2172  }
2173 
2174  /* get row side */
2175  consside = uselhs ? lhs : rhs;
2176 
2177  /* if the bounds are too large or the respective side is infinity, skip this cut */
2178  if( (uselb && REALABS(lbvar) > MAXVARBOUND) || (!uselb && REALABS(ubvar) > MAXVARBOUND)
2179  || SCIPisInfinity(scip, REALABS(consside)) )
2180  {
2181  SCIPdebugMsg(scip, "cut generation for %srow <%s>, %s, and variable <%s> with its %s %g not possible\n",
2182  useprojrow ? "projected " : "", rowname, uselhs ? "lhs" : "rhs", SCIPvarGetName(var),
2183  uselb ? "lower bound" : "upper bound", uselb ? lbvar : ubvar);
2184 
2185  if( REALABS(lbvar) > MAXVARBOUND )
2186  SCIPdebugMsg(scip, " because of lower bound\n");
2187  if( REALABS(ubvar) > MAXVARBOUND )
2188  SCIPdebugMsg(scip, " because of upper bound\n");
2189  if( SCIPisInfinity(scip, REALABS(consside)) )
2190  SCIPdebugMsg(scip, " because of side %g\n", consside);
2191 
2192  *success = FALSE;
2193  return SCIP_OKAY;
2194  }
2195 
2196  /* initialize some factors needed for computation */
2197  coefvar = 0.0;
2198  cstterm = 0.0;
2199  signfactor = (uselb ? 1.0 : -1.0);
2200  boundfactor = (uselb ? -lbvar : ubvar);
2201  *success = TRUE;
2202 
2203  /* create an empty row which we then fill with variables step by step */
2204  (void) SCIPsnprintf(cutname, SCIP_MAXSTRLEN, "rlt_%scut_%s_%s_%s_%s_%" SCIP_LONGINT_FORMAT, useprojrow ? "proj" : "", rowname,
2205  uselhs ? "lhs" : "rhs", SCIPvarGetName(var), uselb ? "lb" : "ub", SCIPgetNLPs(scip));
2206  SCIP_CALL( SCIPcreateEmptyRowSepa(scip, cut, sepa, cutname, -SCIPinfinity(scip), SCIPinfinity(scip),
2207  SCIPgetDepth(scip) > 0 && local, FALSE, FALSE) ); /* TODO SCIPgetDepth() should be replaced by depth that is passed on to the SEPAEXEC calls (?) */
2208 
2209  SCIP_CALL( SCIPcacheRowExtensions(scip, *cut) );
2210 
2211  /* iterate over all variables in the row and add the corresponding terms coef*colvar*(bound factor) to the cuts */
2212  for( i = 0; i < (useprojrow ? projrow->nnonz : SCIProwGetNNonz(row)); ++i )
2213  {
2214  SCIP_VAR* colvar;
2215 
2216  colvar = useprojrow ? projrow->vars[i] : SCIPcolGetVar(SCIProwGetCols(row)[i]);
2217  SCIP_CALL( addRltTerm(scip, sepadata, sol, bestunderest, bestoverest, *cut, var, colvar,
2218  useprojrow ? projrow->coefs[i] : SCIProwGetVals(row)[i], uselb, uselhs, local, computeEqCut,
2219  &coefvar, &cstterm, success) );
2220  }
2221 
2222  if( REALABS(cstterm) > MAXVARBOUND )
2223  {
2224  *success = FALSE;
2225  return SCIP_OKAY;
2226  }
2227 
2228  /* multiply (x-lb) or (ub -x) with the lhs and rhs of the row */
2229  coefvar += signfactor * (rowcst - consside);
2230  finalside = boundfactor * (consside - rowcst) - cstterm;
2231 
2232  assert(!SCIPisInfinity(scip, REALABS(coefvar)));
2233  assert(!SCIPisInfinity(scip, REALABS(finalside)));
2234 
2235  /* set the coefficient of var and update the side */
2236  SCIP_CALL( SCIPaddVarToRow(scip, *cut, var, coefvar) );
2237  SCIP_CALL( SCIPflushRowExtensions(scip, *cut) );
2238  if( uselhs || computeEqCut )
2239  {
2240  SCIP_CALL( SCIPchgRowLhs(scip, *cut, finalside) );
2241  }
2242  if( !uselhs || computeEqCut )
2243  {
2244  SCIP_CALL( SCIPchgRowRhs(scip, *cut, finalside) );
2245  }
2246 
2247  SCIPdebugMsg(scip, "%scut was generated successfully:\n", useprojrow ? "projected " : "");
2248 #ifdef SCIP_DEBUG
2249  SCIP_CALL( SCIPprintRow(scip, *cut, NULL) );
2250 #endif
2251 
2252  return SCIP_OKAY;
2253 }
2254 
2255 /** store a row projected by fixing all variables that are at bound at sol; the result is a simplified row */
2256 static
2258  SCIP* scip, /**< SCIP data structure */
2259  RLT_SIMPLEROW* simplerow, /**< pointer to the simplified row */
2260  SCIP_ROW* row, /**< row to be projected */
2261  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
2262  SCIP_Bool local /**< whether local bounds should be checked */
2263  )
2264 {
2265  int i;
2266  SCIP_VAR* var;
2267  SCIP_Real val;
2268  SCIP_Real vlb;
2269  SCIP_Real vub;
2270 
2271  assert(simplerow != NULL);
2272 
2273  SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(simplerow->name), SCIProwGetName(row),
2274  strlen(SCIProwGetName(row))+1) ); /*lint !e666*/
2275  simplerow->nnonz = 0;
2276  simplerow->size = 0;
2277  simplerow->vars = NULL;
2278  simplerow->coefs = NULL;
2279  simplerow->lhs = SCIProwGetLhs(row);
2280  simplerow->rhs = SCIProwGetRhs(row);
2281  simplerow->cst = SCIProwGetConstant(row);
2282 
2283  for( i = 0; i < SCIProwGetNNonz(row); ++i )
2284  {
2285  var = SCIPcolGetVar(SCIProwGetCols(row)[i]);
2286  val = SCIPgetSolVal(scip, sol, var);
2287  vlb = local ? SCIPvarGetLbLocal(var) : SCIPvarGetLbGlobal(var);
2288  vub = local ? SCIPvarGetUbLocal(var) : SCIPvarGetUbGlobal(var);
2289  if( SCIPisFeasEQ(scip, vlb, val) || SCIPisFeasEQ(scip, vub, val) )
2290  {
2291  /* if we are projecting and the var is at bound, add var as a constant to simplerow */
2292  if( !SCIPisInfinity(scip, -simplerow->lhs) )
2293  simplerow->lhs -= SCIProwGetVals(row)[i]*val;
2294  if( !SCIPisInfinity(scip, simplerow->rhs) )
2295  simplerow->rhs -= SCIProwGetVals(row)[i]*val;
2296  }
2297  else
2298  {
2299  if( simplerow->nnonz + 1 > simplerow->size )
2300  {
2301  int newsize;
2302 
2303  newsize = SCIPcalcMemGrowSize(scip, simplerow->nnonz + 1);
2304  SCIP_CALL( SCIPreallocBufferArray(scip, &simplerow->coefs, newsize) );
2305  SCIP_CALL( SCIPreallocBufferArray(scip, &simplerow->vars, newsize) );
2306  simplerow->size = newsize;
2307  }
2308 
2309  /* add the term to simplerow */
2310  simplerow->vars[simplerow->nnonz] = var;
2311  simplerow->coefs[simplerow->nnonz] = SCIProwGetVals(row)[i];
2312  ++(simplerow->nnonz);
2313  }
2314  }
2315 
2316  return SCIP_OKAY;
2317 }
2318 
2319 /** free the projected row */
2320 static
2321 void freeProjRow(
2322  SCIP* scip, /**< SCIP data structure */
2323  RLT_SIMPLEROW* simplerow /**< simplified row to be freed */
2324  )
2325 {
2326  assert(simplerow != NULL);
2327 
2328  if( simplerow->size > 0 )
2329  {
2330  assert(simplerow->vars != NULL);
2331  assert(simplerow->coefs != NULL);
2332 
2333  SCIPfreeBufferArray(scip, &simplerow->vars);
2334  SCIPfreeBufferArray(scip, &simplerow->coefs);
2335  }
2336  SCIPfreeBlockMemoryArray(scip, &simplerow->name, strlen(simplerow->name)+1);
2337 }
2338 
2339 /** creates the projected problem
2340  *
2341  * All variables that are at their bounds at the current solution are added
2342  * to left and/or right hand sides as constant values.
2343  */
2344 static
2346  SCIP* scip, /**< SCIP data structure */
2347  SCIP_ROW** rows, /**< problem rows */
2348  int nrows, /**< number of rows */
2349  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
2350  RLT_SIMPLEROW** projrows, /**< the projected rows to be filled */
2351  SCIP_Bool local, /**< are local cuts allowed? */
2352  SCIP_Bool* allcst /**< buffer to store whether all projected rows have only constants */
2353  )
2354 {
2355  int i;
2356 
2357  assert(scip != NULL);
2358  assert(rows != NULL);
2359  assert(projrows != NULL);
2360  assert(allcst != NULL);
2361 
2362  *allcst = TRUE;
2363  SCIP_CALL( SCIPallocBufferArray(scip, projrows, nrows) );
2364 
2365  for( i = 0; i < nrows; ++i )
2366  {
2367  /* get a simplified and projected row */
2368  SCIP_CALL( createProjRow(scip, &(*projrows)[i], rows[i], sol, local) );
2369  if( (*projrows)[i].nnonz > 0 )
2370  *allcst = FALSE;
2371  }
2372 
2373  return SCIP_OKAY;
2374 }
2375 
2376 #ifdef SCIP_DEBUG
2377 /* prints the projected LP */
2378 static
2379 void printProjRows(
2380  SCIP* scip, /**< SCIP data structure */
2381  RLT_SIMPLEROW* projrows, /**< the projected rows */
2382  int nrows, /**< number of projected rows */
2383  FILE* file /**< output file (or NULL for standard output) */
2384  )
2385 {
2386  int i;
2387  int j;
2388 
2389  assert(projrows != NULL);
2390 
2391  for( i = 0; i < nrows; ++i )
2392  {
2393  SCIPinfoMessage(scip, file, "\nproj_row[%d]: ", i);
2394  if( !SCIPisInfinity(scip, -projrows[i].lhs) )
2395  SCIPinfoMessage(scip, file, "%.15g <= ", projrows[i].lhs);
2396  for( j = 0; j < projrows[i].nnonz; ++j )
2397  {
2398  if( j == 0 )
2399  {
2400  if( projrows[i].coefs[j] < 0 )
2401  SCIPinfoMessage(scip, file, "-");
2402  }
2403  else
2404  {
2405  if( projrows[i].coefs[j] < 0 )
2406  SCIPinfoMessage(scip, file, " - ");
2407  else
2408  SCIPinfoMessage(scip, file, " + ");
2409  }
2410 
2411  if( projrows[i].coefs[j] != 1.0 )
2412  SCIPinfoMessage(scip, file, "%.15g*", REALABS(projrows[i].coefs[j]));
2413  SCIPinfoMessage(scip, file, "<%s>", SCIPvarGetName(projrows[i].vars[j]));
2414  }
2415  if( projrows[i].cst > 0 )
2416  SCIPinfoMessage(scip, file, " + %.15g", projrows[i].cst);
2417  else if( projrows[i].cst < 0 )
2418  SCIPinfoMessage(scip, file, " - %.15g", REALABS(projrows[i].cst));
2419 
2420  if( !SCIPisInfinity(scip, projrows[i].rhs) )
2421  SCIPinfoMessage(scip, file, " <= %.15g", projrows[i].rhs);
2422  }
2423  SCIPinfoMessage(scip, file, "\n");
2424 }
2425 #endif
2426 
2427 /** frees the projected rows */
2428 static
2429 void freeProjRows(
2430  SCIP* scip, /**< SCIP data structure */
2431  RLT_SIMPLEROW** projrows, /**< the projected LP */
2432  int nrows /**< number of rows in projrows */
2433  )
2434 {
2435  int i;
2436 
2437  for( i = 0; i < nrows; ++i )
2438  freeProjRow(scip, &(*projrows)[i]);
2439 
2440  SCIPfreeBufferArray(scip, projrows);
2441 }
2442 
2443 /** mark a row for rlt cut selection
2444  *
2445  * depending on the sign of the coefficient and violation, set or update mark which cut is required:
2446  * - 1 - cuts for axy < aw case,
2447  * - 2 - cuts for axy > aw case,
2448  * - 3 - cuts for both cases
2449  */
2450 static
2451 void addRowMark(
2452  int ridx, /**< row index */
2453  SCIP_Real a, /**< coefficient of x in the row */
2454  SCIP_Bool violatedbelow, /**< whether the relation auxexpr <= xy is violated */
2455  SCIP_Bool violatedabove, /**< whether the relation xy <= auxexpr is violated */
2456  int* row_idcs, /**< sparse array with indices of marked rows */
2457  unsigned int* row_marks, /**< sparse array to store the marks */
2458  int* nmarked /**< number of marked rows */
2459  )
2460 {
2461  unsigned int newmark;
2462  int pos;
2463  SCIP_Bool exists;
2464 
2465  assert(a != 0.0);
2466 
2467  if( (a > 0.0 && violatedbelow) || (a < 0.0 && violatedabove) )
2468  newmark = 1; /* axy < aw case */
2469  else
2470  newmark = 2; /* axy > aw case */
2471 
2472  /* find row idx in row_idcs */
2473  exists = SCIPsortedvecFindInt(row_idcs, ridx, *nmarked, &pos);
2474 
2475  if( exists )
2476  {
2477  /* we found the row index: update the mark at pos */
2478  row_marks[pos] |= newmark;
2479  }
2480  else /* the given row index does not yet exist in row_idcs */
2481  {
2482  int i;
2483 
2484  /* insert row index at the correct position */
2485  for( i = *nmarked; i > pos; --i )
2486  {
2487  row_idcs[i] = row_idcs[i-1];
2488  row_marks[i] = row_marks[i-1];
2489  }
2490  row_idcs[pos] = ridx;
2491  row_marks[pos] = newmark;
2492  (*nmarked)++;
2493  }
2494 }
2495 
2496 /** mark all rows that should be multiplied by xj */
2497 static
2499  SCIP* scip, /**< SCIP data structure */
2500  SCIP_SEPADATA* sepadata, /**< separator data */
2501  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
2502  SCIP_SOL* sol, /**< point to be separated (can be NULL) */
2503  int j, /**< index of the multiplier variable in sepadata */
2504  SCIP_Bool local, /**< are local cuts allowed? */
2505  SCIP_HASHMAP* row_to_pos, /**< hashmap linking row indices to positions in array */
2506  int* bestunderest, /**< positions of most violated underestimators for each product term */
2507  int* bestoverest, /**< positions of most violated overestimators for each product term */
2508  unsigned int* row_marks, /**< sparse array storing the row marks */
2509  int* row_idcs, /**< sparse array storing the marked row positions */
2510  int* nmarked /**< number of marked rows */
2511  )
2512 {
2513  int i;
2514  int idx;
2515  int ncolrows;
2516  int r;
2517  int ridx;
2518  SCIP_VAR* xi;
2519  SCIP_VAR* xj;
2520  SCIP_Real vlb;
2521  SCIP_Real vub;
2522  SCIP_Real vali;
2523  SCIP_Real valj;
2524  SCIP_Real a;
2525  SCIP_COL* coli;
2526  SCIP_Real* colvals;
2527  SCIP_ROW** colrows;
2529  SCIP_Bool violatedbelow;
2530  SCIP_Bool violatedabove;
2531  SCIP_VAR** bilinadjvars;
2532  int nbilinadjvars;
2533 
2534  *nmarked = 0;
2535 
2536  xj = sepadata->varssorted[j];
2537  assert(xj != NULL);
2538 
2539  valj = SCIPgetSolVal(scip, sol, xj);
2540  vlb = local ? SCIPvarGetLbLocal(xj) : SCIPvarGetLbGlobal(xj);
2541  vub = local ? SCIPvarGetUbLocal(xj) : SCIPvarGetUbGlobal(xj);
2542 
2543  if( sepadata->useprojection && (SCIPisFeasEQ(scip, vlb, valj) || SCIPisFeasEQ(scip, vub, valj)) )
2544  {
2545  /* we don't want to multiply by variables that are at bound */
2546  SCIPdebugMsg(scip, "Rejected multiplier <%s> in [%g,%g] because it is at bound (current value %g)\n", SCIPvarGetName(xj), vlb, vub, valj);
2547  return SCIP_OKAY;
2548  }
2549 
2550  terms = SCIPgetBilinTermsNonlinear(conshdlr);
2551  bilinadjvars = getAdjacentVars(sepadata->bilinvardatamap, xj, &nbilinadjvars);
2552  assert(bilinadjvars != NULL);
2553 
2554  /* for each var which appears in a bilinear product together with xj, mark rows */
2555  for( i = 0; i < nbilinadjvars; ++i )
2556  {
2557  xi = bilinadjvars[i];
2558 
2560  continue;
2561 
2562  vali = SCIPgetSolVal(scip, sol, xi);
2563  vlb = local ? SCIPvarGetLbLocal(xi) : SCIPvarGetLbGlobal(xi);
2564  vub = local ? SCIPvarGetUbLocal(xi) : SCIPvarGetUbGlobal(xi);
2565 
2566  /* if we use projection, we aren't interested in products with variables that are at bound */
2567  if( sepadata->useprojection && (SCIPisFeasEQ(scip, vlb, vali) || SCIPisFeasEQ(scip, vub, vali)) )
2568  continue;
2569 
2570  /* get the index of the bilinear product */
2571  idx = SCIPgetBilinTermIdxNonlinear(conshdlr, xj, xi);
2572  assert(idx >= 0 && idx < SCIPgetNBilinTermsNonlinear(conshdlr));
2573 
2574  /* skip implicit products if we don't want to add RLT cuts for them */
2575  if( !sepadata->hiddenrlt && !terms[idx].existing )
2576  continue;
2577 
2578  /* use the most violated under- and overestimators for this product;
2579  * if equality cuts are computed, we might end up using a different auxiliary expression;
2580  * so this is an optimistic (i.e. taking the largest possible violation) estimation
2581  */
2582  if( bestunderest == NULL || bestunderest[idx] == -1 )
2583  { /* no violated implicit underestimation relations -> either use auxvar or set violatedbelow to FALSE */
2584  if( terms[idx].nauxexprs == 0 && terms[idx].aux.var != NULL )
2585  {
2586  assert(terms[idx].existing);
2587  violatedbelow = SCIPisFeasPositive(scip, SCIPgetSolVal(scip, sol, terms[idx].aux.var) - valj * vali);
2588  }
2589  else
2590  {
2591  assert(bestunderest != NULL);
2592  violatedbelow = FALSE;
2593  }
2594  }
2595  else
2596  {
2597  assert(bestunderest[idx] >= 0 && bestunderest[idx] < terms[idx].nauxexprs);
2598 
2599  /* if we are here, the relation with the best underestimator must be violated */
2600  assert(SCIPisFeasPositive(scip, SCIPevalBilinAuxExprNonlinear(scip, terms[idx].x, terms[idx].y,
2601  terms[idx].aux.exprs[bestunderest[idx]], sol) - valj * vali));
2602  violatedbelow = TRUE;
2603  }
2604 
2605  if( bestoverest == NULL || bestoverest[idx] == -1 )
2606  { /* no violated implicit overestimation relations -> either use auxvar or set violatedabove to FALSE */
2607  if( terms[idx].nauxexprs == 0 && terms[idx].aux.var != NULL )
2608  {
2609  assert(terms[idx].existing);
2610  violatedabove = SCIPisFeasPositive(scip, valj * vali - SCIPgetSolVal(scip, sol, terms[idx].aux.var));
2611  }
2612  else
2613  {
2614  assert(bestoverest != NULL);
2615  violatedabove = FALSE;
2616  }
2617  }
2618  else
2619  {
2620  assert(bestoverest[idx] >= 0 && bestoverest[idx] < terms[idx].nauxexprs);
2621 
2622  /* if we are here, the relation with the best overestimator must be violated */
2623  assert(SCIPisFeasPositive(scip, valj * vali - SCIPevalBilinAuxExprNonlinear(scip, terms[idx].x, terms[idx].y,
2624  terms[idx].aux.exprs[bestoverest[idx]], sol)));
2625  violatedabove = TRUE;
2626  }
2627 
2628  /* only violated products contribute to row marks */
2629  if( !violatedbelow && !violatedabove )
2630  {
2631  SCIPdebugMsg(scip, "the product for vars <%s> and <%s> is not violated\n", SCIPvarGetName(xj), SCIPvarGetName(xi));
2632  continue;
2633  }
2634 
2635  /* get the column of xi */
2636  coli = SCIPvarGetCol(xi);
2637  colvals = SCIPcolGetVals(coli);
2638  ncolrows = SCIPcolGetNNonz(coli);
2639  colrows = SCIPcolGetRows(coli);
2640 
2641  SCIPdebugMsg(scip, "marking rows for xj = <%s>, xi = <%s>\n", SCIPvarGetName(xj), SCIPvarGetName(xi));
2642 
2643  /* mark the rows */
2644  for( r = 0; r < ncolrows; ++r )
2645  {
2646  ridx = SCIProwGetIndex(colrows[r]);
2647 
2648  if( !SCIPhashmapExists(row_to_pos, (void*)(size_t)ridx) )
2649  continue; /* if row index is not in row_to_pos, it means that storeSuitableRows decided to ignore this row */
2650 
2651  a = colvals[r];
2652  if( a == 0.0 )
2653  continue;
2654 
2655  SCIPdebugMsg(scip, "Marking row %d\n", ridx);
2656  addRowMark(ridx, a, violatedbelow, violatedabove, row_idcs, row_marks, nmarked);
2657  }
2658  }
2659 
2660  return SCIP_OKAY;
2661 }
2662 
2663 /** adds McCormick inequalities for implicit products */
2664 static
2666  SCIP* scip, /**< SCIP data structure */
2667  SCIP_SEPA* sepa, /**< separator */
2668  SCIP_SEPADATA* sepadata, /**< separator data */
2669  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
2670  int* bestunderestimators,/**< indices of auxiliary underestimators with largest violation in sol */
2671  int* bestoverestimators, /**< indices of auxiliary overestimators with largest violation in sol */
2672  SCIP_RESULT* result /**< pointer to store the result */
2673  )
2674 {
2675  int i;
2676  int j;
2678  SCIP_ROW* cut;
2679  char name[SCIP_MAXSTRLEN];
2680  SCIP_Bool underestimate;
2681  SCIP_Real xcoef;
2682  SCIP_Real ycoef;
2683  SCIP_Real auxcoef;
2684  SCIP_Real constant;
2685  SCIP_Bool success;
2686  SCIP_CONSNONLINEAR_AUXEXPR* auxexpr;
2687  SCIP_Bool cutoff;
2688  SCIP_Real refpointx;
2689  SCIP_Real refpointy;
2690  SCIP_INTERVAL bndx;
2691  SCIP_INTERVAL bndy;
2692 #ifndef NDEBUG
2693  SCIP_Real productval;
2694  SCIP_Real auxval;
2695 #endif
2696 
2697  assert(sepadata->nbilinterms == SCIPgetNBilinTermsNonlinear(sepadata->conshdlr));
2698  assert(bestunderestimators != NULL && bestoverestimators != NULL);
2699 
2700  cutoff = FALSE;
2701  terms = SCIPgetBilinTermsNonlinear(sepadata->conshdlr);
2702 
2703  for( i = 0; i < sepadata->nbilinterms; ++i )
2704  {
2705  if( terms[i].existing )
2706  continue;
2707 
2708  assert(terms[i].nauxexprs > 0);
2709 
2710  bndx.inf = SCIPvarGetLbLocal(terms[i].x);
2711  bndx.sup = SCIPvarGetUbLocal(terms[i].x);
2712  bndy.inf = SCIPvarGetLbLocal(terms[i].y);
2713  bndy.sup = SCIPvarGetUbLocal(terms[i].y);
2714  refpointx = SCIPgetSolVal(scip, sol, terms[i].x);
2715  refpointy = SCIPgetSolVal(scip, sol, terms[i].y);
2716 
2717  /* adjust the reference points */
2718  refpointx = MIN(MAX(refpointx, bndx.inf), bndx.sup); /*lint !e666*/
2719  refpointy = MIN(MAX(refpointy, bndy.inf), bndy.sup); /*lint !e666*/
2720 
2721  /* one iteration for underestimation and one for overestimation */
2722  for( j = 0; j < 2; ++j )
2723  {
2724  /* if underestimate, separate xy <= auxexpr; if !underestimate, separate xy >= auxexpr;
2725  * the cuts will be:
2726  * if underestimate: McCormick_under(xy) - auxexpr <= 0,
2727  * if !underestimate: McCormick_over(xy) - auxexpr >= 0
2728  */
2729  underestimate = j == 0;
2730  if( underestimate && bestoverestimators[i] != -1 )
2731  auxexpr = terms[i].aux.exprs[bestoverestimators[i]];
2732  else if( !underestimate && bestunderestimators[i] != -1 )
2733  auxexpr = terms[i].aux.exprs[bestunderestimators[i]];
2734  else
2735  continue;
2736  assert(!underestimate || auxexpr->overestimate);
2737  assert(underestimate || auxexpr->underestimate);
2738 
2739 #ifndef NDEBUG
2740  /* make sure that the term is violated */
2741  productval = SCIPgetSolVal(scip, sol, terms[i].x) * SCIPgetSolVal(scip, sol, terms[i].y);
2742  auxval = SCIPevalBilinAuxExprNonlinear(scip, terms[i].x, terms[i].y, auxexpr, sol);
2743 
2744  /* if underestimate, then xy <= aux must be violated; otherwise aux <= xy must be violated */
2745  assert((underestimate && SCIPisFeasLT(scip, auxval, productval)) ||
2746  (!underestimate && SCIPisFeasLT(scip, productval, auxval)));
2747 #endif
2748 
2749  /* create an empty row */
2750  (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "mccormick_%sestimate_implicit_%s*%s_%" SCIP_LONGINT_FORMAT,
2751  underestimate ? "under" : "over", SCIPvarGetName(terms[i].x), SCIPvarGetName(terms[i].y),
2752  SCIPgetNLPs(scip));
2753 
2754  SCIP_CALL(SCIPcreateEmptyRowSepa(scip, &cut, sepa, name, -SCIPinfinity(scip), SCIPinfinity(scip), TRUE,
2755  FALSE, FALSE) );
2756 
2757  xcoef = 0.0;
2758  ycoef = 0.0;
2759  auxcoef = 0.0;
2760  constant = 0.0;
2761  success = TRUE;
2762 
2763  /* subtract auxexpr from the cut */
2764  addAuxexprCoefs(terms[i].x, terms[i].y, auxexpr, -1.0, &auxcoef, &xcoef, &ycoef, &constant);
2765 
2766  /* add McCormick terms: ask for an underestimator if relation is xy <= auxexpr, and vice versa */
2767  SCIPaddBilinMcCormick(scip, 1.0, bndx.inf, bndx.sup, refpointx, bndy.inf, bndy.sup, refpointy, !underestimate,
2768  &xcoef, &ycoef, &constant, &success);
2769 
2770  if( REALABS(constant) > MAXVARBOUND )
2771  success = FALSE;
2772 
2773  if( success )
2774  {
2775  assert(!SCIPisInfinity(scip, REALABS(xcoef)));
2776  assert(!SCIPisInfinity(scip, REALABS(ycoef)));
2777  assert(!SCIPisInfinity(scip, REALABS(constant)));
2778 
2779  SCIP_CALL( SCIPaddVarToRow(scip, cut, terms[i].x, xcoef) );
2780  SCIP_CALL( SCIPaddVarToRow(scip, cut, terms[i].y, ycoef) );
2781  SCIP_CALL( SCIPaddVarToRow(scip, cut, auxexpr->auxvar, auxcoef) );
2782 
2783  /* set side */
2784  if( underestimate )
2785  SCIP_CALL( SCIPchgRowRhs(scip, cut, -constant) );
2786  else
2787  SCIP_CALL( SCIPchgRowLhs(scip, cut, -constant) );
2788 
2789  /* if the cut is violated, add it to SCIP */
2790  if( SCIPisFeasNegative(scip, SCIPgetRowFeasibility(scip, cut)) )
2791  {
2792  SCIP_CALL( SCIPaddRow(scip, cut, FALSE, &cutoff) );
2793  *result = SCIP_SEPARATED;
2794  }
2795  else
2796  {
2797  SCIPdebugMsg(scip, "\nMcCormick cut for hidden product <%s>*<%s> was created successfully, but is not violated",
2798  SCIPvarGetName(terms[i].x), SCIPvarGetName(terms[i].y));
2799  }
2800  }
2801 
2802  /* release the cut */
2803  if( cut != NULL )
2804  {
2805  SCIP_CALL( SCIPreleaseRow(scip, &cut) );
2806  }
2807 
2808  if( cutoff )
2809  {
2810  *result = SCIP_CUTOFF;
2811  SCIPdebugMsg(scip, "exit separator because we found a cutoff -> skip\n");
2812  return SCIP_OKAY;
2813  }
2814  }
2815  }
2816 
2817  return SCIP_OKAY;
2818 }
2819 
2820 /** builds and adds the RLT cuts */
2821 static
2823  SCIP* scip, /**< SCIP data structure */
2824  SCIP_SEPA* sepa, /**< separator */
2825  SCIP_SEPADATA* sepadata, /**< separator data */
2826  SCIP_CONSHDLR* conshdlr, /**< nonlinear constraint handler */
2827  SCIP_SOL* sol, /**< the point to be separated (can be NULL) */
2828  SCIP_HASHMAP* row_to_pos, /**< hashmap linking row indices to positions in array */
2829  RLT_SIMPLEROW* projrows, /**< projected rows */
2830  SCIP_ROW** rows, /**< problem rows */
2831  int nrows, /**< number of problem rows */
2832  SCIP_Bool allowlocal, /**< are local cuts allowed? */
2833  int* bestunderestimators,/**< indices of auxiliary underestimators with largest violation in sol */
2834  int* bestoverestimators, /**< indices of auxiliary overestimators with largest violation in sol */
2835  SCIP_RESULT* result /**< buffer to store whether separation was successful */
2836  )
2837 {
2838  int j;
2839  int r;
2840  int k;
2841  int nmarked;
2842  int cutssize;
2843  int ncuts;
2844  SCIP_VAR* xj;
2845  unsigned int* row_marks;
2846  int* row_idcs;
2847  SCIP_ROW* cut;
2848  SCIP_ROW** cuts;
2849  SCIP_Bool uselb[4] = {TRUE, TRUE, FALSE, FALSE};
2850  SCIP_Bool uselhs[4] = {TRUE, FALSE, TRUE, FALSE};
2851  SCIP_Bool success;
2852  SCIP_Bool infeasible;
2853  SCIP_Bool accepted;
2854  SCIP_Bool buildeqcut;
2855  SCIP_Bool iseqrow;
2856 
2857  assert(!sepadata->useprojection || projrows != NULL);
2858  assert(!sepadata->detecthidden || (bestunderestimators != NULL && bestoverestimators != NULL));
2859 
2860  ncuts = 0;
2861  cutssize = 0;
2862  cuts = NULL;
2863  *result = SCIP_DIDNOTFIND;
2864 
2865  SCIP_CALL( SCIPallocCleanBufferArray(scip, &row_marks, nrows) );
2866  SCIP_CALL( SCIPallocBufferArray(scip, &row_idcs, nrows) );
2867 
2868  /* loop through all variables that appear in bilinear products */
2869  for( j = 0; j < sepadata->nbilinvars && (sepadata->maxusedvars < 0 || j < sepadata->maxusedvars); ++j )
2870  {
2871  xj = sepadata->varssorted[j];
2872 
2873  /* mark all rows for multiplier xj */
2874  SCIP_CALL( markRowsXj(scip, sepadata, conshdlr, sol, j, allowlocal, row_to_pos, bestunderestimators,
2875  bestoverestimators, row_marks, row_idcs, &nmarked) );
2876 
2877  assert(nmarked <= nrows);
2878 
2879  /* generate the projected cut and if it is violated, generate the actual cut */
2880  for( r = 0; r < nmarked; ++r )
2881  {
2882  int pos;
2883  int currentnunknown;
2884  SCIP_ROW* row;
2885 
2886  assert(row_marks[r] != 0);
2887  assert(SCIPhashmapExists(row_to_pos, (void*)(size_t) row_idcs[r])); /*lint !e571 */
2888 
2889  pos = SCIPhashmapGetImageInt(row_to_pos, (void*)(size_t) row_idcs[r]); /*lint !e571 */
2890  row = rows[pos];
2891  assert(SCIProwGetIndex(row) == row_idcs[r]);
2892 
2893  /* check whether this row and var fulfill the conditions */
2894  SCIP_CALL( isAcceptableRow(sepadata, row, xj, &currentnunknown, &accepted) );
2895  if( !accepted )
2896  {
2897  SCIPdebugMsg(scip, "rejected row <%s> for variable <%s> (introduces too many new products)\n", SCIProwGetName(row), SCIPvarGetName(xj));
2898  row_marks[r] = 0;
2899  continue;
2900  }
2901 
2902  SCIPdebugMsg(scip, "accepted row <%s> for variable <%s>\n", SCIProwGetName(rows[r]), SCIPvarGetName(xj));
2903 #ifdef SCIP_DEBUG
2904  SCIP_CALL( SCIPprintRow(scip, rows[r], NULL) );
2905 #endif
2906  iseqrow = SCIPisEQ(scip, SCIProwGetLhs(row), SCIProwGetRhs(row));
2907 
2908  /* if all terms are known and it is an equality row, compute equality cut, that is, multiply row with (x-lb) and/or (ub-x) (but see also @todo at top)
2909  * otherwise, multiply row w.r.t. lhs and/or rhs with (x-lb) and/or (ub-x) and estimate product terms that have no aux.var or aux.expr
2910  */
2911  buildeqcut = (currentnunknown == 0 && iseqrow);
2912 
2913  /* go over all suitable combinations of sides and bounds and compute the respective cuts */
2914  for( k = 0; k < 4; ++k )
2915  {
2916  /* if equality cuts are possible, lhs and rhs cuts are equal so skip rhs */
2917  if( buildeqcut )
2918  {
2919  if( k != 1 )
2920  continue;
2921  }
2922  /* otherwise which cuts are generated depends on the marks */
2923  else
2924  {
2925  if( row_marks[r] == 1 && uselb[k] == uselhs[k] )
2926  continue;
2927 
2928  if( row_marks[r] == 2 && uselb[k] != uselhs[k] )
2929  continue;
2930  }
2931 
2932  success = TRUE;
2933  cut = NULL;
2934 
2935  SCIPdebugMsg(scip, "row <%s>, uselb = %u, uselhs = %u\n", SCIProwGetName(row), uselb[k], uselhs[k]);
2936 
2937  if( sepadata->useprojection )
2938  {
2939  /* if no variables are left in the projected row, the RLT cut will not be violated */
2940  if( projrows[pos].nnonz == 0 )
2941  continue;
2942 
2943  /* compute the rlt cut for a projected row first */
2944  SCIP_CALL( computeRltCut(scip, sepa, sepadata, &cut, NULL, &(projrows[pos]), sol, bestunderestimators,
2945  bestoverestimators, xj, &success, uselb[k], uselhs[k], allowlocal, buildeqcut, TRUE) );
2946 
2947  /* if the projected cut is not violated, set success to FALSE */
2948  if( cut != NULL )
2949  {
2950  SCIPdebugMsg(scip, "proj cut viol = %g\n", -SCIPgetRowFeasibility(scip, cut));
2951  }
2952  if( cut != NULL && !SCIPisFeasPositive(scip, -SCIPgetRowFeasibility(scip, cut)) )
2953  {
2954  SCIPdebugMsg(scip, "projected cut is not violated, feasibility = %g\n", SCIPgetRowFeasibility(scip, cut));
2955  success = FALSE;
2956  }
2957 
2958  /* release the projected cut */
2959  if( cut != NULL )
2960  SCIP_CALL( SCIPreleaseRow(scip, &cut) );
2961  }
2962 
2963  /* if we don't use projection or if the projected cut was generated successfully and is violated,
2964  * generate the actual cut */
2965  if( success )
2966  {
2967  SCIP_CALL( computeRltCut(scip, sepa, sepadata, &cut, row, NULL, sol, bestunderestimators,
2968  bestoverestimators, xj, &success, uselb[k], uselhs[k], allowlocal, buildeqcut, FALSE) );
2969  }
2970 
2971  if( success )
2972  {
2973  success = SCIPisFeasNegative(scip, SCIPgetRowFeasibility(scip, cut)) || (sepadata->addtopool &&
2974  !SCIProwIsLocal(cut));
2975  }
2976 
2977  /* if the cut was created successfully and is violated or (if addtopool == TRUE) globally valid,
2978  * it is added to the cuts array */
2979  if( success )
2980  {
2981  if( ncuts + 1 > cutssize )
2982  {
2983  int newsize;
2984 
2985  newsize = SCIPcalcMemGrowSize(scip, ncuts + 1);
2986  SCIP_CALL( SCIPreallocBufferArray(scip, &cuts, newsize) );
2987  cutssize = newsize;
2988  }
2989  cuts[ncuts] = cut;
2990  (ncuts)++;
2991  }
2992  else
2993  {
2994  SCIPdebugMsg(scip, "the generation of the cut failed or cut not violated and not added to cutpool\n");
2995  /* release the cut */
2996  if( cut != NULL )
2997  {
2998  SCIP_CALL( SCIPreleaseRow(scip, &cut) );
2999  }
3000  }
3001  }
3002 
3003  /* clear row_marks[r] since it will be used for the next multiplier */
3004  row_marks[r] = 0;
3005  }
3006  }
3007 
3008  /* if cuts were found, we apply an additional filtering procedure, which is similar to sepastore */
3009  if( ncuts > 0 )
3010  {
3011  int nselectedcuts;
3012  int i;
3013 
3014  assert(cuts != NULL);
3015 
3016  SCIP_CALL( SCIPselectCutsHybrid(scip, cuts, NULL, NULL, sepadata->goodscore, sepadata->badscore, sepadata->goodmaxparall,
3017  sepadata->maxparall, sepadata->dircutoffdistweight, sepadata->efficacyweight, sepadata->objparalweight,
3018  0.0, ncuts, 0, sepadata->maxncuts == -1 ? ncuts : sepadata->maxncuts, &nselectedcuts) );
3019 
3020  for( i = 0; i < ncuts; ++i )
3021  {
3022  assert(cuts[i] != NULL);
3023 
3024  if( i < nselectedcuts )
3025  {
3026  /* if selected, add global cuts to the pool and local cuts to the sepastore */
3027  if( SCIProwIsLocal(cuts[i]) || !sepadata->addtopool )
3028  {
3029  SCIP_CALL( SCIPaddRow(scip, cuts[i], FALSE, &infeasible) );
3030 
3031  if( infeasible )
3032  {
3033  SCIPdebugMsg(scip, "CUTOFF! The cut <%s> revealed infeasibility\n", SCIProwGetName(cuts[i]));
3034  *result = SCIP_CUTOFF;
3035  }
3036  else
3037  {
3038  SCIPdebugMsg(scip, "SEPARATED: added cut to scip\n");
3039  *result = SCIP_SEPARATED;
3040  }
3041  }
3042  else
3043  {
3044  SCIP_CALL( SCIPaddPoolCut(scip, cuts[i]) );
3045  }
3046  }
3047 
3048  /* release current cut */
3049  SCIP_CALL( SCIPreleaseRow(scip, &cuts[i]) );
3050  }
3051  }
3052 
3053  SCIPdebugMsg(scip, "exit separator because cut calculation is finished\n");
3054 
3055  SCIPfreeBufferArrayNull(scip, &cuts);
3056  SCIPfreeBufferArray(scip, &row_idcs);
3057  SCIPfreeCleanBufferArray(scip, &row_marks);
3058 
3059  return SCIP_OKAY;
3060 }
3061 
3062 /*
3063  * Callback methods of separator
3064  */
3065 
3066 /** copy method for separator plugins (called when SCIP copies plugins) */
3067 static
3068 SCIP_DECL_SEPACOPY(sepaCopyRlt)
3069 { /*lint --e{715}*/
3070  assert(scip != NULL);
3071  assert(sepa != NULL);
3072  assert(strcmp(SCIPsepaGetName(sepa), SEPA_NAME) == 0);
3073 
3074  /* call inclusion method of separator */
3075  SCIP_CALL( SCIPincludeSepaRlt(scip) );
3076 
3077  return SCIP_OKAY;
3078 }
3079 
3080 /** destructor of separator to free user data (called when SCIP is exiting) */
3081 static
3082 SCIP_DECL_SEPAFREE(sepaFreeRlt)
3083 { /*lint --e{715}*/
3084  SCIP_SEPADATA* sepadata;
3085 
3086  assert(strcmp(SCIPsepaGetName(sepa), SEPA_NAME) == 0);
3087 
3088  sepadata = SCIPsepaGetData(sepa);
3089  assert(sepadata != NULL);
3090 
3091  /* free separator data */
3092  SCIPfreeBlockMemory(scip, &sepadata);
3093 
3094  SCIPsepaSetData(sepa, NULL);
3095 
3096  return SCIP_OKAY;
3097 }
3098 
3099 /** solving process deinitialization method of separator (called before branch and bound process data is freed) */
3100 static
3101 SCIP_DECL_SEPAEXITSOL(sepaExitsolRlt)
3102 { /*lint --e{715}*/
3103  SCIP_SEPADATA* sepadata;
3104 
3105  assert(strcmp(SCIPsepaGetName(sepa), SEPA_NAME) == 0);
3106 
3107  sepadata = SCIPsepaGetData(sepa);
3108  assert(sepadata != NULL);
3109 
3110  if( sepadata->iscreated )
3111  {
3112  SCIP_CALL( freeSepaData(scip, sepadata) );
3113  }
3114 
3115  return SCIP_OKAY;
3116 }
3117 
3118 /** LP solution separation method of separator */
3119 static
3120 SCIP_DECL_SEPAEXECLP(sepaExeclpRlt)
3121 { /*lint --e{715}*/
3122  SCIP_ROW** prob_rows;
3123  SCIP_ROW** rows;
3124  SCIP_SEPADATA* sepadata;
3125  int ncalls;
3126  int nrows;
3127  SCIP_HASHMAP* row_to_pos;
3128  RLT_SIMPLEROW* projrows;
3129 
3130  assert(strcmp(SCIPsepaGetName(sepa), SEPA_NAME) == 0);
3131 
3132  sepadata = SCIPsepaGetData(sepa);
3133  *result = SCIP_DIDNOTRUN;
3134 
3135  if( sepadata->maxncuts == 0 )
3136  {
3137  SCIPdebugMsg(scip, "exit separator because maxncuts is set to 0\n");
3138  return SCIP_OKAY;
3139  }
3140 
3141  /* don't run in a sub-SCIP or in probing */
3142  if( SCIPgetSubscipDepth(scip) > 0 && !sepadata->useinsubscip )
3143  {
3144  SCIPdebugMsg(scip, "exit separator because in sub-SCIP\n");
3145  return SCIP_OKAY;
3146  }
3147 
3148  /* don't run in probing */
3149  if( SCIPinProbing(scip) )
3150  {
3151  SCIPdebugMsg(scip, "exit separator because in probing\n");
3152  return SCIP_OKAY;
3153  }
3154 
3155  /* only call separator a given number of times at each node */
3156  ncalls = SCIPsepaGetNCallsAtNode(sepa);
3157  if( (depth == 0 && sepadata->maxroundsroot >= 0 && ncalls >= sepadata->maxroundsroot)
3158  || (depth > 0 && sepadata->maxrounds >= 0 && ncalls >= sepadata->maxrounds) )
3159  {
3160  SCIPdebugMsg(scip, "exit separator because round limit for this node is reached\n");
3161  return SCIP_OKAY;
3162  }
3163 
3164  /* if this is called for the first time, create the sepadata and start the initial separation round */
3165  if( !sepadata->iscreated )
3166  {
3167  *result = SCIP_DIDNOTFIND;
3168  SCIP_CALL( createSepaData(scip, sepadata) );
3169  }
3170  assert(sepadata->iscreated || (sepadata->nbilinvars == 0 && sepadata->nbilinterms == 0));
3171  assert(sepadata->nbilinterms == SCIPgetNBilinTermsNonlinear(sepadata->conshdlr));
3172 
3173  /* no bilinear terms available -> skip */
3174  if( sepadata->nbilinvars == 0 )
3175  {
3176  SCIPdebugMsg(scip, "exit separator because there are no known bilinear terms\n");
3177  return SCIP_OKAY;
3178  }
3179 
3180  /* only call separator, if we are not close to terminating */
3181  if( SCIPisStopped(scip) )
3182  {
3183  SCIPdebugMsg(scip, "exit separator because we are too close to terminating\n");
3184  return SCIP_OKAY;
3185  }
3186 
3187  /* only call separator, if an optimal LP solution is at hand */
3189  {
3190  SCIPdebugMsg(scip, "exit separator because there is no LP solution at hand\n");
3191  return SCIP_OKAY;
3192  }
3193 
3194  /* get the rows, depending on settings */
3195  if( sepadata->isinitialround || sepadata->onlyoriginal )
3196  {
3197  SCIP_CALL( getOriginalRows(scip, &prob_rows, &nrows) );
3198  }
3199  else
3200  {
3201  SCIP_CALL( SCIPgetLPRowsData(scip, &prob_rows, &nrows) );
3202  }
3203 
3204  /* save the suitable rows */
3205  SCIP_CALL( SCIPallocBufferArray(scip, &rows, nrows) );
3206  SCIP_CALL( SCIPhashmapCreate(&row_to_pos, SCIPblkmem(scip), nrows) );
3207 
3208  SCIP_CALL( storeSuitableRows(scip, sepa, sepadata, prob_rows, rows, &nrows, row_to_pos, allowlocal) );
3209 
3210  if( nrows == 0 ) /* no suitable rows found, free memory and exit */
3211  {
3212  SCIPhashmapFree(&row_to_pos);
3213  SCIPfreeBufferArray(scip, &rows);
3214  if( sepadata->isinitialround || sepadata->onlyoriginal )
3215  {
3216  SCIPfreeBufferArray(scip, &prob_rows);
3217  sepadata->isinitialround = FALSE;
3218  }
3219  return SCIP_OKAY;
3220  }
3221 
3222  /* create the projected problem */
3223  if( sepadata->useprojection )
3224  {
3225  SCIP_Bool allcst;
3226 
3227  SCIP_CALL( createProjRows(scip, rows, nrows, NULL, &projrows, allowlocal, &allcst) );
3228 
3229  /* if all projected rows have only constants left, quit */
3230  if( allcst )
3231  goto TERMINATE;
3232 
3233 #ifdef SCIP_DEBUG
3234  printProjRows(scip, projrows, nrows, NULL);
3235 #endif
3236  }
3237  else
3238  {
3239  projrows = NULL;
3240  }
3241 
3242  /* separate the cuts */
3243  if( sepadata->detecthidden )
3244  {
3245  int* bestunderestimators;
3246  int* bestoverestimators;
3247 
3248  /* if we detect implicit products, a term might have more than one estimator in each direction;
3249  * save the indices of the most violated estimators
3250  */
3251  SCIP_CALL( SCIPallocBufferArray(scip, &bestunderestimators, sepadata->nbilinterms) );
3252  SCIP_CALL( SCIPallocBufferArray(scip, &bestoverestimators, sepadata->nbilinterms) );
3253  getBestEstimators(scip, sepadata, NULL, bestunderestimators, bestoverestimators);
3254 
3255  /* also separate McCormick cuts for implicit products */
3256  SCIP_CALL( separateMcCormickImplicit(scip, sepa, sepadata, NULL, bestunderestimators, bestoverestimators,
3257  result) );
3258 
3259  if( *result != SCIP_CUTOFF )
3260  {
3261  SCIP_CALL( separateRltCuts(scip, sepa, sepadata, sepadata->conshdlr, NULL, row_to_pos, projrows, rows, nrows,
3262  allowlocal, bestunderestimators, bestoverestimators, result) );
3263  }
3264 
3265  SCIPfreeBufferArray(scip, &bestoverestimators);
3266  SCIPfreeBufferArray(scip, &bestunderestimators);
3267  }
3268  else
3269  {
3270  SCIP_CALL( separateRltCuts(scip, sepa, sepadata, sepadata->conshdlr, NULL, row_to_pos, projrows, rows, nrows,
3271  allowlocal, NULL, NULL, result) );
3272  }
3273 
3274  TERMINATE:
3275  /* free the projected problem */
3276  if( sepadata->useprojection )
3277  {
3278  freeProjRows(scip, &projrows, nrows);
3279  }
3280 
3281  SCIPhashmapFree(&row_to_pos);
3282  SCIPfreeBufferArray(scip, &rows);
3283 
3284  if( sepadata->isinitialround || sepadata->onlyoriginal )
3285  {
3286  SCIPfreeBufferArray(scip, &prob_rows);
3287  sepadata->isinitialround = FALSE;
3288  }
3289 
3290  return SCIP_OKAY;
3291 }
3292 
3293 /*
3294  * separator specific interface methods
3295  */
3296 
3297 /** creates the RLT separator and includes it in SCIP */
3299  SCIP* scip /**< SCIP data structure */
3300  )
3301 {
3302  SCIP_SEPADATA* sepadata;
3303  SCIP_SEPA* sepa;
3304 
3305  /* create RLT separator data */
3306  SCIP_CALL( SCIPallocClearBlockMemory(scip, &sepadata) );
3307  sepadata->conshdlr = SCIPfindConshdlr(scip, "nonlinear");
3308  assert(sepadata->conshdlr != NULL);
3309 
3310  /* include separator */
3312  SEPA_USESSUBSCIP, SEPA_DELAY, sepaExeclpRlt, NULL, sepadata) );
3313 
3314  /* set non fundamental callbacks via setter functions */
3315  SCIP_CALL( SCIPsetSepaCopy(scip, sepa, sepaCopyRlt) );
3316  SCIP_CALL( SCIPsetSepaFree(scip, sepa, sepaFreeRlt) );
3317  SCIP_CALL( SCIPsetSepaExitsol(scip, sepa, sepaExitsolRlt) );
3318 
3319  /* add RLT separator parameters */
3320  SCIP_CALL( SCIPaddIntParam(scip,
3321  "separating/" SEPA_NAME "/maxncuts",
3322  "maximal number of rlt-cuts that are added per round (-1: unlimited)",
3323  &sepadata->maxncuts, FALSE, DEFAULT_MAXNCUTS, -1, INT_MAX, NULL, NULL) );
3324 
3325  SCIP_CALL( SCIPaddIntParam(scip,
3326  "separating/" SEPA_NAME "/maxunknownterms",
3327  "maximal number of unknown bilinear terms a row is still used with (-1: unlimited)",
3328  &sepadata->maxunknownterms, FALSE, DEFAULT_MAXUNKNOWNTERMS, -1, INT_MAX, NULL, NULL) );
3329 
3330  SCIP_CALL( SCIPaddIntParam(scip,
3331  "separating/" SEPA_NAME "/maxusedvars",
3332  "maximal number of variables used to compute rlt cuts (-1: unlimited)",
3333  &sepadata->maxusedvars, FALSE, DEFAULT_MAXUSEDVARS, -1, INT_MAX, NULL, NULL) );
3334 
3335  SCIP_CALL( SCIPaddIntParam(scip,
3336  "separating/" SEPA_NAME "/maxrounds",
3337  "maximal number of separation rounds per node (-1: unlimited)",
3338  &sepadata->maxrounds, FALSE, DEFAULT_MAXROUNDS, -1, INT_MAX, NULL, NULL) );
3339 
3340  SCIP_CALL( SCIPaddIntParam(scip,
3341  "separating/" SEPA_NAME "/maxroundsroot",
3342  "maximal number of separation rounds in the root node (-1: unlimited)",
3343  &sepadata->maxroundsroot, FALSE, DEFAULT_MAXROUNDSROOT, -1, INT_MAX, NULL, NULL) );
3344 
3346  "separating/" SEPA_NAME "/onlyeqrows",
3347  "if set to true, only equality rows are used for rlt cuts",
3348  &sepadata->onlyeqrows, FALSE, DEFAULT_ONLYEQROWS, NULL, NULL) );
3349 
3351  "separating/" SEPA_NAME "/onlycontrows",
3352  "if set to true, only continuous rows are used for rlt cuts",
3353  &sepadata->onlycontrows, FALSE, DEFAULT_ONLYCONTROWS, NULL, NULL) );
3354 
3356  "separating/" SEPA_NAME "/onlyoriginal",
3357  "if set to true, only original rows and variables are used",
3358  &sepadata->onlyoriginal, FALSE, DEFAULT_ONLYORIGINAL, NULL, NULL) );
3359 
3361  "separating/" SEPA_NAME "/useinsubscip",
3362  "if set to true, rlt is also used in sub-scips",
3363  &sepadata->useinsubscip, FALSE, DEFAULT_USEINSUBSCIP, NULL, NULL) );
3364 
3366  "separating/" SEPA_NAME "/useprojection",
3367  "if set to true, projected rows are checked first",
3368  &sepadata->useprojection, FALSE, DEFAULT_USEPROJECTION, NULL, NULL) );
3369 
3371  "separating/" SEPA_NAME "/detecthidden",
3372  "if set to true, hidden products are detected and separated by McCormick cuts",
3373  &sepadata->detecthidden, FALSE, DEFAULT_DETECTHIDDEN, NULL, NULL) );
3374 
3376  "separating/" SEPA_NAME "/hiddenrlt",
3377  "whether RLT cuts (TRUE) or only McCormick inequalities (FALSE) should be added for hidden products",
3378  &sepadata->hiddenrlt, FALSE, DEFAULT_HIDDENRLT, NULL, NULL) );
3379 
3381  "separating/" SEPA_NAME "/addtopool",
3382  "if set to true, globally valid RLT cuts are added to the global cut pool",
3383  &sepadata->addtopool, FALSE, DEFAULT_ADDTOPOOL, NULL, NULL) );
3384 
3386  "separating/" SEPA_NAME "/goodscore",
3387  "threshold for score of cut relative to best score to be considered good, so that less strict filtering is applied",
3388  &sepadata->goodscore, TRUE, DEFAULT_GOODSCORE, 0.0, 1.0, NULL, NULL) );
3389 
3391  "separating/" SEPA_NAME "/badscore",
3392  "threshold for score of cut relative to best score to be discarded",
3393  &sepadata->badscore, TRUE, DEFAULT_BADSCORE, 0.0, 1.0, NULL, NULL) );
3394 
3396  "separating/" SEPA_NAME "/objparalweight",
3397  "weight of objective parallelism in cut score calculation",
3398  &sepadata->objparalweight, TRUE, DEFAULT_OBJPARALWEIGHT, 0.0, 1.0, NULL, NULL) );
3399 
3401  "separating/" SEPA_NAME "/efficacyweight",
3402  "weight of efficacy in cut score calculation",
3403  &sepadata->efficacyweight, TRUE, DEFAULT_EFFICACYWEIGHT, 0.0, 1.0, NULL, NULL) );
3404 
3406  "separating/" SEPA_NAME "/dircutoffdistweight",
3407  "weight of directed cutoff distance in cut score calculation",
3408  &sepadata->dircutoffdistweight, TRUE, DEFAULT_DIRCUTOFFDISTWEIGHT, 0.0, 1.0, NULL, NULL) );
3409 
3411  "separating/" SEPA_NAME "/goodmaxparall",
3412  "maximum parallelism for good cuts",
3413  &sepadata->goodmaxparall, TRUE, DEFAULT_GOODMAXPARALL, 0.0, 1.0, NULL, NULL) );
3414 
3416  "separating/" SEPA_NAME "/maxparall",
3417  "maximum parallelism for non-good cuts",
3418  &sepadata->maxparall, TRUE, DEFAULT_MAXPARALL, 0.0, 1.0, NULL, NULL) );
3419 
3420  return SCIP_OKAY;
3421 }
enum SCIP_Result SCIP_RESULT
Definition: type_result.h:61
#define SCIPfreeBlockMemoryArray(scip, ptr, num)
Definition: scip_mem.h:110
enum SCIP_BoundType SCIP_BOUNDTYPE
Definition: type_lp.h:59
#define SCIPreallocBlockMemoryArray(scip, ptr, oldnum, newnum)
Definition: scip_mem.h:99
void * SCIPhashmapEntryGetImage(SCIP_HASHMAPENTRY *entry)
Definition: misc.c:3519
#define DEFAULT_GOODMAXPARALL
Definition: sepa_rlt.c:82
SCIP_Real * SCIPvarGetVlbCoefs(SCIP_VAR *var)
Definition: var.c:18133
#define DEFAULT_MAXUNKNOWNTERMS
Definition: sepa_rlt.c:61
SCIP_Bool SCIPvarsHaveCommonClique(SCIP_VAR *var1, SCIP_Bool value1, SCIP_VAR *var2, SCIP_Bool value2, SCIP_Bool regardimplics)
Definition: var.c:11483
#define SCIPallocBlockMemoryArray(scip, ptr, num)
Definition: scip_mem.h:93
SCIP_RETCODE SCIPcacheRowExtensions(SCIP *scip, SCIP_ROW *row)
Definition: scip_lp.c:1635
static SCIP_RETCODE extractProducts(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_VAR **vars_xwy, SCIP_Real *coefs1, SCIP_Real *coefs2, SCIP_Real d1, SCIP_Real d2, SCIP_SIDETYPE sidetype1, SCIP_SIDETYPE sidetype2, SCIP_HASHMAP *varmap, SCIP_Bool f)
Definition: sepa_rlt.c:666
SCIP_Bool SCIPisFeasEQ(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
static SCIP_DECL_SEPAEXITSOL(sepaExitsolRlt)
Definition: sepa_rlt.c:3103
void * SCIPhashtableGetEntry(SCIP_HASHTABLE *hashtable, int entryidx)
Definition: misc.c:2734
SCIP_Bool SCIPisFeasLT(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_SEPA * SCIProwGetOriginSepa(SCIP_ROW *row)
Definition: lp.c:17468
SCIP_RETCODE SCIPhashmapSetImageInt(SCIP_HASHMAP *hashmap, void *origin, int image)
Definition: misc.c:3306
SCIP_Bool SCIPisRelEQ(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_RETCODE SCIPhashtableInsert(SCIP_HASHTABLE *hashtable, void *element)
Definition: misc.c:2496
#define DEFAULT_HIDDENRLT
Definition: sepa_rlt.c:72
SCIP_CONSHDLR * SCIPfindConshdlr(SCIP *scip, const char *name)
Definition: scip_cons.c:886
static SCIP_RETCODE addRltTerm(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_SOL *sol, int *bestunderest, int *bestoverest, SCIP_ROW *cut, SCIP_VAR *var, SCIP_VAR *colvar, SCIP_Real coef, SCIP_Bool uselb, SCIP_Bool uselhs, SCIP_Bool local, SCIP_Bool computeEqCut, SCIP_Real *coefvar, SCIP_Real *cst, SCIP_Bool *success)
Definition: sepa_rlt.c:1875
SCIP_RETCODE SCIPflushRowExtensions(SCIP *scip, SCIP_ROW *row)
Definition: scip_lp.c:1658
int SCIPvarGetNVlbs(SCIP_VAR *var)
Definition: var.c:18111
SCIP_Real SCIPvarGetLbGlobal(SCIP_VAR *var)
Definition: var.c:17919
#define SCIP_MAXSTRLEN
Definition: def.h:302
#define DEFAULT_USEINSUBSCIP
Definition: sepa_rlt.c:69
#define DEFAULT_DIRCUTOFFDISTWEIGHT
Definition: sepa_rlt.c:81
SCIP_Real * SCIPcolGetVals(SCIP_COL *col)
Definition: lp.c:17153
static SCIP_VAR ** getAdjacentVars(SCIP_HASHMAP *adjvarmap, SCIP_VAR *var, int *nadjacentvars)
Definition: sepa_rlt.c:317
int SCIPcalcMemGrowSize(SCIP *scip, int num)
Definition: scip_mem.c:139
SCIP_RETCODE SCIPaddVarToRow(SCIP *scip, SCIP_ROW *row, SCIP_VAR *var, SCIP_Real val)
Definition: scip_lp.c:1695
int SCIProwGetNNonz(SCIP_ROW *row)
Definition: lp.c:17205
hybrid cut selector
static void freeProjRow(SCIP *scip, RLT_SIMPLEROW *simplerow)
Definition: sepa_rlt.c:2323
SCIP_Real SCIPvarGetLbLocal(SCIP_VAR *var)
Definition: var.c:17975
SCIP_CLIQUE ** SCIPvarGetCliques(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18282
static void freeProjRows(SCIP *scip, RLT_SIMPLEROW **projrows, int nrows)
Definition: sepa_rlt.c:2431
const char * SCIProwGetName(SCIP_ROW *row)
Definition: lp.c:17343
SCIP_ROW * SCIPconsGetRow(SCIP *scip, SCIP_CONS *cons)
Definition: misc_linear.c:412
SCIP_RETCODE SCIPreleaseVar(SCIP *scip, SCIP_VAR **var)
Definition: scip_var.c:1254
SCIP_Bool SCIPisFeasNegative(SCIP *scip, SCIP_Real val)
#define DEFAULT_MAXUSEDVARS
Definition: sepa_rlt.c:62
SCIP_Bool SCIPcliqueHasVar(SCIP_CLIQUE *clique, SCIP_VAR *var, SCIP_Bool value)
Definition: implics.c:1141
SCIP_VAR ** vars
Definition: sepa_rlt.c:162
SCIP_Real SCIProwGetLhs(SCIP_ROW *row)
Definition: lp.c:17284
#define FALSE
Definition: def.h:96
SCIP_RETCODE SCIPhashmapCreate(SCIP_HASHMAP **hashmap, BMS_BLKMEM *blkmem, int mapsize)
Definition: misc.c:3023
#define DEFAULT_BADSCORE
Definition: sepa_rlt.c:78
SCIP_Bool SCIPcolIsIntegral(SCIP_COL *col)
Definition: lp.c:17064
int SCIPgetSubscipDepth(SCIP *scip)
Definition: scip_copy.c:2600
#define DEFAULT_EFFICACYWEIGHT
Definition: sepa_rlt.c:80
int SCIPgetNBilinTermsNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_Real SCIPinfinity(SCIP *scip)
int SCIPsnprintf(char *t, int len, const char *s,...)
Definition: misc.c:10764
#define TRUE
Definition: def.h:95
const char * SCIPsepaGetName(SCIP_SEPA *sepa)
Definition: sepa.c:743
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:63
#define SCIPstatisticMessage
Definition: pub_message.h:123
static SCIP_RETCODE addAdjacentVars(SCIP *scip, SCIP_HASHMAP *adjvarmap, SCIP_VAR **vars)
Definition: sepa_rlt.c:243
int SCIPvarGetNVubs(SCIP_VAR *var)
Definition: var.c:18153
SCIP_RETCODE SCIPhashmapInsertInt(SCIP_HASHMAP *hashmap, void *origin, int image)
Definition: misc.c:3141
#define SEPA_USESSUBSCIP
Definition: sepa_rlt.c:58
int SCIPgetBilinTermIdxNonlinear(SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y)
#define DEFAULT_OBJPARALWEIGHT
Definition: sepa_rlt.c:79
SCIP_VAR ** vars
static SCIP_DECL_HASHKEYEQ(hashdataKeyEqConss)
Definition: sepa_rlt.c:180
static SCIP_RETCODE detectProductsImplbnd(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_Real *coefs1, SCIP_VAR **vars_xwy, SCIP_Real side1, SCIP_SIDETYPE sidetype1, int binvarpos, int implvarpos, SCIP_HASHMAP *varmap, SCIP_Bool f)
Definition: sepa_rlt.c:861
void SCIPswapReals(SCIP_Real *value1, SCIP_Real *value2)
Definition: misc.c:10287
#define SCIPfreeBlockMemory(scip, ptr)
Definition: scip_mem.h:108
#define SEPA_MAXBOUNDDIST
Definition: sepa_rlt.c:55
SCIP_VAR ** SCIPvarGetVlbVars(SCIP_VAR *var)
Definition: var.c:18123
SCIP_CONS ** SCIPgetConss(SCIP *scip)
Definition: scip_prob.c:3096
void * SCIPhashmapGetImage(SCIP_HASHMAP *hashmap, void *origin)
Definition: misc.c:3210
SCIP_Bool SCIPisEQ(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
#define DEFAULT_ADDTOPOOL
Definition: sepa_rlt.c:73
void SCIPselectDownIntPtr(int *intarray, void **ptrarray, int k, int len)
#define SCIPfreeBufferArray(scip, ptr)
Definition: scip_mem.h:136
SCIP_RETCODE SCIPsetSepaCopy(SCIP *scip, SCIP_SEPA *sepa, SCIP_DECL_SEPACOPY((*sepacopy)))
Definition: scip_sepa.c:151
#define SCIPdebugMsg
Definition: scip_message.h:78
SCIP_RETCODE SCIPaddIntParam(SCIP *scip, const char *name, const char *desc, int *valueptr, SCIP_Bool isadvanced, int defaultvalue, int minvalue, int maxvalue, SCIP_DECL_PARAMCHGD((*paramchgd)), SCIP_PARAMDATA *paramdata)
Definition: scip_param.c:83
int firstrow
Definition: sepa_rlt.c:97
SCIP_VAR ** x
Definition: circlepacking.c:63
int SCIPvarGetNCliques(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18271
void SCIPinfoMessage(SCIP *scip, FILE *file, const char *formatstr,...)
Definition: scip_message.c:208
SCIP_Real SCIPgetRowFeasibility(SCIP *scip, SCIP_ROW *row)
Definition: scip_lp.c:2118
bilinear nonlinear handler
SCIP_SEPADATA * SCIPsepaGetData(SCIP_SEPA *sepa)
Definition: sepa.c:633
SCIP_RETCODE SCIPhashtableCreate(SCIP_HASHTABLE **hashtable, BMS_BLKMEM *blkmem, int tablesize, SCIP_DECL_HASHGETKEY((*hashgetkey)), SCIP_DECL_HASHKEYEQ((*hashkeyeq)), SCIP_DECL_HASHKEYVAL((*hashkeyval)), void *userptr)
Definition: misc.c:2245
SCIP_Real lhs
Definition: sepa_rlt.c:164
#define DEFAULT_ONLYORIGINAL
Definition: sepa_rlt.c:68
#define SEPA_DESC
Definition: sepa_rlt.c:52
SCIP_Bool SCIPhashmapExists(SCIP_HASHMAP *hashmap, void *origin)
Definition: misc.c:3372
SCIP_VAR ** adjacentvars
Definition: sepa_rlt.c:106
#define SCIPallocCleanBufferArray(scip, ptr, num)
Definition: scip_mem.h:142
static SCIP_RETCODE computeRltCut(SCIP *scip, SCIP_SEPA *sepa, SCIP_SEPADATA *sepadata, SCIP_ROW **cut, SCIP_ROW *row, RLT_SIMPLEROW *projrow, SCIP_SOL *sol, int *bestunderest, int *bestoverest, SCIP_VAR *var, SCIP_Bool *success, SCIP_Bool uselb, SCIP_Bool uselhs, SCIP_Bool local, SCIP_Bool computeEqCut, SCIP_Bool useprojrow)
Definition: sepa_rlt.c:2114
SCIP_Real SCIPvarGetUbGlobal(SCIP_VAR *var)
Definition: var.c:17929
SCIP_VAR * w
Definition: circlepacking.c:67
#define SCIPduplicateBlockMemoryArray(scip, ptr, source, num)
Definition: scip_mem.h:105
SCIP_Real inf
Definition: intervalarith.h:55
#define SCIPhashFour(a, b, c, d)
Definition: pub_misc.h:524
int SCIPhashmapGetNEntries(SCIP_HASHMAP *hashmap)
Definition: misc.c:3490
SCIP_HASHMAPENTRY * SCIPhashmapGetEntry(SCIP_HASHMAP *hashmap, int entryidx)
Definition: misc.c:3498
#define SEPA_NAME
Definition: sepa_rlt.c:51
SCIP_ROW ** SCIPcolGetRows(SCIP_COL *col)
Definition: lp.c:17143
#define SCIPallocBuffer(scip, ptr)
Definition: scip_mem.h:122
static SCIP_RETCODE addProductVars(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_VAR *x, SCIP_VAR *y, SCIP_HASHMAP *varmap, int nlocks)
Definition: sepa_rlt.c:550
SCIP_Bool SCIProwIsLocal(SCIP_ROW *row)
Definition: lp.c:17393
#define SCIPfreeBufferArrayNull(scip, ptr)
Definition: scip_mem.h:137
int SCIPsepaGetNCallsAtNode(SCIP_SEPA *sepa)
Definition: sepa.c:880
BMS_BLKMEM * SCIPblkmem(SCIP *scip)
Definition: scip_mem.c:57
SCIP_Bool SCIPsortedvecFindPtr(void **ptrarray, SCIP_DECL_SORTPTRCOMP((*ptrcomp)), void *val, int len, int *pos)
SCIP_Real * SCIPvarGetVubConstants(SCIP_VAR *var)
Definition: var.c:18185
static SCIP_DECL_SEPAEXECLP(sepaExeclpRlt)
Definition: sepa_rlt.c:3122
const char * SCIPvarGetName(SCIP_VAR *var)
Definition: var.c:17260
void SCIPhashmapFree(SCIP_HASHMAP **hashmap)
Definition: misc.c:3057
void SCIPsepaSetData(SCIP_SEPA *sepa, SCIP_SEPADATA *sepadata)
Definition: sepa.c:643
static SCIP_RETCODE detectProductsUnconditional(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_ROW **rows, int *row_list, SCIP_HASHTABLE *hashtable, SCIP_Real *coefs1, SCIP_VAR **vars_xwy, SCIP_Real side1, SCIP_SIDETYPE sidetype1, int varpos1, int varpos2, SCIP_HASHMAP *varmap, SCIP_Bool f)
Definition: sepa_rlt.c:1000
#define NULL
Definition: lpi_spx1.cpp:164
power and signed power expression handlers
#define REALABS(x)
Definition: def.h:210
static SCIP_RETCODE storeSuitableRows(SCIP *scip, SCIP_SEPA *sepa, SCIP_SEPADATA *sepadata, SCIP_ROW **prob_rows, SCIP_ROW **rows, int *nrows, SCIP_HASHMAP *row_to_pos, SCIP_Bool allowlocal)
Definition: sepa_rlt.c:451
static void addRowMark(int ridx, SCIP_Real a, SCIP_Bool violatedbelow, SCIP_Bool violatedabove, int *row_idcs, unsigned int *row_marks, int *nmarked)
Definition: sepa_rlt.c:2453
#define SCIP_CALL(x)
Definition: def.h:393
#define SCIPensureBlockMemoryArray(scip, ptr, arraysizeptr, minsize)
Definition: scip_mem.h:107
SCIP_Bool SCIPisFeasGT(SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Real * SCIPvarGetVlbConstants(SCIP_VAR *var)
Definition: var.c:18143
SCIP_Real sup
Definition: intervalarith.h:56
SCIP_Bool SCIPvarIsRelaxationOnly(SCIP_VAR *var)
Definition: var.c:17547
static SCIP_DECL_HASHKEYVAL(hashdataKeyValConss)
Definition: sepa_rlt.c:212
SCIP_Real SCIProwGetRhs(SCIP_ROW *row)
Definition: lp.c:17294
SCIP_Real * SCIPvarGetVubCoefs(SCIP_VAR *var)
Definition: var.c:18175
SCIP_RETCODE SCIPaddRow(SCIP *scip, SCIP_ROW *row, SCIP_Bool forcecut, SCIP_Bool *infeasible)
Definition: scip_cut.c:250
SCIP_Real rhs
Definition: sepa_rlt.c:163
SCIP_Bool SCIPsortedvecFindInt(int *intarray, int val, int len, int *pos)
SCIP_COL ** SCIProwGetCols(SCIP_ROW *row)
Definition: lp.c:17230
union SCIP_ConsNonlinear_BilinTerm::@4 aux
SCIP_RETCODE SCIPincludeSepaBasic(SCIP *scip, SCIP_SEPA **sepa, const char *name, const char *desc, int priority, int freq, SCIP_Real maxbounddist, SCIP_Bool usessubscip, SCIP_Bool delay, SCIP_DECL_SEPAEXECLP((*sepaexeclp)), SCIP_DECL_SEPAEXECSOL((*sepaexecsol)), SCIP_SEPADATA *sepadata)
Definition: scip_sepa.c:109
static void getBestEstimators(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_SOL *sol, int *bestunderestimators, int *bestoverestimators)
Definition: sepa_rlt.c:1731
#define SCIPallocBufferArray(scip, ptr, num)
Definition: scip_mem.h:124
SCIP_Real * SCIProwGetVals(SCIP_ROW *row)
Definition: lp.c:17240
SCIP_BOUNDTYPE * SCIPvarGetImplTypes(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18229
static void addAuxexprCoefs(SCIP_VAR *var1, SCIP_VAR *var2, SCIP_CONSNONLINEAR_AUXEXPR *auxexpr, SCIP_Real coef, SCIP_Real *coefaux, SCIP_Real *coef1, SCIP_Real *coef2, SCIP_Real *cst)
Definition: sepa_rlt.c:1834
SCIP_RETCODE SCIPsetSepaExitsol(SCIP *scip, SCIP_SEPA *sepa, SCIP_DECL_SEPAEXITSOL((*sepaexitsol)))
Definition: scip_sepa.c:231
#define SCIP_Bool
Definition: def.h:93
SCIP_RETCODE SCIPchgRowRhs(SCIP *scip, SCIP_ROW *row, SCIP_Real rhs)
Definition: scip_lp.c:1607
SCIP_LPSOLSTAT SCIPgetLPSolstat(SCIP *scip)
Definition: scip_lp.c:168
SCIP_CONSNONLINEAR_BILINTERM * SCIPgetBilinTermsNonlinear(SCIP_CONSHDLR *conshdlr)
SCIP_RETCODE SCIPselectCutsHybrid(SCIP *scip, SCIP_ROW **cuts, SCIP_ROW **forcedcuts, SCIP_RANDNUMGEN *randnumgen, SCIP_Real goodscorefac, SCIP_Real badscorefac, SCIP_Real goodmaxparall, SCIP_Real maxparall, SCIP_Real dircutoffdistweight, SCIP_Real efficacyweight, SCIP_Real objparalweight, SCIP_Real intsupportweight, int ncuts, int nforcedcuts, int maxselectedcuts, int *nselectedcuts)
int SCIPgetDepth(SCIP *scip)
Definition: scip_tree.c:670
constraint handler for nonlinear constraints specified by algebraic expressions
int SCIPvarGetNImpls(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18197
#define SEPA_DELAY
Definition: sepa_rlt.c:59
#define MAX(x, y)
Definition: tclique_def.h:92
int nrows
Definition: sepa_rlt.c:96
SCIP_RETCODE SCIPaddPoolCut(SCIP *scip, SCIP_ROW *row)
Definition: scip_cut.c:361
static SCIP_DECL_SEPAFREE(sepaFreeRlt)
Definition: sepa_rlt.c:3084
int SCIPvarCompare(SCIP_VAR *var1, SCIP_VAR *var2)
Definition: var.c:11950
#define SEPA_PRIORITY
Definition: sepa_rlt.c:53
public methods for LP management
SCIP_RETCODE SCIPcreateEmptyRowSepa(SCIP *scip, SCIP_ROW **row, SCIP_SEPA *sepa, const char *name, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool removable)
Definition: scip_lp.c:1453
SCIP_RETCODE SCIPchgRowLhs(SCIP *scip, SCIP_ROW *row, SCIP_Real lhs)
Definition: scip_lp.c:1583
#define DEFAULT_MAXROUNDS
Definition: sepa_rlt.c:64
void SCIPaddSquareSecant(SCIP *scip, SCIP_Real sqrcoef, SCIP_Real lb, SCIP_Real ub, SCIP_Real *lincoef, SCIP_Real *linconstant, SCIP_Bool *success)
Definition: expr_pow.c:3303
SCIP_Real SCIPevalBilinAuxExprNonlinear(SCIP *scip, SCIP_VAR *x, SCIP_VAR *y, SCIP_CONSNONLINEAR_AUXEXPR *auxexpr, SCIP_SOL *sol)
static SCIP_RETCODE createSepaData(SCIP *scip, SCIP_SEPADATA *sepadata)
Definition: sepa_rlt.c:1596
SCIP_COL * SCIPvarGetCol(SCIP_VAR *var)
Definition: var.c:17630
void SCIPaddBilinMcCormick(SCIP *scip, SCIP_Real bilincoef, SCIP_Real lbx, SCIP_Real ubx, SCIP_Real refpointx, SCIP_Real lby, SCIP_Real uby, SCIP_Real refpointy, SCIP_Bool overestimate, SCIP_Real *lincoefx, SCIP_Real *lincoefy, SCIP_Real *linconstant, SCIP_Bool *success)
#define DEFAULT_ONLYCONTROWS
Definition: sepa_rlt.c:67
static SCIP_RETCODE fillRelationTables(SCIP *scip, SCIP_ROW **prob_rows, int nrows, SCIP_HASHTABLE *hashtable2, SCIP_HASHTABLE *hashtable3, SCIP_HASHMAP *vars_in_2rels, int *row_list)
Definition: sepa_rlt.c:1104
void * SCIPhashtableRetrieve(SCIP_HASHTABLE *hashtable, void *key)
Definition: misc.c:2557
SCIP_Bool SCIPisInfinity(SCIP *scip, SCIP_Real val)
SCIP_Real * SCIPvarGetImplBounds(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18243
int SCIPgetNBinVars(SCIP *scip)
Definition: scip_prob.c:2045
#define DEFAULT_USEPROJECTION
Definition: sepa_rlt.c:70
SCIP_Bool SCIPinProbing(SCIP *scip)
Definition: scip_probing.c:97
void SCIPhashtableFree(SCIP_HASHTABLE **hashtable)
Definition: misc.c:2295
int SCIPgetNVars(SCIP *scip)
Definition: scip_prob.c:2000
reformulation-linearization technique separator
SCIP_Real * r
Definition: circlepacking.c:59
SCIP_VAR ** SCIPvarGetImplVars(SCIP_VAR *var, SCIP_Bool varfixing)
Definition: var.c:18214
SCIP_Real SCIProwGetConstant(SCIP_ROW *row)
Definition: lp.c:17250
static SCIP_RETCODE separateRltCuts(SCIP *scip, SCIP_SEPA *sepa, SCIP_SEPADATA *sepadata, SCIP_CONSHDLR *conshdlr, SCIP_SOL *sol, SCIP_HASHMAP *row_to_pos, RLT_SIMPLEROW *projrows, SCIP_ROW **rows, int nrows, SCIP_Bool allowlocal, int *bestunderestimators, int *bestoverestimators, SCIP_RESULT *result)
Definition: sepa_rlt.c:2824
SCIP_RETCODE SCIPreleaseRow(SCIP *scip, SCIP_ROW **row)
Definition: scip_lp.c:1562
#define SCIPfreeBuffer(scip, ptr)
Definition: scip_mem.h:134
int SCIPcolGetNNonz(SCIP_COL *col)
Definition: lp.c:17118
SCIP_RETCODE SCIPsetSepaFree(SCIP *scip, SCIP_SEPA *sepa, SCIP_DECL_SEPAFREE((*sepafree)))
Definition: scip_sepa.c:167
SCIP_VAR * SCIPcolGetVar(SCIP_COL *col)
Definition: lp.c:17034
#define MAXVARBOUND
Definition: sepa_rlt.c:85
static SCIP_RETCODE getOriginalRows(SCIP *scip, SCIP_ROW ***rows, int *nrows)
Definition: sepa_rlt.c:414
static SCIP_RETCODE markRowsXj(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_CONSHDLR *conshdlr, SCIP_SOL *sol, int j, SCIP_Bool local, SCIP_HASHMAP *row_to_pos, int *bestunderest, int *bestoverest, unsigned int *row_marks, int *row_idcs, int *nmarked)
Definition: sepa_rlt.c:2500
int SCIPgetNConss(SCIP *scip)
Definition: scip_prob.c:3050
static SCIP_DECL_SEPACOPY(sepaCopyRlt)
Definition: sepa_rlt.c:3070
static SCIP_RETCODE freeSepaData(SCIP *scip, SCIP_SEPADATA *sepadata)
Definition: sepa_rlt.c:370
SCIP_Real cst
Definition: sepa_rlt.c:165
SCIP_Real * coefs
Definition: sepa_rlt.c:161
SCIP_VAR * a
Definition: circlepacking.c:66
SCIP_Bool SCIPisFeasPositive(SCIP *scip, SCIP_Real val)
SCIP_VAR ** SCIPgetVars(SCIP *scip)
Definition: scip_prob.c:1955
SCIP_VARSTATUS SCIPvarGetStatus(SCIP_VAR *var)
Definition: var.c:17379
SCIP_RETCODE SCIPcaptureVar(SCIP *scip, SCIP_VAR *var)
Definition: scip_var.c:1220
#define SCIP_Real
Definition: def.h:186
#define SCIPfreeCleanBufferArray(scip, ptr)
Definition: scip_mem.h:146
SCIP_Bool SCIPisStopped(SCIP *scip)
Definition: scip_general.c:703
SCIP_VAR ** y
Definition: circlepacking.c:64
static SCIP_RETCODE createProjRow(SCIP *scip, RLT_SIMPLEROW *simplerow, SCIP_ROW *row, SCIP_SOL *sol, SCIP_Bool local)
Definition: sepa_rlt.c:2259
static SCIP_RETCODE separateMcCormickImplicit(SCIP *scip, SCIP_SEPA *sepa, SCIP_SEPADATA *sepadata, SCIP_SOL *sol, int *bestunderestimators, int *bestoverestimators, SCIP_RESULT *result)
Definition: sepa_rlt.c:2667
#define SCIP_INVALID
Definition: def.h:206
SCIP_RETCODE SCIPprintRow(SCIP *scip, SCIP_ROW *row, FILE *file)
Definition: scip_lp.c:2206
SCIP_VAR ** SCIPvarGetVubVars(SCIP_VAR *var)
Definition: var.c:18165
int SCIPhashtableGetNEntries(SCIP_HASHTABLE *hashtable)
Definition: misc.c:2726
#define DEFAULT_DETECTHIDDEN
Definition: sepa_rlt.c:71
static void implBndToBigM(SCIP *scip, SCIP_VAR **vars_xwy, int binvarpos, int implvarpos, SCIP_BOUNDTYPE bndtype, SCIP_Bool binval, SCIP_Real implbnd, SCIP_Real *coefs, SCIP_Real *side)
Definition: sepa_rlt.c:813
static SCIP_RETCODE ensureVarsSize(SCIP *scip, SCIP_SEPADATA *sepadata, int n)
Definition: sepa_rlt.c:520
int SCIPvarGetIndex(SCIP_VAR *var)
Definition: var.c:17599
SCIP_VARTYPE SCIPvarGetType(SCIP_VAR *var)
Definition: var.c:17425
#define DEFAULT_MAXROUNDSROOT
Definition: sepa_rlt.c:65
int SCIProwGetIndex(SCIP_ROW *row)
Definition: lp.c:17353
SCIP_RETCODE SCIPinsertBilinearTermImplicitNonlinear(SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_VAR *x, SCIP_VAR *y, SCIP_VAR *auxvar, SCIP_Real coefx, SCIP_Real coefy, SCIP_Real coefaux, SCIP_Real cst, SCIP_Bool overestimate)
#define DEFAULT_MAXNCUTS
Definition: sepa_rlt.c:63
SCIP_Bool SCIPisZero(SCIP *scip, SCIP_Real val)
SCIP_Real SCIPvarGetUbLocal(SCIP_VAR *var)
Definition: var.c:17985
#define DEFAULT_GOODSCORE
Definition: sepa_rlt.c:75
void SCIPaddSquareLinearization(SCIP *scip, SCIP_Real sqrcoef, SCIP_Real refpoint, SCIP_Bool isint, SCIP_Real *lincoef, SCIP_Real *linconstant, SCIP_Bool *success)
Definition: expr_pow.c:3235
#define DEFAULT_ONLYEQROWS
Definition: sepa_rlt.c:66
SCIP_RETCODE SCIPhashmapInsert(SCIP_HASHMAP *hashmap, void *origin, void *image)
Definition: misc.c:3105
SCIP_RETCODE SCIPgetLPRowsData(SCIP *scip, SCIP_ROW ***rows, int *nrows)
Definition: scip_lp.c:570
#define SCIPallocClearBlockMemory(scip, ptr)
Definition: scip_mem.h:91
int SCIPhashmapGetImageInt(SCIP_HASHMAP *hashmap, void *origin)
Definition: misc.c:3230
#define DEFAULT_MAXPARALL
Definition: sepa_rlt.c:83
static void clearVarAdjacency(SCIP *scip, SCIP_HASHMAP *adjvarmap)
Definition: sepa_rlt.c:340
static SCIP_RETCODE createProjRows(SCIP *scip, SCIP_ROW **rows, int nrows, SCIP_SOL *sol, RLT_SIMPLEROW **projrows, SCIP_Bool local, SCIP_Bool *allcst)
Definition: sepa_rlt.c:2347
SCIP_Longint SCIPgetNLPs(SCIP *scip)
static SCIP_RETCODE detectHiddenProducts(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_HASHMAP *varmap)
Definition: sepa_rlt.c:1232
SCIP_Bool SCIPvarIsIntegral(SCIP_VAR *var)
Definition: var.c:17451
static SCIP_RETCODE isAcceptableRow(SCIP_SEPADATA *sepadata, SCIP_ROW *row, SCIP_VAR *var, int *currentnunknown, SCIP_Bool *acceptable)
Definition: sepa_rlt.c:1788
SCIP_RETCODE SCIPincludeSepaRlt(SCIP *scip)
Definition: sepa_rlt.c:3300
SCIP_Real SCIPgetSolVal(SCIP *scip, SCIP_SOL *sol, SCIP_VAR *var)
Definition: scip_sol.c:1361
void SCIPvarGetImplicVarBounds(SCIP_VAR *var, SCIP_Bool varfixing, SCIP_VAR *implvar, SCIP_Real *lb, SCIP_Real *ub)
Definition: var.c:11151
SCIP_RETCODE SCIPaddRealParam(SCIP *scip, const char *name, const char *desc, SCIP_Real *valueptr, SCIP_Bool isadvanced, SCIP_Real defaultvalue, SCIP_Real minvalue, SCIP_Real maxvalue, SCIP_DECL_PARAMCHGD((*paramchgd)), SCIP_PARAMDATA *paramdata)
Definition: scip_param.c:139
const char * name
Definition: sepa_rlt.c:160
SCIP_CONSNONLINEAR_AUXEXPR ** exprs
struct SCIP_SepaData SCIP_SEPADATA
Definition: type_sepa.h:52
#define SEPA_FREQ
Definition: sepa_rlt.c:54
SCIP_RETCODE SCIPaddBoolParam(SCIP *scip, const char *name, const char *desc, SCIP_Bool *valueptr, SCIP_Bool isadvanced, SCIP_Bool defaultvalue, SCIP_DECL_PARAMCHGD((*paramchgd)), SCIP_PARAMDATA *paramdata)
Definition: scip_param.c:57
static SCIP_RETCODE detectProductsClique(SCIP *scip, SCIP_SEPADATA *sepadata, SCIP_Real *coefs1, SCIP_VAR **vars_xwy, SCIP_Real side1, SCIP_SIDETYPE sidetype1, int varpos1, int varpos2, SCIP_HASHMAP *varmap, SCIP_Bool f)
Definition: sepa_rlt.c:927
#define SCIPreallocBufferArray(scip, ptr, num)
Definition: scip_mem.h:128
enum SCIP_SideType SCIP_SIDETYPE
Definition: type_lp.h:67