Detailed Description
uct node selector which balances exploration and exploitation by considering node visits
the UCT node selection rule selects the next leaf according to a mixed score of the node's actual lower bound and the number of times it has been visited so far compared to its parent node.
The idea of UCT node selection for MIP appeared in: Ashish Sabharwal and Horst Samulowitz Guiding Combinatorial Optimization with UCT (2011)
The authors adapted a gametree exploration scheme called UCB to MIP trees. Starting from the root node as current node, the algorithm selects the current node's child \(N_i\) which maximizes the UCT score
\( \mbox{score}(N_i) := \mbox{estimate}_{N_i} + \mbox{weight} \cdot \frac{\mbox{visits}(\mbox{parent}(N_i))}{\mbox{visits}(N_i)} \)
where \(\mbox{estimate}\) is the node's lower bound normalized by the root lower bound, and \(\mbox{visits}\) denotes the number of times a leaf in the subtree rooted at this node has been explored so far.
The selected node in the sense of the SCIP node selection is the leaf reached by the above criterion.
The authors suggest that this node selection rule is particularly useful at the beginning of the solving process, but to switch to a different node selection after a number of nodes has been explored to reduce computational overhead. Our implementation uses only information available from the original SCIP tree which does not support the forward path mechanism needed for the most efficient node selection. Instead, the algorithm selects the next leaf by looping over all leaves and comparing the best leaf found so far with the next one. Two leaves l_1, l_2 are compared by following their paths back upwards until their deepest common ancestor \(a\) is reached, together with the two children of \(a\) representing the two paths to l_1, l_2. The leaf represented by the child of \(a\) with higher UCT score is a candidate for the next selected leaf.
The node selector features several parameters:
the nodelimit delimits the number of explored nodes before UCT selection is turned off the weight parameter changes the relevance of the visits quotient in the UCT score (see above score formula) useestimate determines whether the node's estimate or lower bound is taken as estimate
 Note
 It should be avoided to switch to uct node selection after the branch and bound process has begun because the central UCT score information how often a path was taken is not collected if UCT is inactive. A safe use of UCT is to switch it on before SCIP starts optimization.
Definition in file nodesel_uct.c.
#include "blockmemshell/memory.h"
#include "scip/nodesel_uct.h"
#include "scip/pub_message.h"
#include "scip/pub_nodesel.h"
#include "scip/pub_tree.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_nodesel.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_tree.h"
#include <string.h>
Go to the source code of this file.
Macros  
#define  NODESEL_NAME "uct" 
#define  NODESEL_DESC "node selector which balances exploration and exploitation " 
#define  NODESEL_STDPRIORITY 10 
#define  NODESEL_MEMSAVEPRIORITY 0 
#define  DEFAULT_WEIGHT 0.1 
#define  DEFAULT_NODELIMIT 31 
#define  DEFAULT_USEESTIMATE FALSE 
#define  INITIALSIZE 1024 
#define  MAXNODELIMIT 1000000 
Functions  
static int  nodeGetVisits (SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node) 
static void  updateVisits (SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node) 
static SCIP_RETCODE  turnoffNodeSelector (SCIP *scip, SCIP_NODESEL *nodesel) 
static SCIP_Real  nodeGetUctScore (SCIP *scip, SCIP_NODE *node, SCIP_NODESELDATA *nodeseldata) 
static int  compareNodes (SCIP *scip, SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node1, SCIP_NODE *node2) 
static void  selectBestNode (SCIP *scip, SCIP_NODE **selnode, SCIP_NODESELDATA *nodeseldata, SCIP_NODE **nodes, int nnodes) 
static SCIP_RETCODE  ensureMemorySize (SCIP *scip, SCIP_NODESELDATA *nodeseldata) 
static  SCIP_DECL_NODESELCOPY (nodeselCopyUct) 
static  SCIP_DECL_NODESELINITSOL (nodeselInitsolUct) 
static  SCIP_DECL_NODESELEXITSOL (nodeselExitsolUct) 
static  SCIP_DECL_NODESELFREE (nodeselFreeUct) 
static  SCIP_DECL_NODESELSELECT (nodeselSelectUct) 
static  SCIP_DECL_NODESELCOMP (nodeselCompUct) 
SCIP_RETCODE  SCIPincludeNodeselUct (SCIP *scip) 
Macro Definition Documentation
◆ NODESEL_NAME
#define NODESEL_NAME "uct" 
Definition at line 84 of file nodesel_uct.c.
Referenced by SCIP_DECL_NODESELSELECT(), and SCIPincludeNodeselUct().
◆ NODESEL_DESC
#define NODESEL_DESC "node selector which balances exploration and exploitation " 
Definition at line 85 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ NODESEL_STDPRIORITY
#define NODESEL_STDPRIORITY 10 
Definition at line 86 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ NODESEL_MEMSAVEPRIORITY
#define NODESEL_MEMSAVEPRIORITY 0 
Definition at line 87 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ DEFAULT_WEIGHT
#define DEFAULT_WEIGHT 0.1 
default values for user parameters weight of node visits in UCT score
Definition at line 90 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ DEFAULT_NODELIMIT
#define DEFAULT_NODELIMIT 31 
limit of node selections after which UCT node selection is turned off
Definition at line 91 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ DEFAULT_USEESTIMATE
#define DEFAULT_USEESTIMATE FALSE 
should the estimate (TRUE) or the lower bound of a node be used for UCT score?
Definition at line 92 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
◆ INITIALSIZE
#define INITIALSIZE 1024 
initial size of node visits array (increased dynamically if required)
Definition at line 93 of file nodesel_uct.c.
Referenced by ensureMemorySize().
◆ MAXNODELIMIT
#define MAXNODELIMIT 1000000 
the maximum value for user parameter nodelimit
Definition at line 94 of file nodesel_uct.c.
Referenced by SCIPincludeNodeselUct().
Function Documentation
◆ nodeGetVisits()

static 
get the number times node
has been visited so far
 Parameters

nodeseldata node selector data node the node in question
Definition at line 117 of file nodesel_uct.c.
References NULL, and SCIPnodeGetNumber().
Referenced by nodeGetUctScore().
◆ updateVisits()

static 
increases the visits counter along the path from node
to the root node
 Parameters

nodeseldata node selector data node leaf node of path along which the visits are backpropagated
Definition at line 139 of file nodesel_uct.c.
References NULL, SCIPnodeGetDepth(), SCIPnodeGetNumber(), and SCIPnodeGetParent().
Referenced by SCIP_DECL_NODESELSELECT().
◆ turnoffNodeSelector()

static 
switches to a different node selection rule by assigning the lowest priority of all node selectors to uct
 Parameters

scip SCIP data structure nodesel the node selector to be turned off
Definition at line 169 of file nodesel_uct.c.
References MAX, MIN, NULL, SCIP_CALL, SCIP_OKAY, SCIP_VERBLEVEL_NORMAL, SCIPgetNNodesels(), SCIPgetNodesels(), SCIPnodeselGetStdPriority(), SCIPsetNodeselStdPriority(), and SCIPverbMessage().
Referenced by SCIP_DECL_NODESELSELECT().
◆ nodeGetUctScore()

static 
returns UCT score of node
; the UCT score is a mixture of the node's lower bound or estimate and the number of times it has been visited so far in relation with the number of times its parent has been visited so far
 Parameters

scip SCIP data structure node the node for which UCT score is requested nodeseldata node selector data
Definition at line 202 of file nodesel_uct.c.
References MAX, MIN, nodeGetVisits(), NULL, REALABS, SCIP_Real, SCIPgetLowerboundRoot(), SCIPisEQ(), SCIPisGE(), SCIPisInfinity(), SCIPnodeGetEstimate(), SCIPnodeGetLowerbound(), and SCIPnodeGetParent().
Referenced by compareNodes().
◆ compareNodes()

static 
compares two leaf nodes by comparing the UCT scores of the two children of their deepest common ancestor
 Parameters

scip SCIP data structure nodeseldata node selector data node1 first node for comparison node2 second node for comparisons
Definition at line 254 of file nodesel_uct.c.
References nodeGetUctScore(), NULL, SCIP_Real, SCIPisEQ(), SCIPisGT(), SCIPisInfinity(), SCIPisLT(), SCIPnodeGetDepth(), and SCIPnodeGetParent().
Referenced by selectBestNode().
◆ selectBestNode()

static 
selects the best node among nodes
with respect to UCT score
 Parameters

scip SCIP data structure selnode pointer to store the selected node, needs not be empty nodeseldata node selector data nodes array of nodes to select from nnodes size of the nodes array
Definition at line 307 of file nodesel_uct.c.
References compareNodes(), nnodes, and NULL.
Referenced by SCIP_DECL_NODESELSELECT().
◆ ensureMemorySize()

static 
keeps visits array large enough to save visits for all nodes in the branch and bound tree
 Parameters

scip SCIP data structure nodeseldata node selector data
Definition at line 336 of file nodesel_uct.c.
References BMSclearMemoryArray, INITIALSIZE, MIN, NULL, SCIP_CALL, SCIP_OKAY, SCIPallocClearMemoryArray, SCIPdebugMsg, SCIPgetNNodes(), and SCIPreallocMemoryArray.
Referenced by SCIP_DECL_NODESELSELECT().
◆ SCIP_DECL_NODESELCOPY()

static 
copy method for node selector plugins (called when SCIP copies plugins)
Definition at line 376 of file nodesel_uct.c.
References NULL, SCIP_CALL, SCIP_OKAY, and SCIPincludeNodeselUct().
◆ SCIP_DECL_NODESELINITSOL()

static 
solving process initialization method of node selector (called when branch and bound process is about to begin)
Definition at line 386 of file nodesel_uct.c.
References NULL, SCIP_OKAY, SCIPnodeselGetData(), and SCIPnodeselGetStdPriority().
◆ SCIP_DECL_NODESELEXITSOL()

static 
solving process deinitialization method of node selector (called when branch and bound process data gets freed)
Definition at line 404 of file nodesel_uct.c.
References NULL, SCIP_CALL, SCIP_OKAY, SCIPfreeMemoryArray, SCIPnodeselGetData(), and SCIPsetNodeselStdPriority().
◆ SCIP_DECL_NODESELFREE()

static 
destructor of node selector to free user data (called when SCIP is exiting)
Definition at line 430 of file nodesel_uct.c.
References NULL, SCIP_OKAY, SCIPfreeBlockMemory, SCIPfreeMemoryArray, SCIPnodeselGetData(), and SCIPnodeselSetData().
◆ SCIP_DECL_NODESELSELECT()

static 
node selection method of node selector
Definition at line 451 of file nodesel_uct.c.
References ensureMemorySize(), NODESEL_NAME, NULL, SCIP_CALL, SCIP_INVALIDCALL, SCIP_LONGINT_FORMAT, SCIP_OKAY, SCIPdebugMsg, SCIPerrorMessage, SCIPgetNNodes(), SCIPgetNNodesLeft(), SCIPgetOpenNodesData(), SCIPnodeGetNumber(), SCIPnodeselGetData(), SCIPnodeselGetName(), selectBestNode(), turnoffNodeSelector(), and updateVisits().
◆ SCIP_DECL_NODESELCOMP()

static 
node comparison method of UCT node selector
Definition at line 518 of file nodesel_uct.c.
References SCIP_Real, SCIPisGT(), SCIPisLT(), and SCIPnodeGetLowerbound().