# SCIP

Solving Constraint Integer Programs

Overview

# What is SCIP?

SCIP is a framework to solve constraint integer programs (CIPs) and mixed-integer nonlinear programs. In particular,

• SCIP incorporates a mixed-integer programming (MIP) solver as well as
• an LP based mixed-integer nonlinear programming (MINLP) solver, and
• is a framework for branch-and-cut-and-price.

If you are new to SCIP and don't know where to start you should have a look at the first steps walkthrough .

# Structure of this manual

This manual gives an accessible introduction to the functionality of the SCIP code in the following chapters

Setup and news

Tutorials and guides

Examples and applications

References

# Quickstart

Let's consider the following minimal example in LP format. A 4-variable problem with a single, general integer variable and three linear constraints

Maximize
obj: x1 + 2 x2 + 3 x3 + x4
Subject To
c1: - x1 + x2 + x3 + 10 x4 <= 20
c2: x1 - 3 x2 + x3 <= 30
c3: x2 - 3.5 x4 = 0
Bounds
0 <= x1 <= 40
2 <= x4 <= 3
General
x4
End

Saving this file as "simple.lp" allows to read it into SCIP and solve it by calling the scip binary with the -f flag to solve the problem from the provided file and exit.

scip -f simple.lp

reads and optimizes this model in no time:

SCIP version 8.0.3 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: Soplex 6.0.3] [GitHash: 62fab8a2e3]

External libraries:
Soplex 6.0.3         Linear Programming Solver developed at Zuse Institute Berlin (soplex.zib.de) [GitHash: f900e3d0]
CppAD 20180000.0     Algorithmic Differentiation of C++ algorithms developed by B. Bell (github.com/coin-or/CppAD)
ZLIB 1.2.11          General purpose compression library by J. Gailly and M. Adler (zlib.net)
GMP 6.1.2            GNU Multiple Precision Arithmetic Library developed by T. Granlund (gmplib.org)
AMPL/MP 4e2d45c4     AMPL .nl file reader library (github.com/ampl/mp)
bliss 0.77           Computing Graph Automorphism Groups by T. Junttila and P. Kaski (www.tcs.hut.fi/Software/bliss/)

============

original problem has 4 variables (0 bin, 1 int, 0 impl, 3 cont) and 3 constraints

presolving:
(round 1, fast)       2 del vars, 1 del conss, 0 add conss, 4 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 2, fast)       2 del vars, 1 del conss, 0 add conss, 6 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(round 3, fast)       2 del vars, 1 del conss, 0 add conss, 7 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs
(0.0s) probing cycle finished: starting next cycle
(0.0s) symmetry computation started: requiring (bin +, int +, cont +), (fixed: bin -, int -, cont -)
(0.0s) no symmetry present
presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):
2 deleted vars, 1 deleted constraints, 0 added constraints, 7 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
2 implications, 0 cliques
presolved problem has 3 variables (1 bin, 0 int, 0 impl, 2 cont) and 2 constraints
2 constraints of type <linear>
Presolving Time: 0.00

time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl.
t 0.0s|     1 |     0 |     0 |     - | trivial|   0 |   3 |   2 |   0 |   0 |  0 |   0 |   0 | 1.630000e+02 | 3.400000e+01 | 379.41%| unknown
t 0.0s|     1 |     0 |     0 |     - | trivial|   0 |   3 |   2 |   0 |   0 |  0 |   0 |   0 | 1.630000e+02 | 5.300000e+01 | 207.55%| unknown
p 0.0s|     1 |     0 |     0 |     - |   locks|   0 |   3 |   2 |   2 |   0 |  0 |   0 |   0 | 1.630000e+02 | 1.225000e+02 |  33.06%| unknown
0.0s|     1 |     0 |     2 |     - |   599k |   0 |   3 |   2 |   2 |   0 |  0 |   0 |   0 | 1.252083e+02 | 1.225000e+02 |   2.21%| unknown
0.0s|     1 |     0 |     2 |     - |   599k |   0 |   3 |   2 |   2 |   0 |  0 |   0 |   0 | 1.252083e+02 | 1.225000e+02 |   2.21%| unknown
0.0s|     1 |     0 |     3 |     - |   604k |   0 |   3 |   2 |   3 |   1 |  1 |   0 |   0 | 1.225000e+02 | 1.225000e+02 |   0.00%| unknown
0.0s|     1 |     0 |     3 |     - |   604k |   0 |   3 |   2 |   3 |   1 |  1 |   0 |   0 | 1.225000e+02 | 1.225000e+02 |   0.00%| unknown

SCIP Status        : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes      : 1
Primal Bound       : +1.22500000000000e+02 (3 solutions)
Dual Bound         : +1.22500000000000e+02
Gap                : 0.00 %

Version
8.0.3