# 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.

# Structure of this manual

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

# 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.

scip -c "read simple.lp optimize quit"

reads and optimizes this model in no time:

SCIP version 6.0.0 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: SoPlex 4.0.0] [GitHash: b839c35]

External codes:
SoPlex 4.0.0         Linear Programming Solver developed at Zuse Institute Berlin (soplex.zib.de) [GitHash: b09aae8]
CppAD 20180000.0     Algorithmic Differentiation of C++ algorithms developed by B. Bell (www.coin-or.org/CppAD)
ZLIB 1.2.8           General purpose compression library by J. Gailly and M. Adler (zlib.net)
GMP 6.1.0            GNU Multiple Precision Arithmetic Library developed by T. Granlund (gmplib.org)

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

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
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 |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr|  dualbound   | primalbound  |  gap
t 0.0s|     1 |     0 |     0 |     - | 563k|   0 |   - |   3 |   2 |   0 |   0 |   0 |   0 |   0 | 1.630000e+02 | 3.400000e+01 | 379.41%
t 0.0s|     1 |     0 |     0 |     - | 563k|   0 |   - |   3 |   2 |   0 |   0 |   0 |   0 |   0 | 1.630000e+02 | 5.300000e+01 | 207.55%
k 0.0s|     1 |     0 |     0 |     - | 566k|   0 |   - |   3 |   2 |   3 |   2 |   0 |   0 |   0 | 1.630000e+02 | 1.225000e+02 |  33.06%
0.0s|     1 |     0 |     2 |     - | 566k|   0 |   1 |   3 |   2 |   3 |   2 |   0 |   0 |   0 | 1.252083e+02 | 1.225000e+02 |   2.21%
0.0s|     1 |     0 |     2 |     - | 566k|   0 |   1 |   3 |   2 |   3 |   2 |   0 |   0 |   0 | 1.252083e+02 | 1.225000e+02 |   2.21%
0.0s|     1 |     0 |     3 |     - | 568k|   0 |   - |   3 |   2 |   3 |   3 |   1 |   0 |   0 | 1.225000e+02 | 1.225000e+02 |   0.00%
0.0s|     1 |     0 |     3 |     - | 568k|   0 |   - |   3 |   2 |   3 |   3 |   1 |   0 |   0 | 1.225000e+02 | 1.225000e+02 |   0.00%

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
6.0.0