GUROBI for MATLAB LP, MIP, MILP KNAPSACK Test Problems

B The Matlab Interface Routines - Test Routines

B.1 grbaircrew

Purpose
Test of an air-crew schedule generation problem.
Calling Syntax
grbaircrew
Description
Test of an air-crew schedule generation problem. Based on D.M.Ryan, Airline Industry, Encyclopedia of Operations Research and Management Science. Two subfunctions are used (defined at the end of the grbaircrew.m file): The function generateToDs create ToDs, i.e. Tours of Duty. The function sectordata generates some test data.
M-files Used
abc2gap.m, gurobi.m

B.2 grbbiptest

Purpose
Test of TOMLAB /GUROBI level 1 interface solving three larger binary integer linear optimization problems calling the GUROBI solver.
Calling Syntax
function grbbiptest(Cut, PreSolve, grbControl)
Description of Input

Cut	Value of the cut strategy control parameter, default Cut = −1.
	Cut = −1, auto select of Cut= 1 or Cut = 2.
	Cut = 0, no cuts.
	Cut = 1, conservative cut strategy.
	Cut = 2, aggressive cut strategy

PreSolve	Value of the PRESOLVE control parameter, default PreSolve = 1.
	PreSolve = 0: no presolve.
	PreSolve = 1, do presolve.

grbControl	The initial GUROBI parameter structure. Here the user may set additional control parameters. Default empty.

Description
Test of three larger binary integer linear optimization problems calling the GUROBI solver. The test problem 1 and 2 have 1956 variables, 23 equalities and four inequalities with both lower and upper bounds set.

Test problem 1, in bilp1.mat, is randomly generated. It has several minima with optimal zero value. GUROBI runs faster if avoiding the use of a cut strategy, and skipping presolve. Test problem 2, in bilp2.mat, has a unique minimum. Runs faster if avoiding the use of presolve.

Test problem 3, in bilp1211.mat, has 1656 variables, 23 equalities and four inequalities with lower and upper bounds set. Runs very slow without the use of cuts. A call grbbiptest(0,0) gives the fastest execution for the first two problems, but will be extremely slow for the third problem.

Timings are made with the Matlab functions tic and toc.
M-files Used
gurobi.m, grbPrint.m

B.3 grbiptest

Purpose
Test of the TOMLAB /GUROBI level 1 interface solving three larger integer linear optimization problems calling the GUROBI solver.
Calling Syntax
function grbiptest(Cut, PreSolve, grbControl)
Description of Input

Cut	Value of the cut strategy parameters, default Cut = −1.
	Cut = −1, auto select of Cut= 1 or Cut = 2.
	Cut = 0, no cuts. Cut = 1, conservative cut strategy.
	Cut = 2, aggressive cut strategy
	See grbbiptest, page ??.

PreSolve	Value of the PRESOLVE control parameter, default PreSolve = 1.
	PreSolve = 0, no presolve.
	PreSolve = 1, do presolve.

grbControl	The initial grbControl structure. Here the user may set additional control parameter. Default empty.

Description
Test of three larger integer linear optimization problems calling the GUROBI solver. The test problems have 61 variables and 138 linear inequalities. 32 of the 138 inequalities are just zero rows in the matrix A. The three problems are stored in ilp061.mat, ilp062.mat and ilp063.mat.

Code is included to remove the 32 zero rows, and compute better upper bounds using the positivity of the matrix elements, right hand side and the variables. But this does not influence the timing much, the GUROBI presolve will do all these problem changes.

Timings are made with the Matlab functions tic and toc.
M-files Used
gurobi, xprinti, grbPrint

B.4 grbtomtest1

Purpose
Test of using TOMLAB to call GUROBI for problems defined in the TOMLAB IF format.
Calling Syntax
grbtomtest1
Description
Test of using TOMLAB to call GUROBI for problems defined in the TOMLAB IF format. The examples show the solution of LP and MILP problems.
M-files Used
tomRun.
See Also
gurobiTL.

B.5 grbtomtest2

Purpose
Test of using TOMLAB to call GUROBI for problems defined in the TOMLAB format.
Calling Syntax
grbtomtest2
Description
Test of using TOMLAB to call GUROBI for problems defined in the TOMLAB format. The routine mipAssign is used to define the problem. A simple problem is solved with GUROBI both as an LP problem and as a MILP problem.
M-files Used
mipAssign, tomRun and PrintResult.
See Also
gurobiTL and gurobi.

B.6 grbKnaps

Purpose
GUROBI Matlab Level 1 interface Knapsack test routine
Calling Syntax
grbKnaps(P, Cut)
Description of Input

P	Problem number 1-3. Default 1.

Cut	Cut strategy. 0 = no cuts, 1 = cuts, 2 = aggressive cuts. Default 0.

Description
The GUROBI Matlab level 1 interface knapsack test routine runs three different test problems. It is possible to change cut strategy and use heuristics defined in callbacks.

Currently defined knapsack problems:

Problem	Name	Knapsacks	Variables
1	Weingartner 1	2	28
2	Hansen, Plateau 1	4	28
3	PB 4	2	29

M-files Used
gurobi.m

B.7 grbKnapsTL

Purpose
GUROBI Matlab Level 2 interface Knapsack test routine
Calling Syntax
grbKnapsTL(P, Cut)
Description of Input

P	Problem number 1-3. Default 1.
Cut	Cut strategy. 0 = no cuts, 1 = cuts, 2 = aggressive cuts. Default 0.

Description
The GUROBI Matlab level 2 interface knapsack test routine runs three different test problems. It is possible to change cut strategy.

Currently defined knapsack problems:

Problem	Name	Knapsacks	Variables
1	Weingartner 1	2	28
2	Hansen, Plateau 1	4	28
3	PB 4	2	29

M-files Used
gurobi.m

B.8 grbTest1

Purpose
Test routine 1, calls GUROBI Matlab level 1 interface to solve a GAP problem.
Calling Syntax
x = grbTest1
Description
Running a generalized assignment problem (GAP) from Wolsey [, 9.8.16, pp165]. In this test the linear sos1 constraints are defined explicitly.

Given the matrices A (constraints) and C (costs), grbTest1 is using the utility abc2gap to reformulate the problem into the standard form suitable for GUROBI.

The number of iterations are increased, no presolve is used, and an aggressive cut strategy.
M-files Used
abc2gap.m,gurobi.m

B.9 grbTest2

Purpose
Test routine 2, calls GUROBI Matlab level 1 interface to solve a GAP problem.
Calling Syntax
x = grbTest2
Description
Running a generalized assignment problem (GAP) from Wolsey [, 9.8.16, pp165]. In this test sos1 variables are used.

Given the matrices A (constraints) and C (costs), grbTest2 is using the utility abc2gap to reformulate the problem into the standard form suitable for GUROBI.

The number of iterations are increased, no presolve is used, and an aggressive cut strategy is applied.
M-files Used
abc2gap.m, gurobi.m
See Also
grbTest3.m

B.10 grbTest3

Purpose
Test routine 3, calls GUROBI Matlab level 1 interface to solve a GAP problem.
Calling Syntax
x = grbTest3
Description
Running a generalized assignment problem (GAP) from Wolsey [, 9.6, pp159]. In this test the linear sos1 constraints are defined explicitly.

Given the matrices A (constraints) and C (costs), grbTest1 is using the utility abc2gap to reformulate the problem into the standard form suitable for GUROBI.

The number of iterations are increased, no presolve is used, and no cut strategy is used.
M-files Used
abc2gap.m, gurobi.m
See Also
grbTest2

B.11 grbTestIIS

Purpose
Demonstration of the TOMLAB /GUROBI IIS feature.
Calling Syntax
x = grbTestIIS()
Description
Modify bounds to produce an infeasibility and invoke GUROBI again with IIS enabled.

B.12 grbTestSA

Purpose
Demonstration of the GUROBI SA feature.
Calling Syntax
x = grbTestSA()
Description
Run sensitivity analysis for a set of variables in the objective and in the constraints.

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