Advanced Modeling and Optimization

Abstract for Paper 1 of Volume 1, Number 2, 1999, pp. 1-8


The TOMLAB OPERA Toolbox for Linear and Discrete Optimization


Kenneth Holmström, Mattias Björkman and Erik Dotzauer
Center for Mathematical Modeling,
Department of Mathematics and Physics
Mälardalen University, P.O. Box 883, SE­721 23 Västerås,
Sweden

Abstract

The Matlab toolbox OPERA TB is a set of Matlab m­files, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). OPERA TB, like the nonlinear programming toolbox NLPLIB TB, is a part of TOMLAB; an environment in Matlab for research and teaching in optimization. Linear programs are solved either by direct call to a solver routine or to a multi­solver driver routine, or interactively, using the Graphical User Interface (GUI) or a menu system.

From OPERA TB it is possible to call solvers in the Math Works Optimization Toolbox and, using a MEX­file interface, general­purpose solvers implemented in Fortran or C. The focus is on dense problems, but sparse linear programs may be solved using the commercial solver MINOS.

Presently, OPERA TB implements about thirty algorithms and includes a set of test examples and demonstration files. This paper gives an overview of OPERA TB and presents test results for medium size LP problems. The tests show that the OPERA TB solver converges as fast as commercial Fortran solvers and is at least five times faster than the simplex LP solver in the Optimization Toolbox 2.0 and twice as fast as the primal­dual interior­point LP solver in the same toolbox. Running the commercial Fortran solvers using MEX­file interfaces gives a speed­up factor of five to thirty­five.