Advanced Modeling and Optimization

Abstract for Paper 3 of Volume 1, Number 2, 1999, pp. 17-37


Global Optimization Using the DIRECT Algorithm in Matlab


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

Abstract

We discuss the efficiency and implementation details of an algorithm for finding the global minimum of a multi­variate function subject to simple bounds on the variables. The algorithm DIRECT, developed by D. R. Jones, C. D. Perttunen and B. E. Stuckman, is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. We have implemented the DIRECT algorithm in Matlab and the efficiency of our implementation is analyzed by comparing it to the results of Jones's implementation on nine standard test problems for box­bounded global optimization. In fifteen out of eighteen runs the results are in favor of our implementation. We also present performance results for our implementation on the more challenging test set used in the first contest on evolutionary optimization (ICEO). An application from computational finance is also discussed.

Our DIRECT code is available in two versions. One, glbSolve, is integrated in the Matlab optimization environment TOMLAB, as part of the toolbox NLPLIB TB for nonlinear programming and parameter estimation. The other, gblSolve, is a stand­alone version. Both TOMLAB and gblSolve are free for academic use and downloadable at the home page of the Applied Optimization and Modeling group, see the URL: http://www.ima.mdh.se/tom.