Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization

The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a co...

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Bibliographic Details
Published inINFORMS journal on computing Vol. 19; no. 3; pp. 328 - 340
Main Authors Ugray, Zsolt, Lasdon, Leon, Plummer, John, Glover, Fred, Kelly, James, Marti, Rafael
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.08.2007
Institute for Operations Research and the Management Sciences
Subjects
Algorithms
Evaluation
global optimization
gradient methods
Heuristic
Integer programming
Mathematical optimization
mixed integer nonlinear programming
multistart heuristic
Nonlinear programming
Optimization
Population
scatter search
Studies
United States
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Summary:The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for any gradient-based local solver for nonlinear programming (NLP) problems. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to Floudas et al. (1999), most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.
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ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1060.0175