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Global Optimization in Mathematica: A Comparative Numerical Study

Frank Kampas
Organization: Physicist at Large Consulting
János D. Pintér
Organization: Pintér Consulting Service Inc.
URL: http://www.pinterconsulting.com

2005 Wolfram Technology Conference
Conference location

Champaign IL

The built-in global optimization function NMinimize was compared with two third-party tools, Global Optimization (Loehle Enterprises) and MathOptimizer Professional (Pintér Consulting Services and the author). The comparison was performed for 65 small problems (1 to 4 variables, 0 to 2 constraints) and selected larger problems (30 to 60 variables and constraints) and looked at the accuracy of the results and the time required to generate them.

Comparison Details The comparison was made between three NMinimize functions: NelderMead, DifferentialEvolution, and RandomSearch; two Global Optimization functions: GlobalSearch and GlobalPenaltyFunction; and three MathOptimizer Professional functions: MultiStart Global Search (MSLS), Global Adaptive Random Search (GARSLS), and Branch and Bound (BBLS). Each optimization function was run with its default settings. For the 65 small problems, one repetition was used for each function, except for the Global Optimization functions, for which the default number of three was used.

*Applied Mathematics > Optimization
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TechConf2005_presentation_fkampas.nb (2 MB) - Mathematica Notebook