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Adaptive Radial Basis Algorithm (ARBF) for Expensive Black-Box Mixed-Integer Constrained Global Optimization
Mälardalen University, Department of Mathematics and Physics. (Applied Optimization and Modeling)
Mälardalen University, Department of Mathematics and Physics. (Applied Optimization and Modeling)
Tomlab Software AB, Sweden.
2007 (English)In: 2nd Mathematical Programming SocietyInternational Conference on Continuous Optimization ICCOPT 07 - MOPTA 07: Modelling and Optimization: Theory and Applications 2007, 2007, p. 30-Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. com-putationally costly, global black-box nonconvex optimization problems. We describe extensions of these methods to handle linear, nonlinear and integer constraints. In particular standard RBF and new adaptive RBF (ARBF) algorithms are discussed. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems. Solvers in the TOMLAB Optimization Environment (http://tomopt.com/tomlab/) are compared; the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP as well as GENO implementing a stochastic genetic algorithm. Assuming that the objective function is costly to evaluate the performance of the ARBF algorithm proves to be superior.

Place, publisher, year, edition, pages
2007. p. 30-
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-3088OAI: oai:DiVA.org:mdh-3088DiVA, id: diva2:115752
Conference
ICCOPT 07 - MOPTA 07, Ontario, Canada, 13-16 August, 2007
Available from: 2008-03-28 Created: 2008-03-28 Last updated: 2022-10-14Bibliographically approved

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Holmström, Kenneth

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