An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization

Holmström, Kenneth, 1954- (author): Mälardalens högskola,Institutionen för matematik och fysik,Applied Optimization,Department of Mathematics and Physics, Mälardalen University, Västerås, Sweden

Quttineh, Nils-Hassan, 1979- (author): Mälardalens högskola,Akademin för utbildning, kultur och kommunikation,Applied Optimization,Department of Mathematics and Physics, Mälardalen University, Västerås, Sweden,Division of Optimization

(creator_code:org_t)

2008-02-07
2008
English.
In: Optimization and Engineering. - : Springer US. - 1389-4420 .- 1573-2924. ; 9:4, s. 311-339

Related links:: https://urn.kb.se/re...; show more...; https://doi.org/10.1...; https://urn.kb.se/re...; show less...

Abstract Subject headings

Response surface methods based on kriging and radial basis function (RBF) interpolationhave been successfully applied to solve expensive, i.e. computationally costly,global black-box nonconvex optimization problems.In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) aredescribed. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvexproblems with linear and nonlinear constraints, and mixed-integernonlinear problems (MINLP). Solvers in the TOMLAB OptimizationEnvironment (http://tomopt.com/tomlab/) have been compared,specifically the three deterministic derivative-free solversrbfSolve, ARBFMIP and EGO with three derivative-based mixed-integernonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENOsolver implementing a stochastic genetic algorithm. Results showthat the deterministic derivative-free methods compare well with thederivative-based ones, but the stochastic genetic algorithm solver isseveral orders of magnitude too slow for practical use.When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.

By the author/editor: Holmström, Kenne ...; Quttineh, Nils-H ...; Edvall, Marcus

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Computational Ma ...

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