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An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization
Mälardalen University, Department of Mathematics and Physics. (Applied Optimization)
Mälardalen University, School of Education, Culture and Communication. (Applied Optimization)
Tomlab Optimization Inc..
2008 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 9, no 4, p. 311-339Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer US , 2008. Vol. 9, no 4, p. 311-339
Keywords [en]
Global optimization, radial basis functions, response surface model, surrogate model, expensive function, CPU-intensive, optimization software, splines, mixed-integer nonlinear programming, nonconvex, derivative-free, black-box, linear constraints, nonlinear constraints
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-5340DOI: 10.1007/s11081-008-9037-3ISI: 000259577400002Scopus ID: 2-s2.0-54049121839OAI: oai:DiVA.org:mdh-5340DiVA, id: diva2:160483
Available from: 2009-02-13 Created: 2009-02-13 Last updated: 2017-12-14Bibliographically approved

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CiteExportLink to record
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