Constrained efficient global optimization with support vector machines

Anirban Basudhar, Christoph Dribusch, Sylvain Lacaze, Samy Missoum

Research output: Contribution to journalArticle

77 Scopus citations

Abstract

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based "probability of feasibility" using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the "expected improvement" of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binaryoutput are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.

Original languageEnglish (US)
Pages (from-to)201-221
Number of pages21
JournalStructural and Multidisciplinary Optimization
Volume46
Issue number2
DOIs
StatePublished - Aug 2012

Keywords

  • Binary problems
  • Classification
  • Constrained optimization
  • Discontinuities
  • Efficient global optimization
  • Support vector machines

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

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