Constrained Efficient Global Optimization with Probabilistic Support Vector Machines

Abstract

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). The proposed SVM-based method has several advantages. It is more general because it is applicable to a wider variety of problems compared to current techniques. These include problems with discontinuous and binary (pass/fail) states and multiple constraints. In this paper, the objective function is approximated using Kriging while the constraint boundary is approximated using an SVM classifier. The probability of misclassification by the SVM is calculated using a probabilistic support vector machine (PSVM). The existing PSVM models have certain limitations that make them unsuitable for application in the proposed methodology. Therefore, a modified PSVM model is also proposed to overcome these limitations. Several constrained EGO formulations are implemented and compared in this paper. The results are also compared to EGO implementations with Kriging-based constraint approximations from the literature.

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