Constrained efficient global optimization with support vector machines

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 binary A. Basudhar · C. Dribusch · S. Lacaze · S. Missoum (B) Aerospace and Mechanical Engineering Department, output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.

Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

“…The proposed TRICEPS-RBF algorithm is tested on 18 well-known benchmark test problems, mostly from Mallipeddi and Suganthan (2010), Michalewicz and Schoenauer (1996), and on a large-scale black-box optimization problemfrom the auto industry proposed by Don Jones (2008) than the problems typically used in surrogate-based or surrogate-assisted optimization (e.g., Basudhar et al 2012;Egea et al 2009;Viana et al 2010). The goal of this problem is to determine the values of the decision variables (e.g., shape variables) that minimize the mass of the vehicle subject to performance constraints (e.g., crashworthiness, durability).…”

Parallel surrogate-assisted global optimization with expensive functions – a survey

“…This approach looks for identifying islands of feasibility by adaptive sampling, followed by local search in each island. Another approach for constrained EGO developed by Basudhar et al (2012) uses support vector machines for approximating the boundary of the feasible domain.…”

Computational Design Optimization Under Uncertainty of Systems with Nonlinear Aeroelastic Constraints

“…The probability of feasibility P (+1|x) is calculated using a novel probabilistic SVM model, which accounts for the probability of misclassification [8].…”

“…The overall scheme is a two-level optimization (details are available in [8]). A first stage minimizes globally the objective function by maximizing the expected improvement (EI) and constraining the probability of feasibility P (+1|x):…”