High-Dimensional Constrained Discrete Expensive Black-Box Optimization Using a Two-Phase Surrogate Approach

Abstract

This paper develops an extension of a surrogate-based algorithm for high-dimensional discrete constrained black-box optimization called CONDOR that can be used when no feasible initial point is provided. The proposed extension uses a two-phase approach where the first phase searches for a feasible point whose objective value is then improved in the second phase. Each iteration of Phase I identifies the infeasible points that are nondominated according to three criteria: number of constraint violations, maximum constraint violation, and sum of squares of constraint violations. Then, multiple trial points are generated in some neighborhood of a randomly chosen nondominated point. The function evaluation point is then chosen from the trial points according to the predicted values of the above criteria. Moreover, each iteration of Phase II generates multiple trial points in some neighborhood of the current best feasible point. Then, among the trial points that are predicted to be feasible, the function evaluation point is chosen according to the predicted objective value and distance from previous sample points. In the numerical experiments, radial basis function (RBF) surrogates are used and the proposed algorithm is applied to test cases and to a benchmark based on a car structure design problem that has 222 discrete ordinal variables and 54 black-box constraints. The proposed method outperforms a genetic algorithm and a direct search method in terms of the number of function evaluations to obtain a feasible point and in the best feasible objective value obtained within a relatively limited computational budget.