Evolutionary Programming for High-Dimensional Constrained Expensive Black-Box Optimization Using Radial Basis Functions

This paper develops a surrogate-assisted evolutionary programming (EP) algorithm for constrained expensive black-box optimization that can be used for high-dimensional problems with many black-box inequality constraints. The proposed method does not use a penalty function and it builds surrogates for the objective and constraint functions. Each parent generates a large number of trial offspring in each generation. Then, the surrogate functions are used to identify the trial offspring that are predicted to be feasible with the best predicted objective function values or those with the minimum number of predicted constraint violations. The objective and constraint functions are then evaluated only on the most promising trial offspring from each parent, and the method proceeds in the same way as in a standard EP. In the numerical experiments, the type of surrogate used to model the objective and each of the constraint functions is a cubic radial basis function (RBF) augmented by a linear polynomial. The resulting RBF-assisted EP is applied to 18 benchmark problems and to an automotive problem with 124 decision variables and 68 black-box inequality constraints. The proposed method is much better than a traditional EP, a surrogate-assisted penalty-based EP, stochastic ranking evolution strategy, scatter search, and CMODE, and it is competitive with ConstrLMSRBF on the problems used.