Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection

Abstract

GOMORS is a parallel response surface-assisted evolutionary algorithm approach to multi-objective optimization that is designed to obtain good non-dominated solutions to black box problems with relatively few objective function evaluations. GOMORS uses Radial Basic Functions to iteratively compute surrogate response surfaces as an approximation of the computationally expensive objective function. A multi objective search utilizing evolution, local search, multi method search and non-dominated sorting is done on the surrogate radial basis function surface because it is inexpensive to compute. A balance between exploration, exploitation and diversification is obtained through a novel procedure that simultaneously selects evaluation points within an algorithm iteration through different metrics including Approximate Hypervolume Improvement, Maximizing minimum domain distance, Maximizing minimum objective space distance, and surrogate-assisted local search, which can be computed in parallel. The results are compared to ParEGO (a kriging surrogate method solving many weighted single objective optimizations) and the widely used NSGA-II. The results indicate that GOMORS outperforms ParEGO and NSGA-II on problems tested. For example, on a groundwater PDE problem, GOMORS outperforms ParEGO with 100, 200 and 400 evaluations for a 6 dimensional problem, a 12 dimensional problem and a 24 dimensional problem. For a fixed number of evaluations, the differences in performance between GOMORS and ParEGO become larger as the number of dimensions increase. As the number of evaluations increase, the differences between GOMORS and ParEGO become smaller. Both surrogate-based methods are much better than NSGA-II for all cases considered.