A two-phase surrogate approach for high-dimensional constrained discrete multi-objective optimization

Abstract

This paper presents a two-phase surrogate approach for high-dimensional constrained discrete multi-objective optimization. In Phase I, the algorithm searches for a feasible point using surrogates for the constraints and objectives. In Phase I iterations, the algorithm 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. Moreover, the function evaluation point is chosen from a large number of trial points in the neighborhood of a current nondominated point according to the predicted values of the above criteria. In Phase II, the algorithm searches for Pareto optimal solutions using surrogates for the objectives and constraints. In Phase II iterations, the function evaluation point is chosen from trial points that are predicted to be feasible and nondominated in the neighborhood of a current nondominated point using distance criteria in the objective and decision spaces. The algorithm is implemented using RBF surrogates and tested on the Mazda benchmark problem that has 222 discrete variables, 54 constraints and 2 objectives. The proposed method found feasible points much more quickly and obtained much better sets of nondominated objective vectors than an NSGA-II implementation given a budget of only 3330 simulations.