On the Performance of the PSP Method for Mixed-Variable Multi-Objective Design Optimization

Abstract

Practical design optimization problems require use of computationally expensive “black-box” functions. The Pareto set pursuing (PSP) method, for solving multi-objective optimization problems with expensive black-box functions, was originally developed for continuous variables. In this paper, modifications are made to allow solution of problems with mixed continuous-discrete variables. A performance comparison strategy for nongradient-based multi-objective algorithms is discussed based on algorithm efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Results using several methods, along with the modified PSP, are given for a suite of benchmark problems and two engineering design ones. The modified PSP is found to be competitive when the total number of function evaluations is limited, but faces an increased computational challenge when the number of design variables increases.