Multi-Objective Robust Optimization Using Differential Evolution and Sequential Quadratic Programming

Abstract

Multi-Objective Robust Optimization (MORO) can find Pareto solutions to multi-objective engineering problems while keeping the variation of the solutions being within an acceptable range when parameters vary. While the literature reports on many techniques in MORO, few papers focus on the implementation of Multi-Objective Differential Evolution (MODE) for robust optimization and the performance improvement of solutions. In this paper, MODE is first modified and implemented for robust optimization, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid MODE-SQP-RO algorithm is further proposed, where Sequential Quadratic Programming (SQP) is incorporated to enhance the local search. In the hybrid algorithm, two criteria, indicating the convergence speed of MODE-RO and the switch between MODE and SQP are proposed respectively. One numerical and one engineering examples are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving Multi-Objective Robust Optimization problems; while on the average, MODE-SQP-RO significantly improves the quality of robust solutions with comparable numbers of function evaluations.