A New Hybrid Algorithm for Multi-Objective Robust Optimization With Interval Uncertainty

Uncertainty is a very critical but inevitable issue in design optimization. Compared to single-objective optimization problems, the situation becomes more difficult for multi-objective engineering optimization problems under uncertainty. Multi-objective robust optimization (MORO) approaches have been developed to find Pareto robust solutions. While the literature reports on many techniques in MORO, few papers focus on using multi-objective differential evolution (MODE) for robust optimization (RO) and performance improvement of its solutions. In this article, MODE is first modified and developed for RO problems with interval uncertainty, formulating a new MODE-RO algorithm. To improve the solutions' quality of MODE-RO, a new hybrid (MODE-sequential quadratic programming (SQP)-RO) algorithm is proposed further, where SQP is incorporated into the procedure to enhance the local search. The proposed hybrid approach takes the advantage of MODE for its capability of handling not-well behaved robust constraint functions and SQP for its fast local convergence. Two numerical and one engineering examples, with two or three objective functions, are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving MORO problems while, on the average, MODE-SQP-RO improves the quality of robust solutions obtained by MODE-RO with comparable numbers of function evaluations.