Subset simulation for multi-objective optimization

Subset simulation is an efficient Monte Carlo technique originally developed for structural reliability problems, and further modified to solve single-objective optimization problems based on the idea that an extreme event (optimization problem) can be considered as a rare event (reliability problem). In this paper subset simulation is extended to solve multi-objective optimization problems by taking advantages of Markov Chain Monte Carlo and a simple evolutionary strategy. In the optimization process, a non-dominated sorting algorithm is introduced to judge the priority of each sample and handle the constraints. To improve the diversification of samples, a reordering strategy is proposed. A Pareto set can be generated after limited iterations by combining the two sorting algorithms together. Eight numerical multi-objective optimization benchmark problems are solved to demonstrate the efficiency and robustness of the proposed algorithm. A parametric study on the sample size in a simulation level and the proportion of seed samples is performed to investigate the performance of the proposed algorithm. Comparisons are made with three existing algorithms. Finally, the proposed algorithm is applied to the conceptual design optimization of a civil jet.