Multi-objective optimization using self-organizing decomposition and its application to crashworthiness design

Abstract

Abstract There are three main classic decomposition approaches, i.e., weighted sum (WS), Tchebycheff (TCH) and penalty-boundary based intersection (PBI), which have different improvement regions (IRs) during the evolutionary search process. Hence, these three decomposition approaches have their own corresponding advantages and weaknesses on the performance of convergence or diversity due to their different features of IRs. In this paper, in order to take advantages of different decomposition methods, a novel multi-objective evolutionary algorithm using a self-organizing decomposition selection strategy (called MOEA/D-SDSS) is presented for solving multi-objective optimization problems (MOPs) and the crashworthiness design problem. In this approach, two competitive populations are respectively run based on the TCH and PBI decomposition methods. Then, based on their respective performance on both diversity and convergence, a self-organizing selection strategy is performed during the whole evolutionary process, which aims to select one suitable decomposition approach for the next generation. In other words, the two populations based on different decomposition approaches are complementary with each other, which is crucial and beneficial for improving the robustness of evolutionary algorithms on solving various kinds of MOPs. At last, one population with a better performance will be outputted as the final result. In order to evaluate the performance of our proposed MOEA/D-SDSS, thirty-six well-known benchmark problems and the crashworthiness design problem are studied in our experiments. The experimental results validate the promising performance of our proposed algorithm over six state-of-the-art decomposition-based evolutionary algorithms and six other competitive evolutionary algorithms.