A Comparative Benchmark Study of using Different Multi-Objective Optimization Algorithms for Restraint System Design

Vehicle restraint system design is a difficult optimization problem to solve because (1) the nature of the problem is highly nonlinear, non-convex, noisy, and discontinuous; (2) there are large numbers of discrete and continuous design variables; (3) a design has to meet safety performance requirements for multiple crash modes simultaneously, hence there are a large number of design constraints. Based on the above knowledge of the problem, it is understandable why design of experiment (DOE) does not produce a high-percentage of feasible solutions, and it is difficult for response surface methods (RSM) to capture the true landscape of the problem. Furthermore, in order to keep the restraint system more robust, the complexity of restraint system content needs to be minimized in addition to minimizing the relative risk score to achieve New Car Assessment Program (NCAP) 5-star rating. These call for identifying the most appropriate multi-objective optimization algorithm to solve this type of vehicle restraint system design problem. In this paper, several advanced multi-objective optimization algorithms are employed to solve a large-scale restraint system design problem. The accuracy to the “true” Pareto set and percentage of feasible solutions are employed as the performance metrics to judge how well each algorithm performs. A detailed analysis of why some algorithms perform better than others will be investigated, and the experience gained from this benchmark study will offer some guidance as to how to choose multi-objective optimization algorithms for solving future restraint system design problems.