Optimization Strategies to Explore Multiple Optimal Solutions and Its Application to Restraint System Design

Zhendan Xue, Sumeet Parashar, Guosong Li, Yan Fu (Ford)

Design Optimization techniques are often used to drive designs toward a global optimum. However, the achieved optimum solution often appears to be the only choice that the engineer/designer can select as final design. This is often caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optima or both. Problem topology can be unimodal or multi-modal with many local and/or global optima. For multimodal problems, most global algorithms tend to exploit the global optimum quickly but at the same time leaving the engineer with only one choice of design. This paper focuses on algorithm selection for single objective formulation in order to fin multiple equally good solutions.

The four algorithms considered in this paper include Multi-Objective Genetic Algorithms II  (MOGA-II), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Simulated Annealing (MOSA) and Mixed Integer Programming Sequential Quadratic Programming (MIPSQP). modeFRONTIER was used to evaluate the capability of achieving multiple optimal solutions of the selected optimization algorithms. 

The techniques are applied to several mathematical test problems as well as to the design of a vehicle restraint system. In the latter case multiple MADYMO model have been developed and coupled with modeFRONTIER. Incase of the restraint system design problem, NSGA-II has the best performance in terms of solution quality and number of multiple solutions found within the range of five star rating, which contradicts the results obtained in relation to one of the mathematical functions, where MOSA produced the best results.