Xue, Z., Parashar, S., Li, G., and Fu, Y., "Optimization Strategies to Explore Multiple Optimal Solutions and Its Application to Restraint System Design," SAE Int. J. Passeng. Cars - Mech. Syst. 5(1):540-551, 2012, doi:10.4271/2012-01-0578.
Design optimization techniques are widely used to drive designs toward a global or a near global optimal solution. However, the achieved optimal solution often appears to be the only choice that an engineer/designer can select as the final design. This is caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optimal or both. Problem topology can be unimodal or multimodal with many local and/or global optimal solutions. For multimodal problems, most global algorithms tend to exploit the global optimal solution quickly but at the same time leaving the engineer with only one choice of design. The paper explores the application of genetic algorithms (GA), simulated annealing (SA), and mixed integer problem sequential quadratic programming (MIPSQP) to find multiple local and global solutions using single objective optimization formulation. The techniques are applied to a couple of mathematical problems as well as a restraint system design problem. Results are compared thoroughly in terms of the quality of local convergence, convergence speed, and most importantly the ability to explore multiple local and global solutions.