Multi-Objective Optimization Using LS-OPT
Tushar Goel, Nielen Stander · 2007
Summary: Most engineering optimization problems have more than one objective. Often t hese objectives conflict such that no single solution can be considered optimum with respect to all objectives. Then , the optimum to this problem is a set of solutions known as Pareto optimal set. Traditionally, multi-objective optimization problems are solved by converting the problem into a single-objective optimization problem via, a weighted-sum strategy (combine multiple objectives using designer-specified weights) or introducing constraints on all-but-one objectives ( e-constraint strategy). The advantages and disadvantages of such methods are well-documented. However, the most prominent drawback of these methods is that the solution to each optimization problem results into a single optimum without any information about the trade-offs among different objectives. In last few years, there have been significant efforts in developing methods to simultaneously identify many Pareto optimal solutions. Multi-objective evolutionary algorithms (MOEAs) have been among the most suc cessful methods for identifying Pareto optimal fronts. Nevertheless, the applications of such methods for real-world problems, particularly in the area of automobile crash analysis, have been limited. We present one such effort in this area. We implement and utilize a popular MOEA, elitist non-dominated sorting genetic algorithm (NSGA-II). The implementation is validated with three benchmark analytical problems and then a simplified multi-disciplinary car crash worthiness optimization problem that aims to simultaneously minimize HIC and intrusion while constraining the torsional mode frequency was solved.