Multi-Objective Optimization with LS-OPT

Most engineering optimization problems have more than one objective. Often these 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 (ε-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 successful 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.