Abstract

Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN ) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on a number of difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA - two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems eciently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint non-linear problem, are compared with another constrained multi-objective optimizer and much better performance of NSGA-II is observed. Because of NSGA-II's low computational requirements, elitist approach, parameter-less niching approach, and simple constraint-handling strategy, NSGA-II should find increasing applications in the coming years.

Citations