A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II

Multi-obje tive evolutionary algorithms whi h use non-dominated sorting and sharing have been mainly riti ized for their (i) O(MN 3 ) omputational omplexity (where M is the number of obje tives and N is the population size), (ii) non-elitism approa h, and (iii) the need for spe ifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-obje tive evolutionary algorithm (we alled it the Non-dominated Sorting GA-II or NSGA-II) whi h alleviates all the above three diÆ ulties. Spe i(cid:12) ally, a fast non-dominated sorting approa h with O(MN 2 ) omputational omplexity is presented. Se ond, a sele tion operator is presented whi h reates a mating pool by ombining the parent and hild populations and sele ting the best (with respe t to (cid:12)tness and spread) N solutions. Simulation results on a number of diÆ ult test problems show that the proposed NSGA-II, in most problems, is able to (cid:12)nd mu h better spread of solutions and better onvergen e near the true Pareto-optimal front ompared to PAES and SPEA|two other elitist multi-obje tive EAs whi h pay spe ial attention towards reating a diverse Pareto-optimal front. Moreover, we modify the de(cid:12)nition of dominan e in order to solve onstrained multi-obje tive problems eÆ iently. Simulation results of the onstrained NSGA-II on a number of test problems, in luding a (cid:12)ve-obje tive, seven-onstraint non-linear problem, are ompared with another onstrained multi-obje tive optimizer and mu h better performan e of NSGA-II is observed. Be ause of NSGA-II's low omputational requirements, elitist approa h, parameter-less ni hing approa h, and simple onstraint-handling strategy, NSGA-II should (cid:12)nd in reasing appli ations in the oming years.