A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II

Abstract

Abstract—Multiobjective evolutionary algorithms (EAs)<br> that use nondominated sorting and sharing have been criticized<br> mainly for their: 1) ( 3) computational complexity<br> (where is the number of objectives and is the population<br> size); 2) nonelitism approach; and 3) the need for specifying a<br> sharing parameter. In this paper, we suggest a nondominated<br> sorting-based multiobjective EA (MOEA), called nondominated<br> sorting genetic algorithm II (NSGA-II), which alleviates all<br> the above three difficulties. Specifically, a fast nondominated<br> sorting approach with ( 2) computational complexity is<br> presented. Also, a selection operator is presented that creates a<br> mating pool by combining the parent and offspring populations<br> and selecting the best (with respect to fitness and spread)<br> solutions. Simulation results on difficult test problems show that<br> the proposed NSGA-II, in most problems, is able to find much<br> better spread of solutions and better convergence near the true<br> Pareto-optimal front compared to Pareto-archived evolution<br> strategy and strength-Pareto EA—two other elitist MOEAs that<br> pay special attention to creating a diverse Pareto-optimal front.<br> Moreover, we modify the definition of dominance in order to<br> solve constrained multiobjective problems efficiently. Simulation<br> results of the constrained NSGA-II on a number of test problems,<br> including a five-objective seven-constraint nonlinear problem, are<br> compared with another constrained multiobjective optimizer and<br> much better performance of NSGA-II is observed.