A fast and elitist multiobjective genetic algorithm: NSGA-II

Abstract

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

Reliable classification of two-class cancer data using evolutionary algorithms

“…To handle three objectives, we have used a multiobjective GA (NSGA-II) (Deb et al, 2002), which we briefly described here. NSGA-II has the following features:…”

“…This procedure is continued for a maximum of user-defined T iterations. For detail information about NSGA-II, readers are referred to Deb et al (2002). Due to the emphasis of the non-dominated solutions, maintenance of diversity among population members, and an elitist approach, NSGA-II has been successful in converging quickly close to the true Pareto-optimal front with a well-diversed set of solutions in the objective space.…”

Optimizing conservation practices in watersheds: Do community preferences matter?

“…These functions represent the multiple stakeholder interests that can play a key role in adoption of conservation practices and the resultant effect on farm operations. The objective functions were included within a multiobjective optimization algorithm called Nondominated Sorting Genetic Algorithm II (NSGA-II) developed by Deb et al [2002]. The NSGA-II was run with a maximum population size of 100 individuals and maximum number of generation Liu et al [2011], etc., used net of economic costs to either estimate the probability of adoption for a practice [Weaver, 1996], evaluate implementation of practices [Liu et al, 2011], optimize designs based on maximization of benefits [Coiner et al, 2001], as design constrainer , or in the evaluation of practice's cost-effectiveness [Bryan and Kandulu, 2009].…”

Review on Job-Shop and Flow-Shop Scheduling Using

“…During the selection process, the hyperbox with the best fitness is selected and an individual is chosen at random among all inside the selected hyperbox. In Deb 79 an evolution of the NSGA was presented. This algorithm, called NSGAII, uses a new Fast Non-Dominated Sorting procedure (FNDS).…”