文档介绍：182 IEEE TRANSACTIONS ON PUTATION, VOL. 6, NO. 2, APRIL 2002
A Fast and Elitist Multiobjective ic Algorithm:
NSGA-II
Kalyanmoy Deb, Associate Member, IEEE, Amrit Pratap, Sameer Agarwal, and T. Meyarivan
Abstract—Multiobjective evolutionary algorithms (EAs) [20], [26]. The primary reason for this is their ability to find
that use nondominated sorting and sharing have been criti- multiple Pareto-optimal solutions in one single simulation run.
@ Q A
cized mainly for their: 1) plexity Since evolutionary algorithms (EAs) work with a population of
(where is the number of objectives and is the population
size); 2) nonelitism approach; and 3) the need for specifying a solutions, a simple EA can be extended to maintain a diverse
sharing parameter. In this paper, we suggest a nondominated set of solutions. With an emphasis for moving toward the true
sorting-based multiobjective EA (MOEA), called nondominated Pareto-optimal region, an EA can be used to find multiple
sorting ic algorithm II (NSGA-II), which alleviates all Pareto-optimal solutions in one single simulation run.
the above three difficulties. Specifically, a fast nondominated
P The nondominated sorting ic algorithm (NSGA) pro-
sorting approach with @ plexity is
presented. Also, a selection operator is presented that creates a posed in [20] was one of the first such EAs. Over the years, the
mating pool bining the parent and offspring populations main criticisms of the NSGA approach have been as follows.
and selecting the best (with respect to fitness and spread) 1) plexity of nondominated sorting:
solutions. Simulation results on difficult test problems show that
the proposed NSGA-II, in most problems, is able to find much The currently-used nondominated sorting algorithm has a
better spread of solutions and better convergence near the plexity of (where is the
Pareto-optimal pared to Pareto-archived evolution number of objectives and is the population size). This
strategy and strength-Pa