A fast and elitist multiobjective genetic algorithm: NSGA-II

Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 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 N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - 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 multi-objective 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 multi-objective optimizer, and the much better performance of NSGA-II is observed.

[1]  J. D. Schaffer,et al.  Multiple Objective Optimization with Vector Evaluated Genetic Algorithms , 1985, ICGA.

[2]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms: Motivation, Analysis, and First Results , 1989, Complex Syst..

[3]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[4]  Frank Kursawe,et al.  A Variant of Evolution Strategies for Vector Optimization , 1990, PPSN.

[5]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[6]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[7]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[8]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[9]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[10]  C. Poloni.  Hybrid GA for Multi Objective Aerodynamic Shape Optimisation , 1995 .

[11]  Masahiro Tanaka,et al.  GA-based decision support system for multicriteria optimization , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[12]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[13]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

[14]  G. Harik.  Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms , 1997 .

[15]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[16]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[17]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[18]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[19]  Kalyanmoy Deb,et al.  Understanding Interactions among Genetic Algorithm Parameters , 1998, FOGA.

[20]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[21]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[22]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[23]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[24]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[25]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[26]  Ivo F. Sbalzariniy,et al.  Multiobjective optimization using evolutionary algorithms , 2000 .

[27]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

[28]  C. L. Valenzuela.  A simple evolutionary algorithm for multi-objective optimization (SEAMO) , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).