The Multi-Objective Genetic Algorithm Applied to Benchmark Problems An Analysis

The multiobjective genetic algorithm (MOGA) has been applied to various real-world problems in a variety of fields, most prominently in control systems engineering, with considerable success. However, a recent empirical analysis of multi-objective evolutionary algorithms (MOEA's) has suggested that a MOGA-based algorithm performed poorly across a diverse set of two-objective test problems. In this report, it is shown that a conventional MOGA with standard settings can provide improved performance, but this still compares unfavourably to the best-performing contemporary MOEA, the Strength Pareto Evolutionary Algorithm (SPEA). The importance of the MOEA, as a framework is stressed and consequently, a real-coded MOGA for real-parameter multi-criterion problems is developed using modern gudelines for the design of evolutionary algorithms. This MOGA is shown to outperform the "best" MOEA, rather that a considered implementation of the methodology is required in order to reap full rewards. This study also questions the effectiveness of the traditional fitness sharing method of niching, with respect to the current set of multiobjective benchmark problems.

[1]  Marco Laumanns,et al.  Scalable test problems for evolutionary multi-objective optimization , 2001 .

[2]  C. A. Coello Coello,et al.  A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques , 1999, Knowledge and Information Systems.

[3]  Ian Griffin,et al.  Multi-objective optimization approach to the ALSTOM gasifier problem , 2000 .

[4]  Daisuke Sasaki,et al.  Multiobjective evolutionary computation for supersonic wing-shape optimization , 2000, IEEE Trans. Evol. Comput..

[5]  Peter J. Fleming,et al.  Evolutionary Hinfin; design of an electromagnetic suspension control system for a maglev vehicle , 1997 .

[6]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

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

[8]  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.

[9]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[10]  Georges R. Harik,et al.  Foundations of Genetic Algorithms , 1997 .

[11]  Peter J. Fleming,et al.  Multiobjective genetic algorithms made easy: selection sharing and mating restriction , 1995 .

[12]  Peter J. Fleming,et al.  Multiobjective gas turbine engine controller design using genetic algorithms , 1996, IEEE Trans. Ind. Electron..

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

[14]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  Peter J. Fleming,et al.  On-line evolution of robust control systems: an industrial active magnetic bearing application , 2001 .

[17]  Peter L. Brooks,et al.  Visualizing data , 1997 .

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

[19]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[20]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[21]  Jeffrey Horn,et al.  Multiobjective Optimization Using the Niched Pareto Genetic Algorithm , 1993 .

[22]  Keith J. Burnham,et al.  On improving physical selectivity in the treatment of cancer: A systems modelling and optimisation approach , 1997 .

[23]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[24]  Alden H. Wright,et al.  Genetic Algorithms for Real Parameter Optimization , 1990, FOGA.

[25]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

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

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

[28]  Peter J. Fleming,et al.  Multiobjective Genetic Programming: A Nonlinear System Identification Application , 1997 .