Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions

Since the beginning of the 1990s, research and application of muitiobjective evolutionary algorithms (MOEAs) have attracted increasing attention. This is mainly due to the ability of evolutionary algorithms to find multiple Pareto-optimal solutions in one single simulation run. In this chapter, we present an overview of MOEAs and then discuss a particular algorithm in detail. Although MOEAs can find multiple Pareto-optimal solutions, often, users need to impose a particular order of priority to objectives. In this chapter, we present a few classical techniques to identify a preferred or a compromise solution, and finally suggest a biased sharing technique which can be used during the optimization phase to find a biased distribution of Pareto-optimal solutions in the region of interest. The results are encouraging and suggest further application of the proposed strategy to more complex multi-objective optimization problems.

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

[2]  António Gaspar-Cunha,et al.  Use of Genetic Algorithms in Multicriteria Optimization to Solve Industrial Problems , 1997, ICGA.

[3]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[4]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[5]  Kalyanmoy Deb,et al.  Optimization for Engineering Design: Algorithms and Examples , 2004 .

[6]  Ralph L. Keeney,et al.  Decisions with multiple objectives: preferences and value tradeoffs , 1976 .

[7]  Lothar Thiele,et al.  A Comparison of Selection Schemes used in Genetic Algorithms , 1995 .

[8]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

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

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

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

[12]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[13]  Geoffrey T. Parks,et al.  Selective Breeding in a Multiobjective Genetic Algorithm , 1998, PPSN.

[14]  P. Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[15]  Jeffrey Horn,et al.  Multicriterion decision making , 1997 .

[16]  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.

[17]  Marco Laumanns,et al.  A Spatial Predator-Prey Approach to Multi-objective Optimization: A Preliminary Study , 1998, PPSN.

[18]  J. Eheart,et al.  Genetic-algorithm-based design of groundwater quality monitoring system , 1993 .

[19]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

[20]  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.

[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]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

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

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

[25]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[26]  Shigeru Obayashi,et al.  Niching and Elitist Models for MOGAs , 1998, PPSN.

[27]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[28]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

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

[30]  Ian C. Parmee,et al.  Multiobjective Satisfaction within an Interactive Evolutionary Design Environment , 2000, Evolutionary Computation.

[31]  J. D. Schaffer,et al.  Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition) , 1984 .

[32]  Jian-Bo Yang,et al.  Multiple Criteria Decision Support in Engineering Design , 1998 .

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

[34]  Kalyanmoy Deb,et al.  Nonlinear goal programming using multi-objective genetic algorithms , 2001, J. Oper. Res. Soc..

[35]  David E. Goldberg,et al.  Genetic algorithm design of Pareto optimal broadband microwave absorbers , 1996 .

[36]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

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

[38]  Kishalay Mitra,et al.  Multiobjective dynamic optimization of an industrial Nylon 6 semibatch reactor using genetic algorit , 1998 .

[39]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

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

[41]  Carlos A. Coello Coello,et al.  An updated survey of GA-based multiobjective optimization techniques , 2000, CSUR.

[42]  Kalyanmoy Deb,et al.  A flexible optimization procedure for mechanical component design based on genetic adaptive search , 1998 .

[43]  R. Rosenberg.  Simulation of genetic populations with biochemical properties : technical report , 1967 .

[44]  Prabhat Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[45]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[46]  Kalyanmoy Deb,et al.  Evolutionary Algorithms for Multi-Criterion Optimization in Engineering Design , 1999 .

[47]  Zbigniew Michalewicz,et al.  Evolutionary Computation 2 , 2000 .