Evolutionary Algorithms for Multi-Criterion Optimization in Engineering Design

1.1 INTRODUCTION Many real-world engineering design or decision making problems involve simultaneous optimizationof multiple objectives. The principle of multi-criterion optimization is diierent from that in a single-objective optimization. In single-objective optimization, the goal is to nd the best design solution, which corresponds to the minimum or maximum value of the objective function 9, 34]. On the contrary, in a multi-criterion optimization with connicting objectives, there is no single optimal solution. The interaction among diierent objectives gives rise to a set of compromised solutions, largely known as the Pareto-optimal solutions 40, 2]. Since none of these Pareto-optimal solutions can be identiied as better than others without any further consideration, the goal in a multi-criterion optimization is to nd as many Pareto-optimal solutions as possible. Once such solutions are found, it usually requires a higher-level decision-making with other considerations to choose one of them for implementation. Here, we address the rst task of nding multiple Pareto-optimal solutions. There are two objectives in a multi-criterion optimization: (i) nd solutions close to the true Pareto-optimal solutions and (ii) nd solutions that are widely diierent from each other. The rst task is desired to satisfy op-timality conditions in the obtained solutions. The second task is desired to have no bias towards any particular objective function.

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

[2]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

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

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

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

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

[7]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

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

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

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

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

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

[13]  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.

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

[15]  Trevor N. Mudge,et al.  A Parallel Genetic Algorithm for Multiobjective Microprocessor Design , 1995, ICGA.

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

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

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

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

[20]  Pratyush Sen,et al.  A Multiple Criteria Genetic Algorithm for Containership Loading , 1997, ICGA.

[21]  S. Ranji Ranjithan,et al.  The Neighborhood Constraint Method: A Genetic Algorithm-Based Multiobjective Optimization Technique , 1997, ICGA.

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

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

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

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

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

[27]  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.

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

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

[30]  Ian C. Parmee,et al.  Evolutionary Design and Multi-objective Optimisation , 1998 .

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

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

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