Preferences and Their Application in Evolutionary Multiobjective Optimization

The paper describes a new preference method and its use in multiobjective optimization. These preferences are developed with a goal to reduce the cognitive overload associated with the relative importance of a certain criterion within a multiobjective design environment involving large numbers of objectives. Their successful integration with several genetic-algo- rithm-based design search and optimization techniques (weighted sums, weighted Pareto, weighted coevolutionary methods, and weighted scenarios) are described and theoretical results relating to complexity and sensitivity of the algorithm are presented and discussed. Its usefulness has been demonstrated in a real-world project of conceptual airframe design (a joint project with British Aerospace Systems).

[1]  L. Ingber.  Very fast simulated re-annealing , 1989 .

[2]  Carlos A. Coello Coello,et al.  Handling preferences in evolutionary multiobjective optimization: a survey , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[3]  Ian C. Parmee,et al.  Preliminary airframe design using co-evolutionary multiobjective genetic algorithms , 1999 .

[4]  B. Roy.  Decision-aid and decision-making , 1990 .

[5]  Kalyanmoy Deb,et al.  Self-Adaptive Genetic Algorithms with Simulated Binary Crossover , 2001, Evolutionary Computation.

[6]  J. Lin.  Maximal vectors and multi-objective optimization , 1976 .

[7]  Thomas Bäck,et al.  Optimal Mutation Rates in Genetic Search , 1993, ICGA.

[8]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[9]  Kalyanmoy Deb,et al.  Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions , 2003 .

[10]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

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

[12]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[13]  A. Tversky.  Intransitivity of preferences. , 1969 .

[14]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[15]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[16]  Timothy D. Wilson,et al.  Telling more than we can know: Verbal reports on mental processes. , 1977 .

[17]  P. Fishburn.  Nontransitive preferences in decision theory , 1991 .

[18]  Bertrand Mareschal,et al.  The PROMCALC & GAIA decision support system for multicriteria decision aid , 1994, Decis. Support Syst..

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

[20]  Dragan Cvetkovic,et al.  Evolutionary Multi-Objective Decision Support Systems for Conceptual Design , 2000 .

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

[22]  Y. Haimes,et al.  Multiobjectives in water resource systems analysis: The Surrogate Worth Trade Off Method , 1974 .

[23]  Aharon Ben-Tal,et al.  Characterization of Pareto and Lexicographic Optimal Solutions , 1980 .

[24]  Paul Slovic,et al.  Comparison of Bayesian and Regression Approaches to the Study of Information Processing in Judgment. , 1971 .

[25]  F. Lootsma.  A model for the relative importance of the criteria in the Multiplicative AHP and SMART , 1996 .

[26]  Yacov Y. Haimes,et al.  Multiobjective optimization in water resources systems : the surrogate worth trade-off method , 1975 .

[27]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[28]  Heinz Mühlenbein,et al.  The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA) , 1993, Evolutionary Computation.

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

[30]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[31]  J. Branke,et al.  Guidance in evolutionary multi-objective optimization , 2001 .

[32]  Garrison W. Greenwood,et al.  Fitness Functions for Multiple Objective Optimization Problems: Combining Preferences with Pareto Rankings , 1996, FOGA.

[33]  Ian C. Parmee,et al.  Designer’s Preferences and Multi—objective Preliminary Design Processes , 2000 .

[34]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[35]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

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

[37]  Andrzej Osyczka,et al.  Multicriterion optimization in engineering with FORTRAN programs , 1984 .

[38]  F. Lootsma.  Multicriteria decision analysis in a decision tree , 1997 .

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

[40]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

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

[42]  Peter J. Bentley,et al.  Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms , 1998 .

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

[44]  Nicholas R. Jennings,et al.  Intelligent agents: theory and practice , 1995, The Knowledge Engineering Review.