An interactive evolutionary multi-objective optimization algorithm with a limited number of decision maker calls

This paper presents a preference-based method to handle optimization problems with multiple objectives. With an increase in the number of objectives the computational cost in solving a multi-objective optimization problem rises exponentially, and it becomes increasingly difficult for evolutionary multi-objective techniques to produce the entire Pareto-optimal front. In this paper, an evolutionary multi-objective procedure is combined with preference information from the decision maker during the intermediate stages of the algorithm leading to the most preferred point. The proposed approach is different from the existing approaches, as it tries to find the most preferred point with a limited budget of decision maker calls. In this paper, we incorporate the idea into a progressively interactive technique based on polyhedral cones. The idea is also tested on another progressively interactive approach based on value functions. Results are provided on two to five-objective unconstrained as well as constrained test problems.

[1]  Kalyanmoy Deb,et al.  Progressively interactive evolutionary multi-objective optimization method using generalized polynomial value functions , 2010, IEEE Congress on Evolutionary Computation.

[2]  Murat Köksalan,et al.  An Interactive Territory Defining Evolutionary Algorithm: iTDEA , 2010, IEEE Transactions on Evolutionary Computation.

[3]  Lothar Thiele,et al.  A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization , 2009, Evolutionary Computation.

[4]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[5]  Stanley Zionts,et al.  A multiple criteria method for choosing among discrete alternatives , 1981 .

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[8]  J. Branke,et al.  Interactive evolutionary multiobjective optimization driven by robust ordinal regression , 2010 .

[9]  Kaisa Miettinen,et al.  A Preference Based Interactive Evolutionary Algorithm for Multi-objective Optimization: PIE , 2011, EMO.

[10]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

[11]  Kalyanmoy Deb,et al.  Integrating User Preferences into Evolutionary Multi-Objective Optimization , 2005 .

[12]  Khaled Ghédira,et al.  The r-Dominance: A New Dominance Relation for Interactive Evolutionary Multicriteria Decision Making , 2010, IEEE Transactions on Evolutionary Computation.

[13]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

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

[15]  Murat Köksalan,et al.  An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization , 2003, Manag. Sci..

[16]  Dmitry Podkopaev,et al.  Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy , 2012, Eur. J. Oper. Res..

[17]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.

[18]  A. Jaszkiewicz,et al.  Interactive multiobjective optimization with the Pareto memetic algorithm , 2007 .

[19]  Jyrki Wallenius,et al.  A Progressive Algorithm for Modeling and Solving Multiple-Criteria Decision Problems , 1986, Oper. Res..

[20]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[21]  Aravind Srinivasan,et al.  A Population-Based, Parent Centric Procedure for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[22]  椹木 義一,et al.  Theory of multiobjective optimization , 1985 .

[23]  Panu Korhonen,et al.  An algorithm for projecting a reference direction onto the nondominated set of given points , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[24]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[25]  P. Yu.  Multiple-Criteria Decision Making: "Concepts, Techniques, And Extensions" , 2012 .

[26]  Lily Rachmawati,et al.  Preference Incorporation in Multi-objective Evolutionary Algorithms: A Survey , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[27]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multi-objective Optimization Method Based on Polyhedral Cones , 2010, LION.

[28]  M. Powell.  The NEWUOA software for unconstrained optimization without derivatives , 2006 .

[29]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[30]  Jürgen Branke,et al.  Consideration of Partial User Preferences in Evolutionary Multiobjective Optimization , 2008, Multiobjective Optimization.

[31]  Jyrki Wallenius,et al.  Interactive evolutionary multi-objective optimization for quasi-concave preference functions , 2010, Eur. J. Oper. Res..

[32]  Jürgen Branke,et al.  Interactive Evolutionary Multiobjective Optimization Using Robust Ordinal Regression , 2009, EMO.

[33]  M. Wiecek.  Advances in Cone-Based Preference Modeling for Decision Making with Multiple Criteria , 2007 .

[34]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[35]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[36]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

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

[38]  José Rui Figueira,et al.  Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method , 2009, Eur. J. Oper. Res..

[39]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions , 2010, IEEE Transactions on Evolutionary Computation.

[40]  Pekka Korhonen,et al.  A visual reference direction approach to solving discrete multiple criteria problems , 1988 .

[41]  M. Wiecek,et al.  Inclusion of Preferences in the Design of Evolutionary Optimization Algorithms: An Empirical Study , 2008 .

[42]  V. Noghin.  Relative importance of criteria: a quantitative approach , 1997 .