Including preferences into a multiobjective evolutionary algorithm to deal with many-objective engineering optimization problems

Abstract In this paper, we introduce a new preference relation based on a reference point approach. This relation offers an easy approach to integrate decision maker’s preferences into a MOEA without modifying its basic structure. Besides finding the optimal solution of the achievement scalarizing function, the new preference relation allows the decision maker to find a set of solutions around that optimal solution. Then, a MOEA equipped with the proposed preference relation can be integrated into an interactive optimization method. One of the main advantages of the new method is that setting its parameters is an intuitive task to the decision maker. The other advantage is that, since our preference relation induces a finer order on vectors of objective space than that achieved by the Pareto dominance relation, it is appropriate to cope with problems having a high number of objectives. We evaluated the proposed preference relation an engineering problem, the optimization of an airfoil design with 6 objectives.

[1]  Andrzej P. Wierzbicki,et al.  A Methodological Guide to Multiobjective Optimization , 1980 .

[2]  A. Messac,et al.  Smart Pareto filter: obtaining a minimal representation of multiobjective design space , 2004 .

[3]  Jouni Lampinen,et al.  Ranking-Dominance and Many-Objective Optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[4]  K. Deb.  Solving goal programming problems using multi-objective genetic algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[5]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

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

[8]  Qingfu Zhang,et al.  Interactive MOEA/D for multi-objective decision making , 2011, GECCO '11.

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

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

[11]  Andrzej P. Wierzbicki,et al.  A parallel multiple reference point approach for multi-objective optimization , 2010, Eur. J. Oper. Res..

[12]  M. Drela.  XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils , 1989 .

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

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

[15]  Christopher Kennedy.  On “average”∗ , 2008 .

[16]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

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

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

[19]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[20]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[21]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

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

[23]  Ian C. Parmee,et al.  Preferences and their application in evolutionary multiobjective optimization , 2002, IEEE Trans. Evol. Comput..

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

[25]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[26]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

[27]  A. P. Wierzbicki,et al.  Decision Support A parallel multiple reference point approach for multi-objective optimization , 2010 .

[28]  K. Miettinen,et al.  Incorporating preference information in interactive reference point methods for multiobjective optimization , 2009 .

[29]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[30]  Marco Laumanns,et al.  Approximating the Knee of an MOP with Stochastic Search Algorithms , 2008, PPSN.

[31]  Xiaodong Li,et al.  Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm , 2010, IEEE Congress on Evolutionary Computation.

[32]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[33]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[34]  H. Sobieczky.  Parametric Airfoils and Wings , 1999 .

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

[36]  Zbigniew Michalewicz,et al.  Evolutionary Optimization , 2012, Variants of Evolutionary Algorithms for Real-World Applications.

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

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

[39]  Carlos A. Coello Coello,et al.  g-dominance: Reference point based dominance for multiobjective metaheuristics , 2009, Eur. J. Oper. Res..

[40]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[41]  Kalyanmoy Deb,et al.  Towards estimating nadir objective vector using evolutionary approaches , 2006, GECCO.

[42]  Olivier Teytaud,et al.  On the Hardness of Offline Multi-objective Optimization , 2007, Evolutionary Computation.

[43]  Xiaodong Li,et al.  Reference point based multi-objective optimization through decomposition , 2012, 2012 IEEE Congress on Evolutionary Computation.

[44]  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.

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

[46]  Ruxandra Stoean,et al.  Overview of Evolutionary Algorithms , 2014 .

[47]  H. T. Kung,et al.  On the Average Number of Maxima in a Set of Vectors and Applications , 1978, JACM.

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

[49]  Matthias Ehrgott,et al.  Multicriteria Optimization (2. ed.) , 2005 .

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

[51]  Xin Yao,et al.  How well do multi-objective evolutionary algorithms scale to large problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[52]  Jaroslav Hájek,et al.  Aerodynamic optimization via multi-objective micro-genetic algorithm with range adaptation, knowledge-based reinitialization, crowding and epsilon-dominance , 2009, Adv. Eng. Softw..

[53]  Indraneel Das.  On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection , 1999 .

[54]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

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

[56]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[57]  Ian C. Parmee,et al.  Use of Preferences for GA-based Multi-objective Optimisation , 1999, GECCO.

[58]  Andrzej Jaszkiewicz,et al.  The 'Light Beam Search' approach - an overview of methodology and applications , 1999, Eur. J. Oper. Res..