Dominance-Based Rough Set Approach to Interactive Evolutionary Multiobjective Optimization

We present application of Dominance-based Rough Set Approach (DRSA) to interactive Evolutionary Multiobjective Optimization (EMO). In the proposed methodology, the preference information elicited by the decision maker in successive iterations consists in sorting some solutions of the current population as “good” or “bad”, or in comparing some pairs of solutions. The “if ..., then ...” decision rules are then induced from this preference information using Dominance-based Rough Set Approach (DRSA). The rules are used within EMO in order to focus on populations of solutions satisfying the preferences of the decision maker. This allows to speed up convergence to the most preferred region of the Pareto-front. The resulting interactive schemes, corresponding to the two types of preference information, are called DRSA-EMO and DRSA-EMO-PCT, respectively. Within the same methodology, we propose DARWIN and DARWIN-PCT methods, which permit to take into account robustness concerns in multiobjective optimization.

[1]  Salvatore Greco,et al.  Dominance-based Rough Set Approach to decision under uncertainty and time preference , 2010, Ann. Oper. Res..

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

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

[4]  Salvatore Greco,et al.  Rough approximation of a preference relation by dominance relations , 1999, Eur. J. Oper. Res..

[5]  Roman Słowiński,et al.  The Use of Rough Sets and Fuzzy Sets in MCDM , 1999 .

[6]  Kalyanmoy Deb,et al.  I-MODE: An Interactive Multi-objective Optimization and Decision-Making Using Evolutionary Methods , 2007, EMO.

[7]  Robert A. Meyers,et al.  Encyclopedia of Complexity and Systems Science , 2009 .

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

[9]  Z. Pawlak.  Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[10]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

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

[12]  S. Greco,et al.  Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle , 2002 .

[13]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[14]  J. Milnor.  Games Against Nature , 1951 .

[15]  Salvatore Greco,et al.  Rough Set Based Decision Support , 2005 .

[16]  T. Gal,et al.  Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications , 2012 .

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

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

[19]  Kalyanmoy Deb,et al.  Multiobjective optimization , 1997 .

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

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

[22]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

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

[24]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

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

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

[27]  Philippe Vincke,et al.  Multicriteria Decision-Aid , 1992 .

[28]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[29]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO '06.

[30]  Bernard Roy,et al.  Robustness in operational research and decision aiding: A multi-faceted issue , 2010, Eur. J. Oper. Res..

[31]  Kalyanmoy Deb,et al.  An interactive evolutionary multi-objective optimization and decision making procedure , 2010, Appl. Soft Comput..

[32]  Philippe Fortemps,et al.  Multicriteria decision support using rules that represent rough-graded preference relations , 2008, Eur. J. Oper. Res..

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

[34]  Salvatore Greco,et al.  Interactive Evolutionary Multiobjective Optimization using Dominance-based Rough Set Approach , 2010, IEEE Congress on Evolutionary Computation.

[35]  Salvatore Greco,et al.  Dominance-Based Rough Set Approach to Interactive Multiobjective Optimization , 2008, Multiobjective Optimization.

[36]  Jürgen Branke,et al.  Interactive Multiobjective Optimization from a Learning Perspective , 2008, Multiobjective Optimization.

[37]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[38]  K. Arrow,et al.  Social Choice and Multicriterion Decision-Making , 1986 .

[39]  Arkadi Nemirovski,et al.  Robust optimization – methodology and applications , 2002, Math. Program..

[40]  Salvatore Greco,et al.  Rough Sets in Decision Making , 2009, Encyclopedia of Complexity and Systems Science.

[41]  Salvatore Greco,et al.  Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules , 2004, Eur. J. Oper. Res..

[42]  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..

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

[44]  Salvatore Greco,et al.  Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions , 2008, Eur. J. Oper. Res..

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

[46]  Salvatore Greco,et al.  Dominance-Based Rough Set Approach to Preference Learning from Pairwise Comparisons in Case of Decision under Uncertainty , 2010, IPMU.