Interactive Evolutionary Multiobjective Optimization Using Robust Ordinal Regression

This paper proposes the Necessary-preference-enhanced Evolutionary Multiobjective Optimizer (NEMO), a combination of an evolutionary multiobjective optimization method, NSGA-II, and an interactive multiobjective optimization method, GRIP. In the course of NEMO, the decision maker is able to introduce preference information in a holistic way, by simply comparing some pairs of solutions and specifying which solution is preferred, or comparing intensities of preferences between pairs of solutions. From this information, the set of all compatible value functions is derived using GRIP, and a properly modified version of NSGA-II is then used to search for a representative set of all Pareto-optimal solutions compatible with this set of derived value functions. As we show, this allows to focus the search on the region most preferred by the decision maker, and thereby speeds up convergence.

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

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

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

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

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

[6]  Vincent Mousseau,et al.  Inferring an ELECTRE TRI Model from Assignment Examples , 1998, J. Glob. Optim..

[7]  Jean-Marc Martel,et al.  ELECCALC - an interactive software for modelling the decision maker's preferences , 1994, Decis. Support Syst..

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

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

[10]  Dov Pekelman,et al.  Mathematical Programming Models for the Determination of Attribute Weights , 1974 .

[11]  J. March.  Bounded rationality, ambiguity, and the engineering of choice , 1978 .

[12]  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..

[13]  Jürgen Branke,et al.  Interactive Multiobjective Evolutionary Algorithms , 2008, Multiobjective Optimization.

[14]  Allan D. Shocker,et al.  Estimating the weights for multiple attributes in a composite criterion using pairwise judgments , 1973 .

[15]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

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

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

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

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

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

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

[22]  J. Siskos.  Assessing a set of additive utility functions for multicriteria decision-making , 1982 .