Decision making in multiobjective optimization aided by the multicriteria tournament decision method

Abstract This paper proposes a new method for multicriteria analysis, named Multicriteria Tournament Decision (MTD). It provides the ranking of alternatives from best to worst, according to the preferences of a human decision-maker (DM). It has some positive aspects such as: it has a simple algorithm with intuitive appeal; it involves few input parameters (just the importance weight of each criterion). The helpfulness of MTD is demonstrated by using it to select the final solution of multiobjective optimization problems in an a posteriori decision making approach. Having at hand a discrete approximation of the Pareto front (provided by a multiobjective evolutionary search algorithm), the choice of the preferred Pareto-optimal solution is performed using MTD. A simple method, named Gain Analysis method (GAM), for verifying the existence of a better solution (a solution associated to higher marginal rates of return) than the one originally chosen by the DM, is also introduced here. The usefulness of MTD and GAM methods is confirmed by the suitable results shown in this paper.

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

[2]  Philippe Vincke,et al.  Analysis of multicriteria decision aid in Europe , 1986 .

[3]  Petr Ekel,et al.  Fuzzy preference modeling and its application to multiobjective decision making , 2006, Comput. Math. Appl..

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

[5]  F. H. Barron,et al.  SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement , 1994 .

[6]  Jean Pierre Brans,et al.  HOW TO SELECT AND HOW TO RANK PROJECTS: THE PROMETHEE METHOD , 1986 .

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

[8]  Lily Rachmawati,et al.  A Multi-Objective Genetic Algorithm with Controllable Convergence on Knee Regions , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[9]  Quan Zhang,et al.  Decision consolidation: criteria weight determination using multiple preference formats , 2004, Decis. Support Syst..

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

[11]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

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

[13]  Roberta Oliveira Parreiras,et al.  A multiplicative version of Promethee II applied to multiobjective optimization problems , 2007, Eur. J. Oper. Res..

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