An outranking-based general approach to solving group multi-objective optimization problems

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• 作者：Eduardo Fernandez^a ; ^{eddyf@uas.uasnet.mx} ; Rafael Olmedo^b ; ^{rolmedo@uas.uasnet.mx}
• 关键词：Group decisions and negotiations ; Multiple objective programming ; Fuzzy outranking relations
• 刊名：European Journal of Operational Research
• 出版年：2013
• 出版时间：16 March, 2013
• 年：2013
• 卷：225
• 期：3
• 页码：497-506
• 全文大小：347 K

文摘

This paper presents a general approach to solving multi-objective programming problems with multiple decision makers. The proposal is based on optimizing a bi-objective measure of ¡°collective satisfaction¡±. Group satisfaction is understood as a reasonable balance between the strengths of an agreeing and an opposing coalition, considering also the number of decision makers not belonging to any of these coalitions. Accepting the vagueness of ¡°collective satisfaction¡±, even the vagueness of ¡°person satisfaction¡±, fuzzy outranking relations and other fuzzy logic models are used.

Our method transforms a group multi-objective optimization problem into a group choice problem on a decision set composed of a relatively small set of alternatives. This set contains the possible acceptable consensuses in the parameter space. Once such a set has been identified, other well-known techniques can be used to reach the final choice.

Main advantages: (a) Each individual decision maker is concerned with his/her own multi-objective optimization problem, only sharing decision variables; own constraints and own mapping between decision variables and objective space are allowed; (b) the search for the best agreement is not limited to portions of the Pareto frontiers; (c) no voting rule is used by the optimization algorithm; no to some extent arbitrary way of handling collective preferences is needed; (d) no assumptions of transitivity and comparability of preference relations are needed; and (e) the concepts of satisfaction/non-satisfaction do not depend on distance measures or other to some extent arbitrary norms.

Very good performance of the whole proposal is illustrated by a real-size example.