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

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