Solving group multi-objective optimization problems by optimizing consensus through multi-criteria ordinal classification

In this paper good consensus is associated with a high level of group satisfaction and a low level of dissatisfaction. A new method to improve consensus through a reformulation of the original group multi-objective optimization problem is introduced. For each point in the feasible decision set, the level of satisfaction or dissatisfaction from each group member is determined by multi-criteria ordinal classification approaches. Intense satisfaction and dissatisfaction are both modeled. Group satisfaction (respectively, dissatisfaction) is maximized (resp. minimized), finding the best possible consensus solutions in correspondence with a current stage of closeness among group members’ preferences, judgments, beliefs, and conservatism attitudes. Logic models are introduced to evaluate conditions for best consensus. Imperfect information (imprecision, uncertainty, ill-definition, arbitrariness) on the values of objective functions, required and available resources, and decision model parameters is handled by using interval numbers. Two different kinds of multi-criteria decision model are considered: i) an interval outranking approach and ii) an interval weighted-sum value function. The proposal can handle very general cases of group multi-objective optimization problems. The method is illustrated by solving a real size multi-objective project portfolio optimization problem using evolutionary computation tools.