Post-Pareto Optimality Analysis With Sum of Ranking Differences

In multiobjective optimization, objectives are typically conflicting, i.e., they cannot reach their individual optima simultaneously. Identifying the best one among Pareto-optimal solutions is not a simple task for the decision maker (DM), since the Pareto-optimal set can potentially contain a very large number of solutions. To ease this task, it is possible to resort to aggregate objective functions that should take into consideration the DM’s preferences and objectives; however, accurately specifying meaningful weights can be a challenge for many practitioners. Moreover, for the same DM’s preferences, different criteria give different results. A new post-Pareto analysis methodology, based on sum of ranking differences, is proposed to rank and detect the possible groupings of similar solutions of the Pareto front that match the DM’s preferences. This way the proposed technique provides the DM a smaller set of optimal solutions. The proposed method was tested in two practical benchmark problems, in the design of a brushless dc motor and in the optimization of a die press model (TEAM Workshop Problem 25).