Sequential versus simultaneous application of multi-objective optimization and multi-criteria decision making: An empirical investigation

The multi-objective optimization paradigm prescribes that a multi-objective optimization problem should be solved in two steps executed in sequence. First an approximation of the Pareto set is determined, that contains as many non-dominated solutions as possible. Secondly, a solution is chosen among these Pareto-optimal solutions. Although a large majority of papers on multi-objective optimization focuses exclusively on the first step, the second step is equally important: a decision maker generally can only implement a single solution and will need a way to select one according to his preferences. In this paper, we empirically test the soundness of the sequential approach to multiobjective optimization and provide convincing evidence that it can be outperformed by a simultaneous approach, in which the decision maker’s preferences are taken into account during the multi-objective optimization. To this end, we develop a simple tabu search algorithm for the multi-objective knapsack problem and combine it with the promethee multicriteria decision making method, both sequentially and simultaneously. The results of both approaches are compared both in terms of computing times and solution quality. The simultaneous approach is shown to strongly outperform the sequential one.