Multi-Objective Evolutionary Algorithms Using the Working Point and the TOPSIS Method

Abstract

The use of Multi-Ojective Evolutionary Algorithm (MOEA) methodologies, distinguished for its aptitude to obtain a representative Pareto optimal front, cannot always be the most appropriate. In fact, there exist multi-objective engineering problems that identify one feasible solution in the objective space known as Working Point (WP), not necessarily Pareto optimal. In this case, a Decision Maker (DM) can be more interested in a small number of solutions, for example, those that located in a certain region of the Pareto optimal set (the WP-region) dominate the WP. In this paper, we propose WP-TOPSISGA, an algorithm which merges the WP, MOEA techniques and the Multiple Criteria Decision Making (MCDM) method TOPSIS. With TOPSIS, a DM only needs input the preferences or weights w _i , with our method, however, the weights are evaluated by interpolation in every iteration of the algorithm. The idea is to guide the search of solutions towards the WP-region, giving an order to the found solutions in terms of Similarity to the Ideal Solution