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 wi, 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. © Springer-Verlag Berlin Heidelberg 2007.