Multiple-Objective Genetic Algorithm Using the Multiple Criteria Decision Making Method TOPSIS

Abstract

The so called second generation of Multi-Objective Evolutionary Algorithms (MOEAs) like NSGA-II, are highly efficient and obtain Pareto optimal fronts characterized mainly by a wider spread and visually distributed fronts. The subjacent idea is to provide the decision-makers (DM) with the most representative set of alternatives in terms of objective values, reserving the articulation of preferences to an a posteriori stage. Nevertheless, in many real discrete problems the number of solutions that belong the Pareto front is unknown and if the specified size of the non-dominated population in the MOEA is less than the number of solutions of the problem, the found front will be incomplete for a posteriori Making Decision. A possible strategy to overcome this difficulty is to promote those solutions placed in the region of interest while neglecting the others during the search, according to some DM's preferences. We propose TOPSISGA, that merges the second generation of MOEAs (we use NSGA-II) with the well known multiple criteria decision making technique TOPSIS whose main principle is to identify as preferred solutions those ones with the shortest distance to the positive ideal solution and the longest distance from the negative ideal solution. The method induces an ordered list of alternatives in accordance to the DM's preferences based on Similarity to the ideal point.