TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem

A common technique used to solve multi-objective optimization problems consists of first generating the set of all Pareto-optimal solutions and then ranking and/or choosing the most interesting solution for a human decision maker (DM). Sometimes this technique is referred to as generate first–choose later. In this context, this paper proposes a two-stage methodology: a first stage using a multi-objective evolutionary algorithm (MOEA) to generate an approximate Pareto-optimal front of non-dominated solutions and a second stage, which uses the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) devoted to rank the potential solutions to be proposed to the DM. The novelty of this paper lies in the fact that it is not necessary to know the ideal and nadir solutions of the problem in the TOPSIS method in order to determine the ranking of solutions. To show the utility of the proposed methodology, several original experiments and comparisons between different recognized MOEAs were carried out on a welded beam engineering design benchmark problem. The problem was solved with two and three objectives and it is characterized by a lack of knowledge about ideal and nadir values.