Methodology to select solutions from the pareto-optimal set
José Carlos Ferreira, Carlos M. Fonseca, António Gaspar‐Cunha · 2007
The resolution of a Multi-Objective Optimization Problem (MOOP) does not end when the Pareto-optimal set is found. In real problems, a single solution must be selected. Ideally, this solution must belong to the non-dominated solutions set and must take into account the preferences of a Decision Maker (DM). Therefore, the searching for a single solution (or solutions) in MOOP is done in two steps. First, a Pareto optimal set is found. Multi-Objective Evolutionary Algorithms (MOEA), based on the principle of Pareto optimality, are designed to produce the complete set of non-dominated solutions. Second, a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), can be applied. In this work, a method, based on a weighted stress function, is proposed. It is able to integrate the user's preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importance of the criteria.