title: Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front.
abstract: In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.
authors: Polytechnique Montréal Researchers in Software Engineering, École Polytechnique de Montréal, Canada ruben.saborido-infantes@polymtl.ca.
authors: Rubén
authors: R
authors: Saborido
authors: Universidad de Málaga, Department of Applied Economics (Mathematics), Calle Ejido 6, 29071 Málaga, Spain abruiz@uma.es.
authors: Ana B
authors: AB
authors: Ruiz
authors: Universidad de Málaga, Department of Applied Economics (Mathematics), Calle Ejido 6, 29071 Málaga, Spain mluque@uma.es.
authors: Mariano
authors: M
authors: Luque
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D008954:Models, Biological
keywords: Achievement scalarizing function; Evolutionary algorithm.; Multiobjective optimization; Pareto optimal solutions