Saborido Rubén, Ruiz Ana B, Luque Mariano
Polytechnique Montréal Researchers in Software Engineering, École Polytechnique de Montréal, Canada
Universidad de Málaga, Department of Applied Economics (Mathematics), Calle Ejido 6, 29071 Málaga, Spain
Evol Comput. 2017 Summer;25(2):309-349. doi: 10.1162/EVCO_a_00175. Epub 2016 Feb 8.
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.
在本文中，我们提出了一种用于多目标优化的新进化算法，称为全局加权成就标量化函数遗传算法（Global WASF-GA），它属于基于聚合的进化算法。全局加权成就标量化函数遗传算法的主要目的是逼近整个帕累托最优前沿。其适应度函数由基于切比雪夫距离的成就标量化函数（ASF）定义，其中考虑了两个参考点（理想点和最低点目标向量），并且所使用的权重向量取自一组其逆向量分布良好的权重向量集合。在每次迭代中，所有个体被分类到不同的前沿。每个前沿由使用理想向量和最低点向量作为参考点时，针对集合中不同权重向量具有最低ASF值的解组成。在同时考虑理想向量和最低点向量的情况下改变ASF中的权重向量，使得该算法能够获得一组最终的非支配解，这些解逼近整个帕累托最优前沿。我们在二目标、三目标和五目标问题中将全局加权成就标量化函数遗传算法与多目标进化算法（MOEA/D）的不同版本以及非支配排序遗传算法II（NSGA-II）进行了比较。所获得的计算结果使我们能够得出结论，在许多情况下，特别是在三目标和五目标问题中，就超体积指标和ε指标而言，全局加权成就标量化函数遗传算法比其他两种算法具有更好的性能。
