Computer Science Department, Center for Research in Mathematics (CIMAT), Callejón Jalisco s/n, Mineral de Valenciana, Guanajuato, Guanajuato 36240, Mexico
Department of Computer Science, CINVESTAV-IPN, Mexico City 07300, Mexico.
Evol Comput. 2022 Jun 1;30(2):195-219. doi: 10.1162/evco_a_00299.
Most state-of-the-art Multiobjective Evolutionary Algorithms (moeas) promote the preservation of diversity of objective function space but neglect the diversity of decision variable space. The aim of this article is to show that explicitly managing the amount of diversity maintained in the decision variable space is useful to increase the quality of moeas when taking into account metrics of the objective space. Our novel Variable Space Diversity-based MOEA (vsd-moea) explicitly considers the diversity of both decision variable and objective function space. This information is used with the aim of properly adapting the balance between exploration and intensification during the optimization process. Particularly, at the initial stages, decisions made by the approach are more biased by the information on the diversity of the variable space, whereas it gradually grants more importance to the diversity of objective function space as the evolution progresses. The latter is achieved through a novel density estimator. The new method is compared with state-of-art moeas using several benchmarks with two and three objectives. This novel proposal yields much better results than state-of-the-art schemes when considering metrics applied on objective function space, exhibiting a more stable and robust behavior.
大多数最先进的多目标进化算法（MOEAs）促进了目标函数空间的多样性保持，但忽略了决策变量空间的多样性。本文的目的是表明，在考虑目标空间度量时，显式管理决策变量空间中保持的多样性的数量对于提高 MOEAs 的质量是有用的。我们的新型基于变量空间多样性的 MOEA（VSd-MOEA）显式地考虑了决策变量和目标函数空间的多样性。该信息用于在优化过程中适当地平衡探索和强化。特别是，在初始阶段，方法做出的决策更多地受到变量空间多样性信息的影响，而随着进化的进行，它逐渐赋予目标函数空间多样性更高的权重。后者是通过一种新的密度估计器来实现的。该新方法使用具有两个和三个目标的几个基准与最先进的 MOEAs 进行了比较。当考虑应用于目标函数空间的度量时，该新提案的结果明显优于最先进的方案，表现出更稳定和稳健的行为。
