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（moea s）促进了目标函数空间多样性的保持，但忽略了决策变量空间的多样性。本文的目的是表明，在考虑到目标空间的指标时，明确管理决策变量空间中保持的多样性数量对于提高moea的质量是有用的。我们新颖的基于可变空间多样性的 MOEA ( vsd-moea) 明确考虑了决策变量和目标函数空间的多样性。使用这些信息的目的是在优化过程中适当地调整探索和强化之间的平衡。特别是在初始阶段，该方法做出的决策更多地偏向于关于变量空间多样性的信息，而随着进化的进行，它逐渐更加重视目标函数空间的多样性。后者是通过一种新的密度估计器来实现的。将新方法与最先进的moea 进行比较s 使用具有两个和三个目标的多个基准。在考虑应用于目标函数空间的指标时，这种新颖的提议比最先进的方案产生了更好的结果，表现出更稳定和鲁棒的行为。