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Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones

机译：通过边缘旋转锥改进多目标进化算法

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摘要

Given a point in m-dimensional objective space, any ε-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to l/2~(m-1), i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems.
机译：给定m维目标空间中的一个点，一个点的任何ε球都可以划分为无可比拟的，占主导地位和主导地位的区域。无与伦比的区域的大小与主导区域（和主导区域）之间的比率与l / 2〜（m-1）成比例，即与所有其他体积相比，帕累托主导的矫形器的体积成比例地减小。由于这个原因，越来越不可能通过随机的各向同性突变来找到主导点。作为许多目标优化中搜索停滞的一种补救方法，我们建议在进化优化算法的收敛阶段通过使用钝角凸优势锥来增强帕累托优势阶。我们提出了边缘旋转锥作为Pareto优势锥的推广，其开口角只能由单个参数控制。该方法已集成到几种最新的多目标进化算法（MOEA）中，并针对具有四个，五个，六个和八个目标的基准问题进行了测试。计算实验证明了这些边缘旋转圆锥体在多目标优化问题上改善MOEA性能的能力。

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