论文标题
通过边缘旋转的锥体改善多目标进化算法
Improving Many-Objective Evolutionary Algorithms by Means of Edge-Rotated Cones
论文作者
论文摘要
鉴于$ m $维度的目标空间中的一点，可以将任何点的$ \ varepsilon $ - 可以分配到无与伦比的，主导的和主导的区域中。与所有其他体积相比，无与伦比的区域的大小与主导区域的大小与主导区域（和主导）区域之间的比例降低到$ 1/2^{M-1} $，即帕累托占主导地位的体积。由于这个原因，越来越不可能通过各向同性突变来发现主导点。作为在许多客观优化中停滞搜索的一种补救措施，在本文中，我们建议通过在进化优化算法的收敛阶段涉及钝化凸优势锥来增强帕累托优势顺序。我们建议将边缘锥作为帕累托优势锥的概括，仅通过单个参数可以控制开头角度。该方法集成到几种最先进的多目标进化算法（MOEAS）中，并在基准问题上进行了四个，五个，六个，六个和八个目标的测试。计算实验证明了这些边缘旋转锥有能力提高MOEAS在多个目标优化问题上的性能。
Given a point in $m$-dimensional objective space, any $\varepsilon$-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 $1/2^{m-1}$, 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.
