As distribution networks operate in their majority in a radial way, this condition becomes one of the most important constraints of distribution network reconfiguration (DNR) problem. There are diverse ways to represent this in DNR, but a lack of studies that provide an analysis of its behavior is noted, specially regarding its influence in metaheuristics and bio-inspired metaheuristics. This paper presents a discussion between two alternatives to represent this in DNR in conjunction with three new bio-inspired metaheuristics. One is based on the formation of the incidence matrix of the system and its determinant; the other is a modified approach of a method that establishes a set of forbidden switches through the analysis of the system fundamental loops. To solve DNR, three new bio-inspired metaheuristics are presented: monarch butterfly optimization (MBO), gray wolf optimizer (GWO), and marine predators algorithm (MPA). A comparison is performed with selective particle swarm optimization (SPSO). To test the alternatives, three systems are used (33-, 69-, and 84- bus), with results showing the influence of the radiality approach in the results of bio-inspired metaheuristics.

中文翻译：

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新仿生元启发式求解不同径向约束表示下配电网重构问题的行为分析

由于配电网络大部分以径向方式运行，因此这种情况成为配电网络重新配置 (DNR) 问题的最重要约束之一。在 DNR 中有多种方法来表示这一点，但注意到缺乏对其行为进行分析的研究，特别是关于其对元启发式和仿生元启发式的影响。本文结合三个新的仿生元启发式方法，对在 DNR 中表示这一点的两种替代方案进行了讨论。一种是基于系统的关联矩阵及其行列式的形成；另一种是通过对系统基本回路的分析，建立一组禁止开关的方法的改进方法。为了解决 DNR，提出了三种新的仿生元启发式算法：帝王蝶优化 (MBO)、灰狼优化器 (GWO) 和海洋捕食者算法 (MPA)。与选择性粒子群优化 (SPSO) 进行比较。为了测试替代方案，使用了三个系统（33-、69- 和 84- 总线），结果显示了径向方法对仿生元启发式结果的影响。