Binary matrix optimization commonly arise in the real world, e.g., multi-microgrid network structure design problem (MGNSDP), which is to minimize the total length of the power supply line under certain constraints. Finding the global optimal solution for these problems faces a great challenge since such problems could be large-scale, sparse and multimodal. Traditional linear programming is time-consuming and cannot solve nonlinear problems. To address this issue, a novel improved feasibility rule based differential evolution algorithm, termed LBMDE, is proposed. To be specific, a general heuristic solution initialization method is first proposed to generate high-quality solutions. Then, a binary-matrix-based DE operator is introduced to produce offspring. To deal with the constraints, we proposed an improved feasibility rule based environmental selection strategy. The performance and searching behaviors of LBMDE are examined by a set of benchmark problems.

翻译：在现实世界中通常会出现二元矩阵优化,例如,多微型电网结构设计问题(MGNSDP),这是在一定的限制下最大限度地减少电力供应线的总长度。找到这些问题的全球最佳解决办法面临巨大的挑战,因为这类问题可能是大规模、稀少和多式的。传统的线性编程很费时,无法解决非线性问题。为解决这一问题,提出了一种新的改进可行性规则的差别演化算法,称为LBMDE。具体地说,首先建议采用一般的超标准化解决办法初始化方法,以产生高质量的解决办法。然后,引入一个基于二元矩阵的DE操作器来产生后代。为了应对这些制约因素,我们提出了改进基于可行性规则的环境选择战略。LBMDE的绩效和探索行为由一套基准问题来审查。