Large-Scale Binary Matrix Optimization for Multimicrogrids Network Structure Design

The multimicrogrid network structure design problem (MNSDP) represents a binary matrix optimization challenge, targeting the minimization of the cumulative length of power supply circuits within a multimicrogrid system, subject to specific constraints. The optimization of this problem is pivotal for augmenting the stability and resilience of power systems, particularly in remote locales harnessing renewable energy sources. Given its inherent large-scale, sparse, and multimodal nature, the pursuit of the global optimal solution for MNSDP is inherently complex. In this research, we introduce a sophisticated mathematical model of the MNSDP, accommodating three distinct node types, each having disparate reliability prerequisites. We further unveil a benchmark test suite based on real-world scenarios, dubbed MNSDP-LIB. To further our innovations, we present the large-scale binary matrix-based differential evolution (LBMDE) algorithm. This novel algorithm adopts a binary-matrix-centric DE operator with an enhanced feasibility-centric environmental selection strategy. Empirical experiments accentuate the proficiency of LBMDE in addressing large-scale binary matrix optimization challenges. When juxtaposed with extant evolutionary algorithms and a renowned commercial solver, LBMDE demonstrates commendable competitiveness.