Shahid Beheshti University International Journal of Research and Technology in Electrical Industry 2821-0190 4 2 2025 07 01 A Comparative Study of Reordering Techniques for Consecutive Numbering in Power Grids 106597 10.48308/ijrtei.2025.240539.1093 EN Mohammad Shahraeini Department of Electrical Engineering, Golestan University, Golestan , Iran Journal Article 2025 07 02 The structure and ordering of nodes in power grids significantly affect the performance of algorithms used for simulation, optimization, and visualization. While synthetic generation of power grids has gained momentum in both transmission and distribution domains, limited research has addressed how node indexing impacts matrix sparsity patterns and computational performance. This paper presents a comprehensive study of node reordering techniques aimed at achieving consecutive numbering in complex power networks. Four categories of methods are explored: heuristic approaches, optimization-based strategies, graph-theoretic algorithms, and artificial intelligence (AI)-driven models. We revisit existing heuristics and propose a novel metaheuristic optimization method that maximizes diagonal density across multiple bandwidth levels. For radial distribution grids, we develop a graph-based method using depth-first search (DFS) that aligns node numbering with physical structure. In addition, we evaluate the feasibility of using convolutional and feedforward neural networks to learn reordering patterns from data. Despite training on thousands of synthetic graphs, standard AI models fail to produce valid permutations, highlighting the need for permutation-aware architectures. Extensive experiments on synthetic transmission and distribution networks confirm that method selection should align with network topology. Optimization excels in meshed systems, while graph-based DFS is ideal for tree-like networks. A comparative analysis is provided to guide future applications and research in this space.