A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem

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Bibliographic Details
Main Authors:	Aguilar-Moreno, Marina, Pineda, Salvador, Morales, Juan Miguel
Format:	Preprint
Published:	2025
Subjects:	Optimization and Control
Online Access:	Acceder al recurso
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author	Aguilar-Moreno, Marina Pineda, Salvador Morales, Juan Miguel
author_facet	Aguilar-Moreno, Marina Pineda, Salvador Morales, Juan Miguel
contents	The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M constants that lead to weak relaxations and significant computational challenges, particularly when all lines are switchable. In this paper, we propose a two-fold approach: first, using graph theory to derive tighter big-M values by solving a relaxed longest path problem; second, introducing an iterative algorithm that incorporates a heuristic version of the switching problem to efficiently generate low-cost feasible solutions, thereby accelerating the search for optimal solutions in the integer optimization solver. Numerical results on the 118-bus network show that the proposed methodology significantly reduces the computational burden compared to conventional approaches.
format	Preprint
id	arxiv_https___arxiv_org_abs_2502_10333
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem Aguilar-Moreno, Marina Pineda, Salvador Morales, Juan Miguel Optimization and Control The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M constants that lead to weak relaxations and significant computational challenges, particularly when all lines are switchable. In this paper, we propose a two-fold approach: first, using graph theory to derive tighter big-M values by solving a relaxed longest path problem; second, introducing an iterative algorithm that incorporates a heuristic version of the switching problem to efficiently generate low-cost feasible solutions, thereby accelerating the search for optimal solutions in the integer optimization solver. Numerical results on the 118-bus network show that the proposed methodology significantly reduces the computational burden compared to conventional approaches.
title	A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem
topic	Optimization and Control
url	https://arxiv.org/abs/2502.10333

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