Matheuristics with Benders-Inspired Local Sections for Multistage Distribution Network Expansion Planning

A matheuristic is proposed that integrates Iterated Local Search with cut-off plans (inspired by Benders' Decomposition) for the Multistage Expansion Planning of Distribution Systems. The model allocates investments in branches over multiple periods, evaluating operational constraints via linearized power flow. The approach employs subgradient cuts (approximated by finite differences) as a dynamic halting criterion. This strategy mitigates the computational exhaustion phase of the canonical heuristic by estimating the local stabilization of the solution under 0.5% tolerance. Experiments in eight instances (derived from the IEEE systems of 33 and 69 bars, with search spaces between 10³ and 1.5 x 10¹¹ configurations) indicate median acceleration of 12.6 times in the evaluations of the objective function. The quality of the solutions is equal to that of the reference in six instances, with residual deviations of less than 0.5% in the broad synthetic scenarios.