Hybrid Matheuristics Applied to the Trained p-Median Problem

The Enabled p-Medians Problem (PPMC) is an NP-hard problem applied in the contexts of facility localization, logistics, and service planning, which seeks to select facilities and allocate customers while minimizing service costs under capacity constraints. In this work, a hybrid matheuristic called Hybrid Clustering Search Adaptive Iterated Local Search (Hybrid-CS-AILS) is proposed, which integrates an Adaptive Iterated Local Search (AILS)  with a Clustering Search strategy capable of identifying promising regions of the solution space. Computational experiments were conducted in 35 benchmark instances of the PPMC, comparing the proposed method with the most recent approach in the literature. The results show that Hybrid-CS-AILS obtained better solutions in most instances, being 6 times faster on average, evidencing the efficiency of the proposed hybrid approach.