Applying a Local Search for the Uncapacitated p-Median Problem to the Capacitated Problem

Capacitated p-Median Problem (CPMP) is an important combinatorial optimization problem with practical applications such as determining the location and scale of power generation facilities in green energy field. The objective of CPMP is to find p facilities and assign each area to exactly one facility such that the total distance of assigned areas to their corresponding facilities is minimized, and the capacity limit on the facilities is not exceeded. In the CPMP solution, it is important to satisfy the capacity constraints of all opened facilities. In searching high quality solutions, the effectiveness of allowing the search for infeasible space has not been fully investigated in CPMP. In this paper, we present a novel search approach called Extend Space Strategy (ESS) that extends the search to infeasible space by using algorithms for a simplified and related problem not including major constraints. Computational results show that ESS is more effective to obtain better solutions than the standard approach that searches only feasible space.