A parallel variable neighborhood search approach for the obnoxious p‐median problem

Abstract

The obnoxious p‐median problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each nonfacility location, called customers, to its nearest facility is maximized. This is an scriptNP‐hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a variable neighborhood search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely branch and cut, tabu search, and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting nonparametric statistical tests.

Less is more approach: basic variable neighborhood search for the obnoxious p‐median problem

“…The obtained results are compared with those reported in Herrán et al. (). Those results were obtained executing TS algorithm and B&C algorithm from Belotti et al.…”

“…Recently, Herrán et al. () extended the benchmark set introducing 72 new test instances generated in the same manner.…”

“…() and GRASP heuristic proposed in Colmenar et al. () on the benchmark instances as well as P‐VNS (Herrán et al., ). Among the compared heuristics, TS, GRASP, and Basic VNS are single‐thread heuristics, wh P‐VNS executes several threads in parallel.…”

“…All testings in Herrán et al. () were carried on a machine with an Intel i5 660 CPU (3.3 GHz) and 8 GB of RAM, while we used an Intel Xeon E7 4820 CPU (2.00 GHz). Due to the different computing environments, we have normalized the CPU times reported in Herrán et al.…”

“…More recently, Herrán et al. () proposed a parallel heuristic based on variable neighborhood search (VNS).…”