An Iterated Local Search for the Minimum Edge-Dilation K -Center Problem

This paper studies the minimum edge-dilation K -center (MEDKC) problem for edge-weighted, undirected and connected graphs. This problem finds an important application in designing efficient routing schemes in computer networks. This problem is 𝒩𝒫 -hard. To handle such 𝒩𝒫 -hard problems, metaheuristic techniques are appropriate choices for finding solutions of high quality in a reasonable amount of computational time. In literature, there are only two variants of genetic algorithm (GA) proposed for this problem. This paper presents a simple and effective iterated local search (ILS) approach for this problem. In the proposed ILS, a local search strategy is designed in such a way that it effectively exploits the local region around the perturbed solution. The performance of the proposed ILS is evaluated on benchmark instances. Computational results suggest that ILS dominates two existing variants of GA for this problem. ILS, in terms of solution quality, is also superior to an existing polynomial time approximation algorithm developed for this problem. ILS finds new values on 18 instances out of 91 instances. In addition, a statistical analysis is also studied.