An iterated local search algorithm for the minimum differential dispersion problem

Given a set of n elements separated by a pairwise distance matrix, the minimum differential dispersion problem (Min-Diff DP) aims to identify a subset ofm elements (m < n) such that the difference between the maximum sum and the minimum sum of the inter-element distances between any two chosen elements is minimized. We propose an effective iterated local search (denoted by ILS MinDiff) for Min-Diff DP. To ensure an effective exploration and exploitation of the search space, the proposed ILS MinDiff algorithm iterates through three sequential search phases: a fast descent-based neighborhood search phase to find a local optimum from a given starting solution, a local optima exploring phase to visit nearby high-quality solutions around a given local optimum, and a local optima escaping phase to move away from the current search region. Experimental results on six data sets of 190 benchmark instances demonstrate that ILS MinDiff competes favorably with the state-of-the-art algorithms by finding 130 improved best results (new upper bounds). keywords: Combinatorial optimization; dispersion problems; heuristics; iterated local search; three phase search.