An iterated local search algorithm for the minimum differential dispersion problem

Abstract

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 of m 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).

A Tabu Search Approach With Dynamical Neighborhood Size for Solving the Maximum Min-Sum Dispersion Problem

“…According to the constraint on the cardinality of subset M , the dispersion problems can be divided to two categories. The first category includes the maximum diversity problem [2], [33], the max-min diversity problem [12], [27], [29], the minimum differential dispersion problem [14], [22], [26], [31], [36], and the maximum min-sum dispersion problem (Max-Minsum DP) [1], [20], [28], where the cardinality of subset M is limited to a given integer m. The second category includes the Max-Mean dispersion problem (MaxMean DP) [6], [13], [19], [24] and the The associate editor coordinating the review of this manuscript and approving it for publication was Md. Asaduzzaman .…”

“…On the other hand, according to the objective function (i.e., the dispersion criterion), the dispersion problems can also be divided into two categories, i.e., efficiencybased dispersion problems and equity-based dispersion problems [1], [28], [36]. The equity-based dispersion problems include the minimum differential dispersion problem, the maximum min-sum dispersion problem, and the maximum mean dispersion problem, and the efficiency-based dispersion problems include the maximum diversity problem and the max-min diversity problem.…”

A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

“…The results were compared with both previously published metaheuristics and optimal results yielded by CPLEX. Other approaches have been proposed to solve this problem, such as a hybridization between TS and memetic search [40], iterated local search [41], or an intensification-driven TS [42].…”