An iterated local search algorithm for the minimum differential dispersion problem

TL;DR

This paper introduces an iterated local search algorithm, ILS_MinDiff, for solving the minimum differential dispersion problem, effectively improving solution quality on benchmark instances through a multi-phase search process.

Contribution

The paper presents a novel iterated local search algorithm with three phases specifically designed for Min-Diff DP, outperforming existing algorithms on benchmark data.

Findings

Found 130 improved best results on benchmark instances.

Demonstrated competitive performance against state-of-the-art algorithms.

Validated effectiveness through extensive experiments on six data sets.

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).