A Hybrid Heuristic Approach Based on a Quadratic Knapsack Formulation for the Max-Mean Dispersion Problem

Abstract

The paper deals with the Max-Mean Dispersion Problem ($Max-Mean DP$) belonging to the general category of clustering problems. The aim of such problems is to find a subset of a set which maximizes a measure of dispersion/similarity between elements. To tackle the problem a two phases hybrid heuristic combining a mixed integer non linear solver and a local branching procedure is developed. Computational results, performed on literature instances, show that the proposed procedure outperforms the state-of-the-art approaches.