A branch and bound algorithm for the maximum diversity problem

Rafael Martí, Micael Gallego and Abraham Duarte

European Journal of Operational Research, 2010, vol. 200, issue 1, 36-44

Abstract: This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the MDP. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium-sized instances (with 50 elements) as well as some large-sized instances (with 100 elements). We compare our method with the best previous linear integer formulation solved with the well-known software Cplex. The comparison favors the proposed procedure.

Keywords: Maximum; diversity; problem; Branch; and; bound; Integer; programming (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:200:y:2010:i:1:p:36-44

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