A note on heuristic approach based on UBQP formulation of the maximum diversity problem

Bahram Alidaee () and Haibo Wang ()
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Bahram Alidaee: The University of Mississippi
Haibo Wang: Texas A&M International University

Journal of the Operational Research Society, 2017, vol. 68, issue 1, 102-110

Abstract: Abstract The maximum diversity problem (MDP) is a challenging NP-hard problem with a wide range of real applications. Several researchers have pointed out close relationship between the MDP and unconstrained binary quadratic program (UBQP). In this paper, we provide procedures to solve MDP ideas from the UBQP formulation of the problem. We first give some local optimality results for r-flip improvement procedures on MDP. Then, a set of highly effective diversification approaches based on sequential improvement steps for MDP are presented. Four versions of the approaches are used within a simple tabu search and applied to 140 benchmark MDP problems available on the Internet. The procedures solve all 80 small- to medium-sized problems instantly to the best known solutions. For 22 of the 60 large problems, the procedures improved by significant amounts the best known solutions in reasonably short CPU time.

Keywords: combinatorial optimization problem; unconstrained binary quadratic programming; maximum diversity problem; r-flip local search; diversification strategy (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1057/s41274-016-0031-4

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