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

Author

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  • Bahram Alidaee

    (The University of Mississippi)

  • Haibo Wang

    (Texas A&M International University)

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.

Suggested Citation

  • Bahram Alidaee & Haibo Wang, 2017. "A note on heuristic approach based on UBQP formulation of the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 102-110, January.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:1:d:10.1057_s41274-016-0031-4
    DOI: 10.1057/s41274-016-0031-4
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    References listed on IDEAS

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    1. Duarte, Abraham & Marti, Rafael, 2007. "Tabu search and GRASP for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 178(1), pages 71-84, April.
    2. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    3. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1992. "New Insertion and Postoptimization Procedures for the Traveling Salesman Problem," Operations Research, INFORMS, vol. 40(6), pages 1086-1094, December.
    4. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    5. Wu, Qinghua & Hao, Jin-Kao, 2013. "A hybrid metaheuristic method for the Maximum Diversity Problem," European Journal of Operational Research, Elsevier, vol. 231(2), pages 452-464.
    6. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    7. Bahram Alidaee & Gary Kochenberger & Haibo Wang, 2010. "Theorems Supporting r-flip Search for Pseudo-Boolean Optimization," International Journal of Applied Metaheuristic Computing (IJAMC), IGI Global Scientific Publishing, vol. 1(1), pages 93-109, January.
    8. R Aringhieri & R Cordone, 2011. "Comparing local search metaheuristics for the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 266-280, February.
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    Cited by:

    1. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.

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