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Solving the maximum edge weight clique problem via unconstrained quadratic programming

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  • Alidaee, Bahram
  • Glover, Fred
  • Kochenberger, Gary
  • Wang, Haibo

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  • 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.
    • Handle: RePEc:eee:ejores:v:181:y:2007:i:2:p:592-597
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    References listed on IDEAS

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    1. Macambira, Elder Magalhaes & de Souza, Cid Carvalho, 2000. "The edge-weighted clique problem: Valid inequalities, facets and polyhedral computations," European Journal of Operational Research, Elsevier, vol. 123(2), pages 346-371, June.
    2. 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.
    3. Hunting, Marcel & Faigle, Ulrich & Kern, Walter, 2001. "A Lagrangian relaxation approach to the edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 119-131, May.
    4. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.
    5. Sorensen, Michael M., 2004. "New facets and a branch-and-cut algorithm for the weighted clique problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 57-70, April.
    6. Gary Kochenberger & Fred Glover & Bahram Alidaee & Karen Lewis, 2005. "Using the unconstrained quadratic program to model and solve Max 2-SAT problems," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 89-100.
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    Cited by:

    1. Ammar, E.E., 2009. "On fuzzy random multiobjective quadratic programming," European Journal of Operational Research, Elsevier, vol. 193(2), pages 329-341, March.
    2. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2020. "A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 747-762, July.
    3. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2018. "A nonconvex quadratic optimization approach to the maximum edge weight clique problem," Journal of Global Optimization, Springer, vol. 72(2), pages 219-240, October.
    4. Immanuel M. Bomze & Michael Kahr & Markus Leitner, 2021. "Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 301-316, February.
    5. Lozano, M. & Molina, D. & GarcI´a-MartI´nez, C., 2011. "Iterated greedy for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 214(1), pages 31-38, October.
    6. Teobaldo Bulhões & Anand Subramanian & Gilberto F. Sousa Filho & Lucídio dos Anjos F. Cabral, 2017. "Branch-and-price for p-cluster editing," Computational Optimization and Applications, Springer, vol. 67(2), pages 293-316, June.
    7. Rinaldi, Marco & Viti, Francesco, 2017. "Exact and approximate route set generation for resilient partial observability in sensor location problems," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 86-119.
    8. Almeida, Maria Teresa & Carvalho, Filipa D., 2014. "An analytical comparison of the LP relaxations of integer models for the k-club problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 489-498.
    9. Carvalho, Filipa D. & Almeida, M. Teresa, 2011. "Upper bounds and heuristics for the 2-club problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 489-494, May.
    10. Yang Wang & Jin-Kao Hao & Fred Glover & Zhipeng Lü & Qinghua Wu, 2016. "Solving the maximum vertex weight clique problem via binary quadratic programming," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 531-549, August.
    11. Yi Chu & Boxiao Liu & Shaowei Cai & Chuan Luo & Haihang You, 2020. "An efficient local search algorithm for solving maximum edge weight clique problem in large graphs," Journal of Combinatorial Optimization, Springer, vol. 39(4), pages 933-954, May.
    12. 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.
    13. Zhou, Yi & Hao, Jin-Kao & Goëffon, Adrien, 2017. "PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem," European Journal of Operational Research, Elsevier, vol. 257(1), pages 41-54.
    14. 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.
    15. Xia, Yong & Sheu, Ruey-Lin & Sun, Xiaoling & Li, Duan, 2012. "Improved estimation of duality gap in binary quadratic programming using a weighted distance measure," European Journal of Operational Research, Elsevier, vol. 218(2), pages 351-357.
    16. Shing Chih Tsai, 2013. "Rapid Screening Procedures for Zero-One Optimization via Simulation," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 317-331, May.
    17. Juan Francisco Monge, 2017. "Cardinality constrained portfolio selection via factor models," Papers 1708.02424, arXiv.org.

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