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Using SVM to combine global heuristics for the Standard Quadratic Problem

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  • Dellepiane, Umberto
  • Palagi, Laura

Abstract

The Standard Quadratic Problem (StQP) is an NP-hard problem with many local minimizers (stationary points). In the literature, heuristics based on unconstrained continuous non-convex formulations have been proposed (Bomze & Palagi, 2005; Bomze, Grippo, & Palagi, 2012) but none dominates the other in terms of best value found. Following (Cassioli, DiLorenzo, Locatelli, Schoen, & Sciandrone, 2012) we propose to use Support Vector Machines (SVMs) to define a multistart global strategy which selects the “best” heuristic. We test our method on StQP arising from the Maximum Clique Problem on a graph which is a challenging combinatorial problem. We use as benchmark the clique problems in the DIMACS challenge.

Suggested Citation

  • Dellepiane, Umberto & Palagi, Laura, 2015. "Using SVM to combine global heuristics for the Standard Quadratic Problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 596-605.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:596-605
    DOI: 10.1016/j.ejor.2014.09.054
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    References listed on IDEAS

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    1. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
    2. Immanuel Bomze & Luigi Grippo & Laura Palagi, 2012. "Unconstrained formulation of standard quadratic optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 35-51, April.
    3. A. Cassioli & D. Di Lorenzo & M. Locatelli & F. Schoen & M. Sciandrone, 2012. "Machine learning for global optimization," Computational Optimization and Applications, Springer, vol. 51(1), pages 279-303, January.
    4. Luana E. Gibbons & Donald W. Hearn & Panos M. Pardalos & Motakuri V. Ramana, 1997. "Continuous Characterizations of the Maximum Clique Problem," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 754-768, August.
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    Cited by:

    1. Riccardo Bisori & Matteo Lapucci & Marco Sciandrone, 2022. "A study on sequential minimal optimization methods for standard quadratic problems," 4OR, Springer, vol. 20(4), pages 685-712, December.
    2. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.

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