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A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

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  • Schöbel, Anita
  • Scholz, Daniel

Abstract

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used.

Suggested Citation

  • Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:2:p:266-275
    DOI: 10.1016/j.ejor.2013.07.003
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    References listed on IDEAS

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    1. Drezner, Zvi & Nickel, Stefan, 2009. "Solving the ordered one-median problem in the plane," European Journal of Operational Research, Elsevier, vol. 195(1), pages 46-61, May.
    2. José Fernández & Blas Pelegrín & Frank Plastria & Boglárka Tóth, 2007. "Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure," Networks and Spatial Economics, Springer, vol. 7(1), pages 19-44, March.
    3. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
    4. Tammy Drezner & Zvi Drezner, 2007. "Equity Models in Planar Location," Computational Management Science, Springer, vol. 4(1), pages 1-16, January.
    5. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    6. Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    7. Daniel Scholz, 2012. "Theoretical rate of convergence for interval inclusion functions," Journal of Global Optimization, Springer, vol. 53(4), pages 749-767, August.
    8. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    9. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    10. Frank Plastria & Mohamed Elosmani, 2008. "On the convergence of the Weiszfeld algorithm for continuous single facility location–allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 388-406, December.
    11. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
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    2. Li, Yifu & Qi, Xiangtong, 2022. "A geometric branch-and-bound algorithm for the service bundle design problem," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1044-1056.

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