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A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem

Author

Listed:
  • Manuel Laguna

    (University of Colorado, Boulder, Colorado)

  • Thomas A. Feo

    (University of Texas, Austin, Texas)

  • Hal C. Elrod

    (Princeton Transportation Consulting Group, Inc., Burlington, Massachusetts)

Abstract

We present a greedy randomized adaptive search procedure ( GRASP ) for the network 2-partition problem. The heuristic is empirically compared with the Kernighan-Lin (K&L) method on a wide range of instances. The GRASP approach dominates K&L with respect to solution value on a large percentage of the instances tested. The ability of GRASP to find optimal solutions is assessed by comparing its performance with a general purpose mixed integer programming package.

Suggested Citation

  • Manuel Laguna & Thomas A. Feo & Hal C. Elrod, 1994. "A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem," Operations Research, INFORMS, vol. 42(4), pages 677-687, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:677-687
    DOI: 10.1287/opre.42.4.677
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    Cited by:

    1. A J Higgins & L A Laredo, 2006. "Improving harvesting and transport planning within a sugar value chain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 367-376, April.
    2. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    3. Corberan, A. & Marti, R. & Sanchis, J. M., 2002. "A GRASP heuristic for the mixed Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 70-80, October.
    4. Drexl, Andreas & Salewski, Frank, 1997. "Distribution requirements and compactness constraints in school timetabling," European Journal of Operational Research, Elsevier, vol. 102(1), pages 193-214, October.
    5. Jan Böttcher & Andreas Drexl & Rainer Kolisch & Frank Salewski, 1999. "Project Scheduling Under Partially Renewable Resource Constraints," Management Science, INFORMS, vol. 45(4), pages 543-559, April.
    6. Sánchez-Oro, J. & López-Sánchez, A.D. & Hernández-Díaz, A.G. & Duarte, A., 2022. "GRASP with strategic oscillation for the α-neighbor p-center problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 143-158.
    7. Drexl, Andreas & Salewski, Frank, 1996. "Distribution Requirements and Compactness Constraints in School Timetabling. Part II: Methods," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 384, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Andreas Schirmer, 2000. "Case‐based reasoning and improved adaptive search for project scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 201-222, April.
    9. Dell'Amico, Mauro & Trubian, Marco, 1998. "Solution of large weighted equicut problems," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 500-521, April.
    10. A. D. López-Sánchez & J. Sánchez-Oro & M. Laguna, 2021. "A New Scatter Search Design for Multiobjective Combinatorial Optimization with an Application to Facility Location," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 629-642, May.
    11. Serigne Gueye & Philippe Michelon, 2005. "“Miniaturized” Linearizations for Quadratic 0/1 Problems," Annals of Operations Research, Springer, vol. 140(1), pages 235-261, November.
    12. Charles Fleurent & Fred Glover, 1999. "Improved Constructive Multistart Strategies for the Quadratic Assignment Problem Using Adaptive Memory," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 198-204, May.
    13. Salewski, Frank & Bartsch, Thomas, 1994. "A comparison of genetic and greedy randomized algorithms for medium-to-short-term audit-staff scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 356, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    14. Nonobe, Koji & Ibaraki, Toshihide, 1998. "A tabu search approach to the constraint satisfaction problem as a general problem solver," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 599-623, April.
    15. Xu Wang & Guohua Gan & Ling-Yun Wu, 2020. "Framework and algorithms for identifying honest blocks in blockchain," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-14, January.
    16. Schirmer, Andreas, 1998. "Case-based reasoning and improved adaptive search for project scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 472, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    17. Böttcher, Jan & Drexl, Andreas & Kolisch, Rainer & Salewski, Frank, 1996. "Project scheduling under partially renewable resource constraints," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 398, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Raúl Martín-Santamaría & Ana D. López-Sánchez & María Luisa Delgado-Jalón & J. Manuel Colmenar, 2021. "An Efficient Algorithm for Crowd Logistics Optimization," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    19. Schirmer, Andreas & Riesenberg, Sven, 1997. "Parameterized heuristics for project scheduling: Biased random sampling methods," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 456, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    20. M. T. Alonso & R. Alvarez-Valdes & F. Parreño, 2020. "A GRASP algorithm for multi container loading problems with practical constraints," 4OR, Springer, vol. 18(1), pages 49-72, March.
    21. Panos M. Pardalos & Tianbing Qian & Mauricio G.C. Resende, 1998. "A Greedy Randomized Adaptive Search Procedure for the Feedback Vertex Set Problem," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 399-412, December.
    22. El-Ghazali Talbi, 2016. "Combining metaheuristics with mathematical programming, constraint programming and machine learning," Annals of Operations Research, Springer, vol. 240(1), pages 171-215, May.
    23. Sacramento Quintanilla & Francisco Ballestín & Ángeles Pérez, 2020. "Mathematical models to improve the current practice in a Home Healthcare Unit," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 43-74, March.
    24. Schirmer, Andreas & Riesenberg, Sven, 1998. "Class-based control schemes for parameterized project scheduling heuristics," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 471, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    25. Alejandra Casado & Sergio Pérez-Peló & Jesús Sánchez-Oro & Abraham Duarte, 2022. "A GRASP algorithm with Tabu Search improvement for solving the maximum intersection of k-subsets problem," Journal of Heuristics, Springer, vol. 28(1), pages 121-146, February.

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