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Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space

Author

Listed:
  • John J. Bartholdi, III

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Loren K. Platzman

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We describe a family of heuristics to solve combinatorial problems such as routing and partitioning. These heuristics exploit geometry but ignore specific distance measures. Consequently they are simple and fast, but nonetheless fairly accurate, and so seem well-suited to operational problems where time or computing resources are limited. We survey promising new application areas, and show how procedures may be customized to reflect the structure of particular applications.

Suggested Citation

  • John J. Bartholdi, III & Loren K. Platzman, 1988. "Heuristics Based on Spacefilling Curves for Combinatorial Problems in Euclidean Space," Management Science, INFORMS, vol. 34(3), pages 291-305, March.
    • Handle: RePEc:inm:ormnsc:v:34:y:1988:i:3:p:291-305
    DOI: 10.1287/mnsc.34.3.291
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    Cited by:

    1. Liu, Yu-Hsin, 2008. "Diversified local search strategy under scatter search framework for the probabilistic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 332-346, December.
    2. Schmitt, Lawrence J. & Amini, Mohammad M., 1998. "Performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation: An empirical study," European Journal of Operational Research, Elsevier, vol. 108(3), pages 551-570, August.
    3. Bertsimas, Dimitris & Chervi, Philippe. & Peterson, Michael., 1991. "Computational approaches to stochastic vehicle routing problems," Working papers 3285-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. L’Ecuyer, Pierre & Munger, David & Lécot, Christian & Tuffin, Bruno, 2018. "Sorting methods and convergence rates for Array-RQMC: Some empirical comparisons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 191-201.
    5. Bertsimas, Dimitris & Van Ryzin, Garrett., 1991. "Stochastic and dynamic vehicle routing with general demand and interarrival time distributions," Working papers 3314-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    7. Bertsimas, Dimitris & Van Ryzin, Garrett., 1991. "A stochastic and dynamic vehicle routing problem in the Euclidean plane," Working papers 3286-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Kemal Ihsan Kilic & Leonardo Mostarda, 2022. "Novel Concave Hull-Based Heuristic Algorithm For TSP," SN Operations Research Forum, Springer, vol. 3(2), pages 1-45, June.
    9. Pan, C-H. & Liu, S-Y., 1995. "A comparative study of order batching algorithms," Omega, Elsevier, vol. 23(6), pages 691-700, December.
    10. Chris Clifton & Ananth Iyer & Richard Cho & Wei Jiang & Murat Kantarc{i}ou{g}lu & Jaideep Vaidya, 2008. "An Approach to Securely Identifying Beneficial Collaboration in Decentralized Logistics Systems," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 108-125, January.
    11. Bowerman, Robert & Hall, Brent & Calamai, Paul, 1995. "A multi-objective optimization approach to urban school bus routing: Formulation and solution method," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 107-123, March.
    12. Warren B. Powell & Wayne Snow & Raymond K. Cheung, 2000. "Adaptive Labeling Algorithms for the Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 34(1), pages 50-66, February.

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    Keywords

    integer algorithms; heuristic;

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