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Worst-Case Analysis of Heuristic Algorithms

Author

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  • Marshall L. Fisher

    (University of Pennsylvania)

Abstract

The increased focus on heuristics for the approximate solution of integer programs has led to more sophisticated analysis methods for studying their performance. This paper is concerned with the worst-case approach to the analysis of heuristic performance. A worst-case study establishes the maximum deviation from optimality that can occur when a specified heuristic is applied within a given problem class. This is an important piece of information that can be combined with empirical testing and other analyses to provide a more complete evaluation of a heuristic. In this paper the basic ground rules of worst-case analysis of heuristics are reviewed, and a large variety of the existing types of worst-case results are described in terms of the knapsack problem. A selected sample of results for four other problems is given. The paper concludes with a discussion of possibilities for further research.

Suggested Citation

  • Marshall L. Fisher, 1980. "Worst-Case Analysis of Heuristic Algorithms," Management Science, INFORMS, vol. 26(1), pages 1-17, January.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:1:p:1-17
    DOI: 10.1287/mnsc.26.1.1
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    Citations

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    Cited by:

    1. Kohli, Rajeev & Krishnamurti, Ramesh & Mirchandani, Prakash, 2004. "Average performance of greedy heuristics for the integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 36-45, April.
    2. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    3. 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.
    4. Kwon, Roy H., 2005. "Data dependent worst case bounds for weighted set packing," European Journal of Operational Research, Elsevier, vol. 167(1), pages 68-76, November.
    5. Nicholas G. Hall, 1989. "The inventory packing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 399-418, August.
    6. Hauser, John R. & Urban, Glen L. & Weinberg, Bruce D., 1992. "Time flies when you're having fun : how consumers allocate their time when evaluating products," Working papers 3439-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Nicholas G. Hall & Marc E. Posner, 2001. "Generating Experimental Data for Computational Testing with Machine Scheduling Applications," Operations Research, INFORMS, vol. 49(6), pages 854-865, December.
    8. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    9. Sharma, R.R.K. & Berry, V., 2007. "Developing new formulations and relaxations of single stage capacitated warehouse location problem (SSCWLP): Empirical investigation for assessing relative strengths and computational effort," European Journal of Operational Research, Elsevier, vol. 177(2), pages 803-812, March.
    10. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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