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Interval estimation of a global optimum for large combinatorial problems

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  • Bruce L. Golden
  • Frank B. Alt

Abstract

Consider an “intractable” optimization problem for which no efficient solution technique exists. Given a systematic procedure for generating independent heuristic solutions, we seek to obtain interval estimates for the globally optimal solution using statistical inference. In previous work, accurate point estimates have been derived. Determining interval estimates, however, is a considerably more difficult task. In this paper, we develop straightforward procedures which compute confidence intervals efficiently in order to evaluate heuristic solutions and assess deviations from optimality. The strategy presented is applicable to a host of combinatorial optimization problems. The assumptions of our model, along with computational experience, are discussed.

Suggested Citation

  • Bruce L. Golden & Frank B. Alt, 1979. "Interval estimation of a global optimum for large combinatorial problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(1), pages 69-77, March.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:1:p:69-77
    DOI: 10.1002/nav.3800260108
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    Cited by:

    1. Robert L. Nydick & Howard J. Weiss, 1994. "An analytical evaluation of optimal solution value estimation procedures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(2), pages 189-202, March.
    2. Kenneth Carling & Xiangli Meng, 2016. "On statistical bounds of heuristic solutions to location problems," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1518-1549, May.
    3. Constantine Goulimis & Gaston Simone, 2020. "Reel Stock Analysis for an Integrated Paper Packaging Company," Papers 2011.05858, arXiv.org, revised Nov 2020.

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