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Minimum and Worst-Case Performance Ratios of Rollout Algorithms

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  • Luca Bertazzi

    (University of Brescia)

Abstract

Rollout algorithms are heuristic algorithms that can be applied to solve deterministic and stochastic dynamic programming problems. The basic idea is to use the cost obtained by applying a well known heuristic, called the base policy, to approximate the value of the optimal cost-to-go. We develop a theoretical approach to prove, for the 0-1 knapsack problem, that the minimum performance ratio of the rollout algorithms tends to be significantly greater when the performance ratio of the corresponding base policy is poor and that the worst-case performance ratio is significantly better than the one of the corresponding base policies.

Suggested Citation

  • Luca Bertazzi, 2012. "Minimum and Worst-Case Performance Ratios of Rollout Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 378-393, February.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9902-7
    DOI: 10.1007/s10957-011-9902-7
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Ramazan Demir, 2002. "An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems," Management Science, INFORMS, vol. 48(4), pages 550-565, April.
    2. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    3. F. Guerriero, 2008. "Hybrid Rollout Approaches for the Job Shop Scheduling Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 419-438, November.
    4. Hans Kellerer & Ulrich Pferschy, 1999. "A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 59-71, July.
    5. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
    6. Caprara, Alberto & Kellerer, Hans & Pferschy, Ulrich & Pisinger, David, 2000. "Approximation algorithms for knapsack problems with cardinality constraints," European Journal of Operational Research, Elsevier, vol. 123(2), pages 333-345, June.
    7. Hans Kellerer & Ulrich Pferschy, 2004. "Improved Dynamic Programming in Connection with an FPTAS for the Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 5-11, March.
    8. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
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    Cited by:

    1. Andrew Mastin & Patrick Jaillet, 2015. "Average-Case Performance of Rollout Algorithms for Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 964-984, June.
    2. Goodson, Justin C. & Thomas, Barrett W. & Ohlmann, Jeffrey W., 2017. "A rollout algorithm framework for heuristic solutions to finite-horizon stochastic dynamic programs," European Journal of Operational Research, Elsevier, vol. 258(1), pages 216-229.
    3. Bertazzi, Luca & Secomandi, Nicola, 2018. "Faster rollout search for the vehicle routing problem with stochastic demands and restocking," European Journal of Operational Research, Elsevier, vol. 270(2), pages 487-497.
    4. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    5. Zhenyuan Liu & Jiongbing Lu & Zaisheng Liu & Guangrui Liao & Hao Howard Zhang & Junwu Dong, 2019. "Patient scheduling in hemodialysis service," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 337-362, January.

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