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Bayesian Stopping Rules for Greedy Randomized Procedures

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Abstract

A greedy randomized adaptive search procedure (GRASP) is proposed for the approximate solution of general mixed binary programming problems (MBP). Examples are provided of practical applications that can be formulated as MBP requiring the solution of a large number of problem instances. This justifies, from both a practical and a theoretical perspective, the development of stopping rules aimed at controlling the number of iterations in a GRASP. To this end, a bayesian framework is laid down, two different prior distributions are proposed and stopping conditions are explicitly derived in analytical form. Numerical evidence shows that the stopping rules lead to an optimal trade-off between accuracy and computational effort, saving from unneeded iterations and still achieving good approximations.

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References

  1. Betrò B., Schoen F. (1987) Sequential stopping rules for the multistart algorithm in global optimisation. Math. Program. 38, 271–286

    Article  Google Scholar 

  2. Betrò B., Schoen F. (1992) Optimal and suboptimal stopping rules for the multistart algorithm in global optimisation. Math. Program. 57, 445–458

    Article  Google Scholar 

  3. Betrò B., Vercellis C. (1986) Bayesian nonparametric inference and Monte Carlo optimization. Optimization 17, 681–694

    Article  Google Scholar 

  4. Boender C., Rinnooy Kan A. (1987) Bayesian stopping rules for multistart global optimization methods. Math. Program. 37, 59–80

    Article  Google Scholar 

  5. Boender C., Rinnooy Kan A., Vercellis, C. Stochastic Optimization Methods. pp. 94–112. World Scientific (1987)

  6. Canuto S., Resende M., Ribeiro C. (2001) Local search with perturbations for the prize-collecting steiner tree problem in graphs. Networks 38, 50–58

    Article  Google Scholar 

  7. Feo T., Resende M. (1995) Greedy randomized adaptative search procedures. J. Global Optimiz. 6, 109–133

    Article  Google Scholar 

  8. Festa, P., Resende, M. GRASP: An Annotated Bibliography. pp. 325–367. Kluwer Academic Publishers (2002)

  9. Fumero F., Vercellis C. (1996) Capacity management through lagrangean relaxation: an application to tires production. Prod. Plan. Control 7, 604–614

    Article  Google Scholar 

  10. Fumero F., Vercellis C. (1997) Integrating distribution, lot-sizing and machine loading via lagrangean relaxation. Int. J. Prod. Econ. 49, 45–54

    Article  Google Scholar 

  11. Hart W. (1999) Sequential stopping rules for random optimization methods with applications to multistart local search. SIAM J. Optimiz. 9, 270–290

    Article  Google Scholar 

  12. Hettich, S., Blake C., Merz, C. UCI repository of machine learning databases. (1998). URL http://www.ics.uci.edu/~mlearn/MLRepository.html

  13. Orsenigo C., Vercellis C. (2003) Multivariate classification trees based on minimum features discrete support vector machines. IMA J. Manage. Math. 14, 221–234

    Article  Google Scholar 

  14. Orsenigo C., Vercellis C. (2004a) Discrete support vector decision trees via tabu-search. J. Comput. Stat. Data Anal. 47, 311–322

    Article  Google Scholar 

  15. Orsenigo, C., Vercellis, C. One-against-all multicategory classification via discrete support vector machines. In: Ebecken N. et al. (eds.) Data Mining IV. pp. 255–264. WIT Press (2004b)

  16. Prais M., Ribeiro C. (2000) Reactive grasp: An application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J. Comput. 12, 164–176

    Article  Google Scholar 

  17. Resende, M., Ribeiro, C. Greedy Randomized Adaptive Search Procedures. pp. 219–249. Kluwer Academic Publishers (2003)

  18. Wilks, S. Mathematical Statistics. Wiley (1962)

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Correspondence to Carlo Vercellis.

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Orsenigo, C., Vercellis, C. Bayesian Stopping Rules for Greedy Randomized Procedures. J Glob Optim 36, 365–377 (2006). https://doi.org/10.1007/s10898-006-9014-3

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  • DOI: https://doi.org/10.1007/s10898-006-9014-3

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