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The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance

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  • Raymond R. Hill

    () (Air Force Institute of Technology, AFIT/ENS, Building 640, 2950 P Street, Wright-Patterson Air Force Base, Ohio 45433-7765)

  • Charles H. Reilly

    () (Department of Industrial Engineering and Management Systems, University of Central Florida, 4000 Central Florida Boulevard, P.O. Box 162450, Orlando, Florida 32816-2450)

Abstract

This paper presents the results of an empirical study of the effects of coefficient correlation structure and constraint slackness settings on the performance of solution procedures on synthetic two-dimensional knapsack problems (2KP). The population correlation structure among 2KP coefficients, the level of constraint slackness, and the type of correlation (product moment or rank) are varied in this study. Representative branch-and-bound and heuristic solution procedures are used to investigate the influence of these problem parameters on solution procedure performance. Population correlation structure, and in particular the interconstraint component of the correlation structure, is found to be a significant factor influencing the performance of both the algorithm and the heuristic. In addition, the interaction between constraint slackness and population correlation structure is found to influence solution procedure performance.

Suggested Citation

  • Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:302-317
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    File URL: http://dx.doi.org/10.1287/mnsc.46.2.302.11930
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    References listed on IDEAS

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    1. Frieze, A. M. & Clarke, M. R. B., 1984. "Approximation algorithms for the m-dimensional 0-1 knapsack problem: Worst-case and probabilistic analyses," European Journal of Operational Research, Elsevier, vol. 15(1), pages 100-109, January.
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    Citations

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    Cited by:

    1. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    2. Vasquez, Michel & Vimont, Yannick, 2005. "Improved results on the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 165(1), pages 70-81, August.
    3. Lutfu Sagbansua, 2009. "A New Algorithm for Minimum Cost MRGAP," European Journal of Economic and Political Studies, Fatih University, vol. 2(2), pages 23-40.
    4. Reilly, Charles H. & Sapkota, Nabin, 2015. "A family of composite discrete bivariate distributions with uniform marginals for simulating realistic and challenging optimization-problem instances," European Journal of Operational Research, Elsevier, vol. 241(3), pages 642-652.

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