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Heuristic And Exact Solution Method For Convex Nonlinear Knapsack Problem

Author

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  • BIN ZHANG

    (Lingnan College, Sun Yat-Sen University, Guangzhou 510275, P. R. China)

  • BO CHEN

    (School of Management, Hefei University of Technology, Hefei, Anhui 230009, P. R. China)

Abstract

In this paper, we consider a class of convex nonlinear knapsack problems in which all decision variables are integer and the objective and knapsack functions are nonlinear. This generalized problem is characterized by positive marginal cost (PMC) and increasing marginal loss-cost ratio (IMLCR). By analyzing the structural properties of the problem, we develop an efficient heuristic and propose search and branching rules to improve the branch and bound method for solving exact solution. Numerical study is done for showing the effectiveness of the proposed heuristic and the modified branch and bound method.

Suggested Citation

  • Bin Zhang & Bo Chen, 2012. "Heuristic And Exact Solution Method For Convex Nonlinear Knapsack Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-14.
    • Handle: RePEc:wsi:apjorx:v:29:y:2012:i:05:n:s0217595912500315
    DOI: 10.1142/S0217595912500315
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    References listed on IDEAS

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    1. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, April.
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    Cited by:

    1. Evgeny Gurevsky & Dmitry Kopelevich & Sergey Kovalev & Mikhail Y. Kovalyov, 2023. "Integer knapsack problems with profit functions of the same value range," 4OR, Springer, vol. 21(3), pages 405-419, September.

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