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The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm

Author

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  • Yanhong Feng

    (School of Economics and Management, China University of Geosciences, Beijing 100083, China
    Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Natural Resources, Beijing 100083, China
    School of Information Engineering, Hebei GEO University, Shijiazhuang 050031, China)

  • Haizhong An

    (School of Economics and Management, China University of Geosciences, Beijing 100083, China
    Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Natural Resources, Beijing 100083, China)

  • Xiangyun Gao

    (School of Economics and Management, China University of Geosciences, Beijing 100083, China
    Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Natural Resources, Beijing 100083, China)

Abstract

Moth search (MS) algorithm, originally proposed to solve continuous optimization problems, is a novel bio-inspired metaheuristic algorithm. At present, there seems to be little concern about using MS to solve discrete optimization problems. One of the most common and efficient ways to discretize MS is to use a transfer function, which is in charge of mapping a continuous search space to a discrete search space. In this paper, twelve transfer functions divided into three families, S-shaped (named S1, S2, S3, and S4), V-shaped (named V1, V2, V3, and V4), and other shapes (named O1, O2, O3, and O4), are combined with MS, and then twelve discrete versions MS algorithms are proposed for solving set-union knapsack problem (SUKP). Three groups of fifteen SUKP instances are employed to evaluate the importance of these transfer functions. The results show that O4 is the best transfer function when combined with MS to solve SUKP. Meanwhile, the importance of the transfer function in terms of improving the quality of solutions and convergence rate is demonstrated as well.

Suggested Citation

  • Yanhong Feng & Haizhong An & Xiangyun Gao, 2018. "The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm," Mathematics, MDPI, vol. 7(1), pages 1-25, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:17-:d:193027
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    References listed on IDEAS

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    1. M. Fernanda P. Costa & Ana Maria A. C. Rocha & Rogério B. Francisco & Edite M. G. P. Fernandes, 2014. "Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization," Advances in Operations Research, Hindawi, vol. 2014, pages 1-12, October.
    2. Yang, Xinan & Vernitski, Alexei & Carrea, Laura, 2016. "An approximate dynamic programming approach for improving accuracy of lossy data compression by Bloom filters," European Journal of Operational Research, Elsevier, vol. 252(3), pages 985-994.
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    Cited by:

    1. Marcelo Becerra-Rozas & José Lemus-Romani & Felipe Cisternas-Caneo & Broderick Crawford & Ricardo Soto & Gino Astorga & Carlos Castro & José García, 2022. "Continuous Metaheuristics for Binary Optimization Problems: An Updated Systematic Literature Review," Mathematics, MDPI, vol. 11(1), pages 1-32, December.

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