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A New Approximation Algorithm for the d-dimensional Knapsack Problem Based on Hopfield Networks

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Recent Advances in Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2018)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 109))

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Abstract

In this paper, we study the d-dimensional knapsack problem (d-KP). The problem d-KP is a generalized version of the well-known knapsack problem (1-KP) which is known to be an NP-complete problem. It is also known that there is no fully polynomial-time approximation scheme for d-KP for \(d >1\) unless \(P=NP\). In this work, we design an approximation algorithm for d-KP based on the Hopfield networks. Experimental results show that our proposed algorithm outperforms a well-known greedy algorithm in many cases.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taipei University, New Taipei City, Taiwan

    Hsin-Lung Wu, Jui-Sheng Chang & Jen-Chun Chang

Authors
  1. Hsin-Lung Wu
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  2. Jui-Sheng Chang
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  3. Jen-Chun Chang
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Corresponding author

Correspondence to Hsin-Lung Wu .

Editor information

Editors and Affiliations

  1. College of Information Science and Engineering, Fujian University of Technology, Fuzhou, Fujian, China

    Jeng-Shyang Pan

  2. Graduate School of Engineering, Tohoku University, Sendai, Miyagi, Japan

    Akinori Ito

  3. Swinburne University of Technology, Hawthorn, VIC, Australia

    Pei-Wei Tsai

  4. Centre for Artificial Intelligence, Faculty of Engineering and Information Technology, University of Technology Sydney, Canberra, ACT, Australia

    Lakhmi C. Jain

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Wu, HL., Chang, JS., Chang, JC. (2019). A New Approximation Algorithm for the d-dimensional Knapsack Problem Based on Hopfield Networks. In: Pan, JS., Ito, A., Tsai, PW., Jain, L. (eds) Recent Advances in Intelligent Information Hiding and Multimedia Signal Processing. IIH-MSP 2018. Smart Innovation, Systems and Technologies, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-03745-1_5

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