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Hybrid Optimization Algorithm of Particle Swarm Optimization with Lagrangian Relaxation for Solving the Multidimensional Knapsack Problem

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Advances in Smart Vehicular Technology, Transportation, Communication and Applications (VTCA 2018)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 128))

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Abstract

A hybrid algorithm that integrates PSO with Lagrangian relaxation is proposed for solving the multidimensional knapsack problem (MKP). An efficiency measure for MKP based on the LR dual information is defined to combine the object function and the constraints of the MKP together. The efficiency measure is used to determine the core problem for MKP with the aim of reducing the problem scale. Then a hybrid algorithm combines the Quantum Particle Swarm Optimization with a local search method is presented to solve the core problem. Numerical experiments are made on certain knapsack problems and computational results show that the proposed algorithm is very promising.

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Acknowledgements

This study was supported by the Research Program Foundation of Minjiang University under Grants No. MYK17021 and supported by the Major Project of Sichuan Province Key Laboratory of Digital Media Art under Grants No. 17DMAKL01 and supported by Fujian Province Guiding Project under Grants No. 2018H0028 and supported by National Nature Science Foundation of China (Grant number: 61871204). We also acknowledge the solution from National Natural Science Foundation of China (61772254), Key Project of College Youth Natural Science Foundation of Fujian Province (JZ160467), Fujian Provincial Leading Project(2017H0030), Fuzhou Science and Technology Planning Project (2016-S-116), Program for New Century Excellent Talents in Fujian Province University (NCETFJ) and Program for Young Scholars in Minjiang University (Mjqn201601).

Author information

Authors and Affiliations

  1. Department of Mathematics, Minjiang University, Fuzhou, 350108, People’s Republic of China

    Jinyan Luo & Geng Lin

  2. Fujian Provincial Key Laboratory of Information Processing and Intelligent Control, Minjiang University, Fuzhou, 350121, People’s Republic of China

    Fuquan Zhang

  3. Digital Performance and Simulation Technology Laboratory, School of Computer Science and Technology, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Fuquan Zhang

  4. Key Laboratory of Nondestructive Testing, Fuqing Branch of Fujian Normal University, Fuzhou, 350300, People’s Republic of China

    Lin Xu

Authors
  1. Jinyan Luo
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  2. Geng Lin
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  3. Fuquan Zhang
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  4. Lin Xu
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Corresponding author

Correspondence to Jinyan Luo .

Editor information

Editors and Affiliations

  1. College of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, China

    Yong Zhao

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

    Tsu-Yang Wu

  3. School of Transportation, Fujian University of Technology, Fuzhou, Fujian, China

    Tang-Hsien Chang

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

    Jeng-Shyang Pan

  5. University of Technology Sydney, Sydney, NSW, Australia

    Lakhmi C. Jain

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Luo, J., Lin, G., Zhang, F., Xu, L. (2019). Hybrid Optimization Algorithm of Particle Swarm Optimization with Lagrangian Relaxation for Solving the Multidimensional Knapsack Problem. In: Zhao, Y., Wu, TY., Chang, TH., Pan, JS., Jain, L. (eds) Advances in Smart Vehicular Technology, Transportation, Communication and Applications. VTCA 2018. Smart Innovation, Systems and Technologies, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-04585-2_30

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