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DGSA: discrete gravitational search algorithm for solving knapsack problem

Author

Listed:
  • Hedieh Sajedi

    (University of Tehran)

  • Seyedeh Fatemeh Razavi

    (University of Tehran)

Abstract

The 0–1 knapsack problem is one of the classic NP-hard problems. It is an open issue in discrete optimization problems, which plays an important role in the real applications. Therefore, several algorithms have been developed to solve it. The Gravitational Search Algorithm (GSA) is an optimization algorithm based on the law of gravity and mass interactions. In the GSA, the searcher agents are a collection of masses that interact with each other based on the Newtonian gravity and the laws of motion. In this algorithm the position of the agents can be considered as the solutions. The GSA is a nature-inspired algorithm that is used for finding the optimum value of continuous functions. This paper introduces a Discrete version of the GSA (DGSA) for solving 0–1 knapsack problem. In this regard, we introduce an approach for discretely updating the position of each agent. In addition, a fitness function has been proposed for 0–1 knapsack problem. Our experimental results show the effectiveness of the DGSA in comparison with other similar algorithms in terms of the accuracy and overcoming the defect of local convergence.

Suggested Citation

  • Hedieh Sajedi & Seyedeh Fatemeh Razavi, 2017. "DGSA: discrete gravitational search algorithm for solving knapsack problem," Operational Research, Springer, vol. 17(2), pages 563-591, July.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0240-2
    DOI: 10.1007/s12351-016-0240-2
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    References listed on IDEAS

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    1. Shams, Masumeh & Rashedi, Esmat & Hakimi, Ahmad, 2015. "Clustered-gravitational search algorithm and its application in parameter optimization of a low noise amplifier," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 436-453.
    2. Wan-li Xiang & Mei-qing An & Yin-zhen Li & Rui-chun He & Jing-fang Zhang, 2014. "A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, April.
    3. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
    4. Mavrotas, George & Diakoulaki, Danae & Kourentzis, Athanasios, 2008. "Selection among ranked projects under segmentation, policy and logical constraints," European Journal of Operational Research, Elsevier, vol. 187(1), pages 177-192, May.
    5. Lin, Feng-Tse, 2008. "Solving the knapsack problem with imprecise weight coefficients using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 185(1), pages 133-145, February.
    6. Florios, Kostas & Mavrotas, George & Diakoulaki, Danae, 2010. "Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 203(1), pages 14-21, May.
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