IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v219y2024icp378-403.html
   My bibliography  Save this article

Modeling and solving of knapsack problem with setup based on evolutionary algorithm

Author

Listed:
  • He, Yichao
  • Wang, Jinghong
  • Liu, Xuejing
  • Wang, Xizhao
  • Ouyang, Haibin

Abstract

The knapsack problem with setup (KPS) is a combinatorial optimization problem with important application in the industrial field. In order to solve KPS more quickly and effectively with evolutionary algorithms, a new mathematical model is first established. On the basis of the random algorithm RGSA to generate the potential solution and the repair and optimization algorithm gROA to handle with the infeasible solution, an algorithm framework EA-KPS for solving KPS is given by using evolutionary algorithm. According to EA-KPS, a heuristic algorithm RA-GTOA for solving KPS is proposed by group theory-based optimization algorithm. The comparison of calculation results between RA-GTOA and six representative algorithms for solving 200 KPS benchmark instances shows that RA-GTOA is superior to others in solution accuracy, speed and robustness. This not only shows that RA-GTOA is an efficient algorithm for solving KPS, but also demonstrates that using evolutionary algorithms to solve KPS is an effective method.

Suggested Citation

  • He, Yichao & Wang, Jinghong & Liu, Xuejing & Wang, Xizhao & Ouyang, Haibin, 2024. "Modeling and solving of knapsack problem with setup based on evolutionary algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 378-403.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:378-403
    DOI: 10.1016/j.matcom.2023.12.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423005402
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.12.033?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yassine Adouani & Bassem Jarboui & Malek Masmoudi, 2020. "Efficient matheuristic for the generalised multiple knapsack problem with setup," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 14(5), pages 715-741.
    2. Ragab, Mahmoud & Roesler, Uwe, 2014. "The Quicksort process," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1036-1054.
    3. Yanchun Yang & Robert L. Bulfin, 2009. "An exact algorithm for the Knapsack Problem with Setup," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(3), pages 280-291.
    4. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Boyer, V. & Elkihel, M. & El Baz, D., 2009. "Heuristics for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(3), pages 658-664, December.
    3. Akinc, Umit, 2006. "Approximate and exact algorithms for the fixed-charge knapsack problem," European Journal of Operational Research, Elsevier, vol. 170(2), pages 363-375, April.
    4. Genserik L. L. Reniers & Kenneth Sörensen, 2013. "An Approach for Optimal Allocation of Safety Resources: Using the Knapsack Problem to Take Aggregated Cost‐Efficient Preventive Measures," Risk Analysis, John Wiley & Sons, vol. 33(11), pages 2056-2067, November.
    5. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    6. Büther, Marcel & Briskorn, Dirk, 2007. "Reducing the 0-1 knapsack problem with a single continuous variable to the standard 0-1 knapsack problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 629, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. van der Merwe, D.J. & Hattingh, J.M., 2006. "Tree knapsack approaches for local access network design," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1968-1978, November.
    8. Roesler, Uwe, 2020. "Almost sure convergence to the Quicksort process," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5290-5309.
    9. Mhand Hifi & Hedi Mhalla & Slim Sadfi, 2005. "Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 239-260, November.
    10. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    11. Benati, Stefano, 2004. "The computation of the worst conditional expectation," European Journal of Operational Research, Elsevier, vol. 155(2), pages 414-425, June.
    12. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    13. Simon Thevenin & Nicolas Zufferey & Marino Widmer, 2016. "Order acceptance and scheduling with earliness and tardiness penalties," Journal of Heuristics, Springer, vol. 22(6), pages 849-890, December.
    14. Ben O’Neill, 2022. "Smallest covering regions and highest density regions for discrete distributions," Computational Statistics, Springer, vol. 37(3), pages 1229-1254, July.
    15. Kohli, Rajeev & Krishnamurti, Ramesh & Mirchandani, Prakash, 2004. "Average performance of greedy heuristics for the integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 36-45, April.
    16. R. Pablo Arribillaga & G. Bergantiños, 2022. "Cooperative and axiomatic approaches to the knapsack allocation problem," Annals of Operations Research, Springer, vol. 318(2), pages 805-830, November.
    17. Stefan Hajkowicz & Andrew Higgins & Kristen Williams & Daniel P. Faith & Michael Burton, 2007. "Optimisation and the selection of conservation contracts," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 51(1), pages 39-56, March.
    18. Joonyup Eun & Chang Sup Sung & Eun-Seok Kim, 2017. "Maximizing total job value on a single machine with job selection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(9), pages 998-1005, September.
    19. Peter Lindberg, 2010. "Optimal partial hedging in a discrete-time market as a knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 433-451, December.
    20. Wishon, Christopher & Villalobos, J. Rene, 2016. "Robust efficiency measures for linear knapsack problem variants," European Journal of Operational Research, Elsevier, vol. 254(2), pages 398-409.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:378-403. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.