IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p602-d750456.html
   My bibliography  Save this article

A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem

Author

Listed:
  • Jaeyoung Yang

    (Samsung Electronics, 129 Samsung-ro, Yeongtong-gu, Suwon-si 16677, Korea)

  • Yong-Hyuk Kim

    (School of Software, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul 01897, Korea
    Department of Cell and Regenerative Biology, School of Medicine and Public Health, University of Wisconsin-Madison, 1111 Highland Ave., Madison, WI 53705, USA)

  • Yourim Yoon

    (Department of Computer Engineering, College of Information Technology, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si 13120, Korea)

Abstract

We propose a memetic algorithm for the multiple-choice multidimensional knapsack problem (MMKP). In this study, we focus on finding good solutions for the MMKP instances, for which feasible solutions rarely exist. To find good feasible solutions, we introduce a novel repair heuristic based on the tendency function and a genetic search for the function approximation. Even when the density of feasible solutions over the entire solution space is very low, the proposed repair heuristic could successfully change infeasible solutions into feasible ones. Based on the proposed repair heuristic and effective local search, we designed a memetic algorithm that performs well on problem instances with a low density of feasible solutions. By performing experiments, we could show the superiority of our method compared with previous genetic algorithms.

Suggested Citation

  • Jaeyoung Yang & Yong-Hyuk Kim & Yourim Yoon, 2022. "A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:602-:d:750456
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/602/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/602/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chih-Hao Lin & Chia-Chun Chuang, 2013. "A Rough Penalty Genetic Algorithm for Multicast Routing in Mobile Ad Hoc Networks," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, August.
    2. Abdelkader Sbihi, 2007. "A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 13(4), pages 337-351, May.
    3. Yourim Yoon & Yong-Hyuk Kim, 2020. "Gene-Similarity Normalization in a Genetic Algorithm for the Maximum k -Coverage Problem," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    4. Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    5. Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
    6. Junghwan Lee & Yong-Hyuk Kim, 2019. "Epistasis-Based Basis Estimation Method for Simplifying the Problem Space of an Evolutionary Search in Binary Representation," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    7. Yourim Yoon & Yong-Hyuk Kim, 2013. "A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, May.
    8. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    9. N. Cherfi & M. Hifi, 2010. "A column generation method for the multiple-choice multi-dimensional knapsack problem," Computational Optimization and Applications, Springer, vol. 46(1), pages 51-73, May.
    10. Gao, Chao & Lu, Guanzhou & Yao, Xin & Li, Jinlong, 2017. "An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 260(1), pages 1-11.
    11. Yoon, Yourim & Kim, Yong-Hyuk & Moon, Byung-Ro, 2012. "A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 366-376.
    12. Caserta, Marco & Voß, Stefan, 2015. "An exact algorithm for the reliability redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 110-116.
    13. Nawal Cherfi & Mhand Hifi, 2009. "Hybrid algorithms for the Multiple-choice Multi-dimensional Knapsack Problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 89-109.
    14. M Hifi & M Michrafy & A Sbihi, 2004. "Heuristic algorithms for the multiple-choice multidimensional knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1323-1332, December.
    15. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yong-Hyuk Kim & Fabio Caraffini, 2023. "Preface to “Swarm and Evolutionary Computation—Bridging Theory and Practice”," Mathematics, MDPI, vol. 11(5), pages 1-3, March.
    2. Xin Zhang & Yiyan Cao, 2022. "Memetic Algorithm with Isomorphic Transcoding for UAV Deployment Optimization in Energy-Efficient AIoT Data Collection," Mathematics, MDPI, vol. 10(24), pages 1-18, December.

    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. Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
    2. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
    3. Gao, Chao & Lu, Guanzhou & Yao, Xin & Li, Jinlong, 2017. "An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 260(1), pages 1-11.
    4. Diallo, Claver & Venkatadri, Uday & Khatab, Abdelhakim & Liu, Zhuojun, 2018. "Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 234-245.
    5. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    6. Ewa M. Bednarczuk & Janusz Miroforidis & Przemysław Pyzel, 2018. "A multi-criteria approach to approximate solution of multiple-choice knapsack problem," Computational Optimization and Applications, Springer, vol. 70(3), pages 889-910, July.
    7. N. Cherfi & M. Hifi, 2010. "A column generation method for the multiple-choice multi-dimensional knapsack problem," Computational Optimization and Applications, Springer, vol. 46(1), pages 51-73, May.
    8. Sylvain Barde, 2015. "Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 337-358, February.
    9. Chen, Yuning & Hao, Jin-Kao, 2014. "A “reduce and solve” approach for the multiple-choice multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(2), pages 313-322.
    10. Sylvain Barde, 2012. "Back to the future: economic rationality and maximum entropy prediction," Studies in Economics 1202, School of Economics, University of Kent.
    11. V. Van Peteghem & M. Vanhoucke, 2009. "An Artificial Immune System for the Multi-Mode Resource-Constrained Project Scheduling Problem," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/555, Ghent University, Faculty of Economics and Business Administration.
    12. Debasis Bhattacharya & Soma Roychowdhury, 2017. "A redundancy strategy for minimizing cost in systems with non-disjoint subsystems under reliability constraint," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 645-655, November.
    13. Mhand Hifi & Slim Sadfi & Abdelkader Sbihi, 2004. "An Exact Algorithm for the Multiple-choice Multidimensional Knapsack Problem," Post-Print halshs-03322716, HAL.
    14. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
    15. 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.
    16. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    17. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    18. Teng, Junn-Yuan & Tzeng, Gwo-Hshiung, 1996. "A multiobjective programming approach for selecting non-independent transportation investment alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 291-307, August.
    19. Mancini, Simona & Triki, Chefi & Piya, Sujan, 2022. "Optimal selection of touristic packages based on user preferences during sports mega-events," European Journal of Operational Research, Elsevier, vol. 302(3), pages 819-830.
    20. Yuxiong Li & Xianzhen Huang & Xinong En & Pengfei Ding, 2019. "A New System Reliability Optimization Model Based on Swapping Existing Components," Complexity, Hindawi, vol. 2019, pages 1-14, November.

    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:gam:jmathe:v:10:y:2022:i:4:p:602-:d:750456. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.