IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2022i1p17-d1009604.html
   My bibliography  Save this article

A Partition-Based Random Search Method for Multimodal Optimization

Author

Listed:
  • Ziwei Lin

    (Politecnico di Milano, Department of Mechanical Engineering, 20133 Milan, Italy)

  • Andrea Matta

    (Politecnico di Milano, Department of Mechanical Engineering, 20133 Milan, Italy)

  • Sichang Du

    (Department of Industrial Engineering and Management, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Evren Sahin

    (Laboratoire Genie Industriel, CentraleSupelec, Paris Saclay University, 3 Rue Joliot-Curie, 91192 Gif-sur-Yvette, France)

Abstract

Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima.

Suggested Citation

  • Ziwei Lin & Andrea Matta & Sichang Du & Evren Sahin, 2022. "A Partition-Based Random Search Method for Multimodal Optimization," Mathematics, MDPI, vol. 11(1), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:17-:d:1009604
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/1/17/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/1/17/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. L. Jeff Hong & Barry L. Nelson, 2006. "Discrete Optimization via Simulation Using COMPASS," Operations Research, INFORMS, vol. 54(1), pages 115-129, February.
    2. Jie Xu & Barry L. Nelson & L. Jeff Hong, 2013. "An Adaptive Hyperbox Algorithm for High-Dimensional Discrete Optimization via Simulation Problems," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 133-146, February.
    3. Leyuan Shi & Sigurdur Ólafsson, 2009. "The Nested Partitions Method," International Series in Operations Research & Management Science, in: Nested Partitions Method, Theory and Applications, chapter 2, pages 19-46, Springer.
    4. Socha, Krzysztof & Dorigo, Marco, 2008. "Ant colony optimization for continuous domains," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1155-1173, March.
    5. Leyuan Shi & Sigurdur Ólafsson, 2009. "Nested Partitions Method, Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-71909-2, April.
    6. M. M. Ali & C. Storey & A. Törn, 1997. "Application of Stochastic Global Optimization Algorithms to Practical Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 545-563, December.
    7. Smrutiranjan Nayak & Sanjeeb Kumar Kar & Subhransu Sekhar Dash & Pradeep Vishnuram & Sudhakar Babu Thanikanti & Benedetto Nastasi, 2022. "Enhanced Salp Swarm Algorithm for Multimodal Optimization and Fuzzy Based Grid Frequency Controller Design," Energies, MDPI, vol. 15(9), pages 1-22, April.
    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. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    2. Jia, Shuai & Li, Chung-Lun & Xu, Zhou, 2020. "A simulation optimization method for deep-sea vessel berth planning and feeder arrival scheduling at a container port," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 174-196.
    3. Chang, Kuo-Hao & Chen, Tzu-Li & Yang, Fu-Hao & Chang, Tzu-Yin, 2023. "Simulation optimization for stochastic casualty collection point location and resource allocation problem in a mass casualty incident," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1237-1262.
    4. Lihua Sun & L. Jeff Hong & Zhaolin Hu, 2014. "Balancing Exploitation and Exploration in Discrete Optimization via Simulation Through a Gaussian Process-Based Search," Operations Research, INFORMS, vol. 62(6), pages 1416-1438, December.
    5. Zhou, Tianli & Fields, Evan & Osorio, Carolina, 2023. "A data-driven discrete simulation-based optimization algorithm for car-sharing service design," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
    6. Snoeck, André & Winkenbach, Matthias & Fransoo, Jan C., 2023. "On-demand last-mile distribution network design with omnichannel inventory," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 180(C).
    7. Snoeck, André & Winkenbach, Matthias & Fransoo, Jan C., 2023. "On-demand last-mile distribution network design with omnichannel inventory," Other publications TiSEM 83b06c9f-2a65-4aaf-880b-2, Tilburg University, School of Economics and Management.
    8. Deniz Preil & Michael Krapp, 2023. "Genetic multi-armed bandits: a reinforcement learning approach for discrete optimization via simulation," Papers 2302.07695, arXiv.org.
    9. Bera, Sasadhar & Mukherjee, Indrajit, 2016. "A multistage and multiple response optimization approach for serial manufacturing system," European Journal of Operational Research, Elsevier, vol. 248(2), pages 444-452.
    10. Zhang, Zhe & Song, Xiaoling & Gong, Xue & Yin, Yong & Lev, Benjamin & Zhou, Xiaoyang, 2024. "Coordinated seru scheduling and distribution operation problems with DeJong’s learning effects," European Journal of Operational Research, Elsevier, vol. 313(2), pages 452-464.
    11. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    12. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    13. Alfieri, Arianna & Matta, Andrea, 2012. "Mathematical programming formulations for approximate simulation of multistage production systems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 773-783.
    14. Arianna Alfieri & Andrea Matta & Giulia Pedrielli, 2015. "Mathematical programming models for joint simulation–optimization applied to closed queueing networks," Annals of Operations Research, Springer, vol. 231(1), pages 105-127, August.
    15. P. Kaelo & M. M. Ali, 2006. "Some Variants of the Controlled Random Search Algorithm for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 253-264, August.
    16. Ali, M.M., 2007. "Synthesis of the [beta]-distribution as an aid to stochastic global optimization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 133-149, September.
    17. Qi Fan & Jiaqiao Hu, 2018. "Surrogate-Based Promising Area Search for Lipschitz Continuous Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 677-693, November.
    18. Anand Kumar & Manoj Thakur & Garima Mittal, 2018. "A new ants interaction scheme for continuous optimization problems," 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. 9(4), pages 784-801, August.
    19. Nikolaos Ploskas & Nikolaos V. Sahinidis, 2022. "Review and comparison of algorithms and software for mixed-integer derivative-free optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 433-462, March.
    20. Ozgur Kisi & Armin Azad & Hamed Kashi & Amir Saeedian & Seyed Ali Asghar Hashemi & Salar Ghorbani, 2019. "Modeling Groundwater Quality Parameters Using Hybrid Neuro-Fuzzy Methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(2), pages 847-861, January.

    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:11:y:2022:i:1:p:17-:d:1009604. 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.