IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1494-d806484.html
   My bibliography  Save this article

Out of the Niche: Using Direct Search Methods to Find Multiple Global Optima

Author

Listed:
  • Javier Cano

    (Department of Computer Science and Statistics, Rey Juan Carlos University, 28933 Madrid, Spain
    Department of Statistics, University of Auckland, Auckland 1010, New Zealand)

  • Cesar Alfaro

    (Department of Computer Science and Statistics, Rey Juan Carlos University, 28933 Madrid, Spain)

  • Javier Gomez

    (Department of Computer Science and Statistics, Rey Juan Carlos University, 28933 Madrid, Spain)

  • Abraham Duarte

    (Department of Computer Science and Statistics, Rey Juan Carlos University, 28933 Madrid, Spain)

Abstract

Multimodal optimization deals with problems where multiple feasible global solutions coexist. Despite sharing a common objective function value, some global optima may be preferred to others for various reasons. In such cases, it is paramount to devise methods that are able to find as many global optima as possible within an affordable computational budget. Niching strategies have received an overwhelming attention in recent years as the most suitable technique to tackle these kinds of problems. In this paper we explore a different approach, based on a systematic yet versatile use of traditional direct search methods. When tested over reference benchmark functions, our proposal, despite its apparent simplicity, noticeably resists the comparison with state-of-the-art niching methods in most cases, both in the number of global optima found and in the number of function evaluations required. However, rather than trying to outperform niching methods—far more elaborated—our aim is to enrich them with the knowledge gained from exploiting the distinctive features of direct search methods. To that end, we propose two new performance measures that can be used to evaluate, compare and monitor the progress of optimization algorithms of (possibly) very different nature in their effort to find as many global optima of a given multimodal objective function as possible. We believe that adopting these metrics as reference criteria could lead to more sophisticated and computationally-efficient algorithms, which could benefit from the brute force of derivative-free local search methods.

Suggested Citation

  • Javier Cano & Cesar Alfaro & Javier Gomez & Abraham Duarte, 2022. "Out of the Niche: Using Direct Search Methods to Find Multiple Global Optima," Mathematics, MDPI, vol. 10(9), pages 1-20, April.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1494-:d:806484
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1494/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/9/1494/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhao, Zhiwei & Yang, Jingming & Hu, Ziyu & Che, Haijun, 2016. "A differential evolution algorithm with self-adaptive strategy and control parameters based on symmetric Latin hypercube design for unconstrained optimization problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 30-45.
    2. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    3. Locatelli, Marco & Schoen, Fabio, 2012. "Local search based heuristics for global optimization: Atomic clusters and beyond," European Journal of Operational Research, Elsevier, vol. 222(1), pages 1-9.
    4. Chang, Kuo-Hao, 2012. "Stochastic Nelder–Mead simplex method – A new globally convergent direct search method for simulation optimization," European Journal of Operational Research, Elsevier, vol. 220(3), pages 684-694.
    5. Abraham Duarte & Rafael Martí & Fred Glover & Francisco Gortazar, 2011. "Hybrid scatter tabu search for unconstrained global optimization," Annals of Operations Research, Springer, vol. 183(1), pages 95-123, March.
    6. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    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. Árpád Bűrmen & Tadej Tuma, 2022. "Preface to the Special Issue on “Optimization Theory and Applications”," Mathematics, MDPI, vol. 10(24), pages 1-3, 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. 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. Jonas Bjerg Thomsen & Francesco Ferri & Jens Peter Kofoed & Kevin Black, 2018. "Cost Optimization of Mooring Solutions for Large Floating Wave Energy Converters," Energies, MDPI, vol. 11(1), pages 1-23, January.
    3. Chang, Kuo-Hao & Kuo, Po-Yi, 2018. "An efficient simulation optimization method for the generalized redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1094-1101.
    4. Cai, Yutong & Ong, Ghim Ping & Meng, Qiang, 2022. "Dynamic bicycle relocation problem with broken bicycles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    5. Gilberto F. Sousa Filho & Teobaldo L. Bulhões Júnior & Lucidio A. F. Cabral & Luiz Satoru Ochi & Fábio Protti, 2017. "New heuristics for the Bicluster Editing Problem," Annals of Operations Research, Springer, vol. 258(2), pages 781-814, November.
    6. Gabriela Simonet & Julie Subervie & Driss Ezzine-De-Blas & Marina Cromberg & Amy Duchelle, 2015. "Paying smallholders not to cut down the amazon forest: impact evaluation of a REDD+ pilot project," Working Papers 1514, Chaire Economie du climat.
    7. Somayeh Moazeni & Warren B. Powell & Boris Defourny & Belgacem Bouzaiene-Ayari, 2017. "Parallel Nonstationary Direct Policy Search for Risk-Averse Stochastic Optimization," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 332-349, May.
    8. Liu, Ling & Martín Barragán, Belén & Prieto Fernández, Francisco Javier, 2016. "A Partial parametric path algorithm for multiclass classification," DES - Working Papers. Statistics and Econometrics. WS 22390, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Venkatesh Pandiri & Alok Singh, 2020. "Two multi-start heuristics for the k-traveling salesman problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1164-1204, December.
    10. Jakubik, Johannes & Binding, Adrian & Feuerriegel, Stefan, 2021. "Directed particle swarm optimization with Gaussian-process-based function forecasting," European Journal of Operational Research, Elsevier, vol. 295(1), pages 157-169.
    11. Christophe Gouel & Nicolas Legrand, 2017. "Estimating the Competitive Storage Model with Trending Commodity Prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 744-763, June.
    12. Zhao, Jake, 2020. "Accounting for the corporate cash increase," European Economic Review, Elsevier, vol. 123(C).
    13. H. Asefi & S. Lim & M. Maghrebi & S. Shahparvari, 2019. "Mathematical modelling and heuristic approaches to the location-routing problem of a cost-effective integrated solid waste management," Annals of Operations Research, Springer, vol. 273(1), pages 75-110, February.
    14. Hannes Schwarz & Valentin Bertsch & Wolf Fichtner, 2018. "Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 265-310, January.
    15. Zhaowei Miao & Feng Yang & Ke Fu & Dongsheng Xu, 2012. "Transshipment service through crossdocks with both soft and hard time windows," Annals of Operations Research, Springer, vol. 192(1), pages 21-47, January.
    16. Breitmoser, Yves & Valasek, Justin, 2017. "A rationale for unanimity in committees," Discussion Papers, Research Unit: Economics of Change SP II 2017-308, WZB Berlin Social Science Center.
    17. Krese, Gorazd & Lampret, Žiga & Butala, Vincenc & Prek, Matjaž, 2018. "Determination of a Building's balance point temperature as an energy characteristic," Energy, Elsevier, vol. 165(PB), pages 1034-1049.
    18. Tavakol Aghaei, Vahid & Ağababaoğlu, Arda & Bawo, Biram & Naseradinmousavi, Peiman & Yıldırım, Sinan & Yeşilyurt, Serhat & Onat, Ahmet, 2023. "Energy optimization of wind turbines via a neural control policy based on reinforcement learning Markov chain Monte Carlo algorithm," Applied Energy, Elsevier, vol. 341(C).
    19. H-Y Lin & C-J Liao & C-T Tseng, 2011. "An application of variable neighbourhood search to hospital call scheduling of infant formula promotion," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 949-959, June.
    20. Andrzej Wędzik & Tomasz Siewierski & Michał Szypowski, 2019. "The Use of Black-Box Optimization Method for Determination of the Bus Connection Capacity in Electric Power Grid," Energies, MDPI, vol. 13(1), pages 1-21, December.

    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:9:p:1494-:d:806484. 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.