IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p999-d545203.html
   My bibliography  Save this article

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

Author

Listed:
  • Alberto Pajares

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Xavier Blasco

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Juan Manuel Herrero

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Miguel A. Martínez

    (Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain)

Abstract

In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature ( A r c h i v e U p d a t e P Q , ϵ D x y , A r c h i v e _ n e v M O G A , and t a r g e t S e l e c t ) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.

Suggested Citation

  • Alberto Pajares & Xavier Blasco & Juan Manuel Herrero & Miguel A. Martínez, 2021. "A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization," Mathematics, MDPI, vol. 9(9), pages 1-28, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:999-:d:545203
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/999/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/999/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cai Dai & Xiujuan Lei, 2019. "A Multiobjective Brain Storm Optimization Algorithm Based on Decomposition," Complexity, Hindawi, vol. 2019, pages 1-11, January.
    2. Alberto Pajares & Xavier Blasco & Juan M. Herrero & Gilberto Reynoso-Meza, 2018. "A Multiobjective Genetic Algorithm for the Localization of Optimal and Nearly Optimal Solutions Which Are Potentially Useful: nevMOGA," Complexity, Hindawi, vol. 2018, pages 1-22, October.
    3. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    4. Xiaojun Zhou & Jianpeng Long & Chongchong Xu & Guanbo Jia, 2019. "An External Archive-Based Constrained State Transition Algorithm for Optimal Power Dispatch," Complexity, Hindawi, vol. 2019, pages 1-11, January.
    5. O. Schütze & C. Hernández & E-G. Talbi & J. Q. Sun & Y. Naranjani & F.-R. Xiong, 2019. "Archivers for the representation of the set of approximate solutions for MOPs," Journal of Heuristics, Springer, vol. 25(1), pages 71-105, February.
    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. El Mehdi, Er Raqabi & Ilyas, Himmich & Nizar, El Hachemi & Issmaïl, El Hallaoui & François, Soumis, 2023. "Incremental LNS framework for integrated production, inventory, and vessel scheduling: Application to a global supply chain," Omega, Elsevier, vol. 116(C).
    2. Saeed Vasebi & Yeganeh M. Hayeri, 2021. "Collective Driving to Mitigate Climate Change: Collective-Adaptive Cruise Control," Sustainability, MDPI, vol. 13(16), pages 1-30, August.
    3. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    4. Oliver Stein & Maximilian Volk, 2023. "Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1156-1190, September.
    5. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    6. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    7. Francisco Salas-Molina & Juan A. Rodriguez-Aguilar & Pablo Díaz-García, 2018. "Selecting cash management models from a multiobjective perspective," Annals of Operations Research, Springer, vol. 261(1), pages 275-288, February.
    8. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    9. Mitrović, Sandra & Baesens, Bart & Lemahieu, Wilfried & De Weerdt, Jochen, 2018. "On the operational efficiency of different feature types for telco Churn prediction," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1141-1155.
    10. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.
    11. A. Garcia-Bernabeu & J. V. Salcedo & A. Hilario & D. Pla-Santamaria & Juan M. Herrero, 2019. "Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA," Complexity, Hindawi, vol. 2019, pages 1-12, December.
    12. Rebeca Ramirez Acosta & Chathura Wanigasekara & Emilie Frost & Tobias Brandt & Sebastian Lehnhoff & Christof Büskens, 2023. "Integration of Intelligent Neighbourhood Grids to the German Distribution Grid: A Perspective," Energies, MDPI, vol. 16(11), pages 1-16, May.
    13. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Papers 1706.01254, arXiv.org.
    14. Markus Hartikainen & Alberto Lovison, 2015. "PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 62(2), pages 243-261, June.
    15. Duc Nam Nguyen & Thanh-Phong Dao & Ngoc Le Chau & Van Anh Dang, 2019. "Hybrid Approach of Finite Element Method, Kigring Metamodel, and Multiobjective Genetic Algorithm for Computational Optimization of a Flexure Elbow Joint for Upper-Limb Assistive Device," Complexity, Hindawi, vol. 2019, pages 1-13, January.
    16. Hu, Shuozhuo & Li, Jian & Yang, Fubin & Yang, Zhen & Duan, Yuanyuan, 2020. "Multi-objective optimization of organic Rankine cycle using hydrofluorolefins (HFOs) based on different target preferences," Energy, Elsevier, vol. 203(C).
    17. Smedberg, Henrik & Bandaru, Sunith, 2023. "Interactive knowledge discovery and knowledge visualization for decision support in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1311-1329.
    18. Hadj Salem, Khadija & Silva, Elsa & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "Mathematical models for the two-dimensional variable-sized cutting stock problem in the home textile industry," European Journal of Operational Research, Elsevier, vol. 306(2), pages 549-566.
    19. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.
    20. Seyed Sina Mohri & Meisam Akbarzadeh, 2019. "Locating key stations of a metro network using bi-objective programming: discrete and continuous demand mode," Public Transport, Springer, vol. 11(2), pages 321-340, August.

    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:9:y:2021:i:9:p:999-:d:545203. 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.