IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v27y2021i4d10.1007_s10732-021-09470-4.html
   My bibliography  Save this article

Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics

Author

Listed:
  • Mohamed Abouhawwash

    (Mansoura University
    Michigan State University)

  • Kalyanmoy Deb

    (Michigan State University)

Abstract

In a preference-based multi-objective optimization task, the goal is to find a subset of the Pareto-optimal set close to a supplied set of aspiration points. The reference point based non-dominated sorting genetic algorithm (R-NSGA-II) was proposed for such problem-solving tasks. R-NSGA-II aims to finding Pareto-optimal points close, in the sense of Euclidean distance in the objective space, to the supplied aspiration points, instead of finding the entire Pareto-optimal set. In this paper, R-NSGA-II method is modified using recently proposed Karush–Kuhn–Tucker proximity measure (KKTPM) and achievement scalarization function (ASF) metrics, instead of Euclidean distance metric. While a distance measure may not produce desired solutions, KKTPM-based distance measure allows a theoretically-convergent local or global Pareto solutions satisfying KKT optimality conditions and the ASF measure allows Pareto-compliant solutions to be found. A new technique for calculating KKTPM measure of a solution in the presence of an aspiration point is developed in this paper. The proposed modified R-NSGA-II methods are able to solve as many as 10-objective problems as effectively or better than the existing R-NSGA-II algorithm.

Suggested Citation

  • Mohamed Abouhawwash & Kalyanmoy Deb, 2021. "Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics," Journal of Heuristics, Springer, vol. 27(4), pages 575-614, August.
    • Handle: RePEc:spr:joheur:v:27:y:2021:i:4:d:10.1007_s10732-021-09470-4
    DOI: 10.1007/s10732-021-09470-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-021-09470-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-021-09470-4?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. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
    2. 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.
    3. Shukla, Pradyumn Kumar & Deb, Kalyanmoy, 2007. "On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1630-1652, September.
    4. Xiaoning Shen & Yu Guo & Qingwei Chen & Weili Hu, 2010. "A multi-objective optimization evolutionary algorithm incorporating preference information based on fuzzy logic," Computational Optimization and Applications, Springer, vol. 46(1), pages 159-188, May.
    5. Christian Lücken & Benjamín Barán & Carlos Brizuela, 2014. "A survey on multi-objective evolutionary algorithms for many-objective problems," Computational Optimization and Applications, Springer, vol. 58(3), pages 707-756, July.
    6. Molina, Julin & Santana, Luis V. & Hernandez-Daz, Alfredo G. & Coello Coello, Carlos A. & Caballero, Rafael, 2009. "g-dominance: Reference point based dominance for multiobjective metaheuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 685-692, September.
    7. Dariush Khezrimotlagh & Yao Chen, 2018. "The Optimization Approach," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 107-134, Springer.
    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. 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.
    2. Wang, Long & Wang, Tongguang & Wu, Jianghai & Chen, Guoping, 2017. "Multi-objective differential evolution optimization based on uniform decomposition for wind turbine blade design," Energy, Elsevier, vol. 120(C), pages 346-361.
    3. He, Li-Jun & Ju, Xue-Wei & Zhang, Wei-Bo, 2018. "A fitness assignment strategy based on the grey and entropy parallel analysis and its application to MOEAAuthor-Name: Zhu, Guang-Yu," European Journal of Operational Research, Elsevier, vol. 265(3), pages 813-828.
    4. Wang, Yongli & Wang, Yudong & Huang, Yujing & Yang, Jiale & Ma, Yuze & Yu, Haiyang & Zeng, Ming & Zhang, Fuwei & Zhang, Yanfu, 2019. "Operation optimization of regional integrated energy system based on the modeling of electricity-thermal-natural gas network," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Yang, Lin & Pang, Shujiang & Wang, Xiaoyan & Du, Yi & Huang, Jieyu & Melching, Charles S., 2021. "Optimal allocation of best management practices based on receiving water capacity constraints," Agricultural Water Management, Elsevier, vol. 258(C).
    10. Wu, Jiansong & Zhang, Linlin & Bai, Yiping & Reniers, Genserik, 2022. "A safety investment optimization model for power grid enterprises based on System Dynamics and Bayesian network theory," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    11. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    12. 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.
    13. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    14. Wang, Yongli & Li, Jiapu & Wang, Shuo & Yang, Jiale & Qi, Chengyuan & Guo, Hongzhen & Liu, Ximei & Zhang, Hongqing, 2020. "Operational optimization of wastewater reuse integrated energy system," Energy, Elsevier, vol. 200(C).
    15. 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.
    16. Changyu Zhou & Guohe Huang & Jiapei Chen, 2019. "A Type-2 Fuzzy Chance-Constrained Fractional Integrated Modeling Method for Energy System Management of Uncertainties and Risks," Energies, MDPI, vol. 12(13), pages 1-21, June.
    17. Hu, Lin & Hu, Xiaosong & Che, Yunhong & Feng, Fei & Lin, Xianke & Zhang, Zhiyong, 2020. "Reliable state of charge estimation of battery packs using fuzzy adaptive federated filtering," Applied Energy, Elsevier, vol. 262(C).
    18. Hao, Ran & Lu, Tianguang & Ai, Qian & Wang, Zhe & Wang, Xiaolong, 2020. "Distributed online learning and dynamic robust standby dispatch for networked microgrids," Applied Energy, Elsevier, vol. 274(C).
    19. Yuhong Shuai & Liming Yao, 2021. "Adjustable Robust Optimization for Multi-Period Water Allocation in Droughts Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(12), pages 4043-4065, September.
    20. Yinhe Bu & Xingping Zhang, 2021. "On the Way to Integrate Increasing Shares of Variable Renewables in China: Experience from Flexibility Modification and Deep Peak Regulation Ancillary Service Market Based on MILP-UC Programming," Sustainability, MDPI, vol. 13(5), pages 1-22, February.

    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:spr:joheur:v:27:y:2021:i:4:d:10.1007_s10732-021-09470-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.