IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v26y2020i4d10.1007_s10732-020-09438-w.html
   My bibliography  Save this article

Pareto-based evolutionary multiobjective approaches and the generalized Nash equilibrium problem

Author

Listed:
  • Rodica Ioana Lung

    (Babes-Bolyai University)

  • Noémi Gaskó

    (Babes-Bolyai University)

  • Mihai Alexandru Suciu

    (Babes-Bolyai University)

Abstract

Pareto-based evolutionary multiobjective approaches are methods that use the Pareto dominance concept to guide the search of evolutionary algorithms towards the Pareto frontier of a problem. To address the challenge of providing an entire set of optimal solutions they use specially designed mechanisms for preserving search diversity and maintaining the non-dominated solutions set. The limitation of the Pareto dominance relation in high-dimensional spaces has rendered these methods inefficient for many-objective optimization. In this paper we aim to exploit existing Pareto-based methods to compute the generalized Nash equilibrium for multi-player games by replacing the Pareto dominance relation with an equilibrium generative relation. The generalized Nash equilibrium extends the Nash equilibrium concept by considering constraints over players’ strategies. Numerical experiments indicate that the selected methods can be employed for equilibria computation even for games with up to twenty players.

Suggested Citation

  • Rodica Ioana Lung & Noémi Gaskó & Mihai Alexandru Suciu, 2020. "Pareto-based evolutionary multiobjective approaches and the generalized Nash equilibrium problem," Journal of Heuristics, Springer, vol. 26(4), pages 561-584, August.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:4:d:10.1007_s10732-020-09438-w
    DOI: 10.1007/s10732-020-09438-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-020-09438-w
    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/s10732-020-09438-w?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. Jianzhong Zhang & Biao Qu & Naihua Xiu, 2010. "Some projection-like methods for the generalized Nash equilibria," Computational Optimization and Applications, Springer, vol. 45(1), pages 89-109, January.
    2. Luiz Matioli & Wilfredo Sosa & Jinyun Yuan, 2012. "A numerical algorithm for finding solutions of a generalized Nash equilibrium problem," Computational Optimization and Applications, Springer, vol. 52(1), pages 281-292, May.
    3. Ibrahim Abada & Steven Gabriel & Vincent Briat & Olivier Massol, 2013. "A Generalized Nash–Cournot Model for the Northwestern European Natural Gas Markets with a Fuel Substitution Demand Function: The GaMMES Model," Networks and Spatial Economics, Springer, vol. 13(1), pages 1-42, March.
    4. Anna Nagurney & Min Yu & Deniz Besik, 2017. "Supply chain network capacity competition with outsourcing: a variational equilibrium framework," Journal of Global Optimization, Springer, vol. 69(1), pages 231-254, September.
    5. Ibrahim Abada & Pierre-André Jouvet, 2013. "A stochastic generalized Nash-Cournot model for the northwestern European natural gas markets: The S-GaMMES model," Working Papers 1308, Chaire Economie du climat.
    6. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    7. Nagurney, Anna & Flores, Emilio Alvarez & Soylu, Ceren, 2016. "A Generalized Nash Equilibrium network model for post-disaster humanitarian relief," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 1-18.
    8. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    9. Anselmi, Jonatha & Ardagna, Danilo & Passacantando, Mauro, 2014. "Generalized Nash equilibria for SaaS/PaaS Clouds," European Journal of Operational Research, Elsevier, vol. 236(1), pages 326-339.
    10. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    11. OGGIONI, Giorgia & SMEERS, Yves, 2013. "Market failures of market coupling and counter-trading in Europe: an illustrative model based discussion," LIDAM Reprints CORE 2553, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Cardell, Judith B. & Hitt, Carrie Cullen & Hogan, William W., 1997. "Market power and strategic interaction in electricity networks," Resource and Energy Economics, Elsevier, vol. 19(1-2), pages 109-137, March.
    13. Breton, Michele & Zaccour, Georges & Zahaf, Mehdi, 2006. "A game-theoretic formulation of joint implementation of environmental projects," European Journal of Operational Research, Elsevier, vol. 168(1), pages 221-239, January.
    14. Mauro Passacantando & Danilo Ardagna & Anna Savi, 2016. "Service Provisioning Problem in Cloud and Multi-Cloud Systems," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 265-277, May.
    15. de MAERE d'AERTRYCKE, Gauthier & SMEERS, Yves, 2013. "Liquidity risks on power exchanges: a generalized Nash equilibrium model," LIDAM Reprints CORE 2551, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    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. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    2. Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.
    3. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    4. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    5. Tom Brijs & Daniel Huppmann & Sauleh Siddiqui & Ronnie Belmans, 2016. "Auction-Based Allocation of Shared Electricity Storage Resources through Physical Storage Rights," Discussion Papers of DIW Berlin 1566, DIW Berlin, German Institute for Economic Research.
    6. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    7. Abhishek Singh & Debdas Ghosh & Qamrul Hasan Ansari, 2024. "Inexact Newton Method for Solving Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1333-1363, June.
    8. Yann BRAOUEZEC & Keyvan KIANI, 2021. "Economic foundations of generalized games with shared constraint: Do binding agreements lead to less Nash equilibria?," Working Papers 2021-ACF-06, IESEG School of Management.
    9. Braouezec, Yann & Kiani, Keyvan, 2023. "Economic foundations of generalized games with shared constraint: Do binding agreements lead to less Nash equilibria?," European Journal of Operational Research, Elsevier, vol. 308(1), pages 467-479.
    10. Nagurney, Anna & Besik, Deniz & Li, Dong, 2019. "Strict quotas or tariffs? Implications for product quality and consumer welfare in differentiated product supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 129(C), pages 136-161.
    11. Sreekumaran, Harikrishnan & Hota, Ashish R. & Liu, Andrew L. & Uhan, Nelson A. & Sundaram, Shreyas, 2021. "Equilibrium strategies for multiple interdictors on a common network," European Journal of Operational Research, Elsevier, vol. 288(2), pages 523-538.
    12. Nagurney, Anna, 2021. "Supply chain game theory network modeling under labor constraints: Applications to the Covid-19 pandemic," European Journal of Operational Research, Elsevier, vol. 293(3), pages 880-891.
    13. Veronika Grimm & Lars Schewe & Martin Schmidt & Gregor Zöttl, 2019. "A multilevel model of the European entry-exit gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 223-255, April.
    14. Masao Fukushima, 2011. "Restricted generalized Nash equilibria and controlled penalty algorithm," Computational Management Science, Springer, vol. 8(3), pages 201-218, August.
    15. Zheng Peng & Wenxing Zhu, 2013. "An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 533-551, May.
    16. Anna Nagurney & Min Yu & Deniz Besik, 2017. "Supply chain network capacity competition with outsourcing: a variational equilibrium framework," Journal of Global Optimization, Springer, vol. 69(1), pages 231-254, September.
    17. Wu, Yuxin & Yan, Haoyuan & Liu, Min & Zhao, Tianyang & Qiu, Jiayu & Liu, Shengwei, 2023. "Distributed energy trading on networked energy hubs under network constraints," Renewable Energy, Elsevier, vol. 209(C), pages 491-504.
    18. Oliver Stein & Nathan Sudermann-Merx, 2016. "The Cone Condition and Nonsmoothness in Linear Generalized Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 687-709, August.
    19. Csercsik, Dávid & Hubert, Franz & Sziklai, Balázs R. & Kóczy, László Á., 2019. "Modeling transfer profits as externalities in a cooperative game-theoretic model of natural gas networks," Energy Economics, Elsevier, vol. 80(C), pages 355-365.
    20. Arnaud Z. Dragicevic, 2019. "Market Coordination Under Non-Equilibrium Dynamics," Networks and Spatial Economics, Springer, vol. 19(3), pages 697-715, September.

    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:26:y:2020:i:4:d:10.1007_s10732-020-09438-w. 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.