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App. Res. of Comp. Accepted Paper
Vol. 42, 2025 No. 5

Solving generalized nash equilibrium problem based on enhanced differential evolutionary algorithm

Wang Kai1,2
Jia Wensheng1,2
1. College of Mathematics & Statistics, Guizhou University, Guiyang Guizhou 550025, China
2. Provincial Key Laboratory of Game Decision-making & Control System, Guiyang Guizhou 550025, China
DOI: 10.19734/j.issn.1001-3695.2024.09.0364

Abstract

Addressing the problems that classical mathematical methods for solving the generalized Nash equilibrium problem face, such as reliance on initial point selection, high differentiability requirements, information loss during problem transformation, and insufficient performance of meta-heuristic algorithms, this paper proposes an enhanced differential evolution algorithm to directly solve the generalized Nash equilibrium problem using the Nikaido-Isoda function. First, to improve the diversity and convergence speed of the differential evolution algorithm, we introduce the ideas of tent chaotic mapping, adaptive coefficients, and the slime mould algorithm to design an improved version of the differential evolution algorithm. We also provide a theoretical proof of the algorithm's convergence. Secondly, we define a dominance strategy and a relative fitness function using the Nikaido-Isoda function to enhance population variation and selection in the differential evolution algorithm. Finally, the results of arithmetic cases in different dimensions demonstrate that the algorithm successfully resolves the generalized Nash equilibrium problem. Therefore, the method proposed in this paper for solving the generalized Nash equilibrium problem does not rely on initial point selection or differentiability, and it avoids information loss during problem transformation, offering certain advantages and effectiveness.

Foundation Support

国家自然科学基金资助项目(12061020)
贵州省优秀青年科技人才项目(20215640)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2024.09.0364
Publish at: Application Research of Computers Accepted Paper, Vol. 42, 2025 No. 5

Publish History

[2025-03-06] Accepted Paper

Cite This Article

王凯, 贾文生. 基于增强型差分进化算法求解广义Nash均衡问题 [J]. 计算机应用研究, 2025, 42 (5). (2025-03-06). https://doi.org/10.19734/j.issn.1001-3695.2024.09.0364. (Wang Kai, Jia Wensheng. Solving generalized nash equilibrium problem based on enhanced differential evolutionary algorithm [J]. Application Research of Computers, 2025, 42 (5). (2025-03-06). https://doi.org/10.19734/j.issn.1001-3695.2024.09.0364. )

About the Journal

  • Application Research of Computers Monthly Journal
  • Journal ID ISSN 1001-3695
    CN  51-1196/TP

Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

Aiming at the urgently needed cutting-edge technology in this discipline, Application Research of Computers reflects the mainstream technology, hot technology and the latest development trend of computer application research at home and abroad in a timely manner. The main contents of the journal include high-level academic papers in this discipline, the latest scientific research results and major application results. The contents of the columns involve new theories of computer discipline, basic computer theory, algorithm theory research, algorithm design and analysis, blockchain technology, system software and software engineering technology, pattern recognition and artificial intelligence, architecture, advanced computing, parallel processing, database technology, computer network and communication technology, information security technology, computer image graphics and its latest hot application technology.

Application Research of Computers has many high-level readers and authors, and its readers are mainly senior and middle-level researchers and engineers engaged in the field of computer science, as well as teachers and students majoring in computer science and related majors in colleges and universities. Over the years, the total citation frequency and Web download rate of Application Research of Computers have been ranked among the top of similar academic journals in this discipline, and the academic papers published are highly popular among the readers for their novelty, academics, foresight, orientation and practicality.

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