Differential evolution particle swarm optimization algorithm based on good point set for computing Nash equilibrium of finite noncooperative game

Li, Huimin; Xiang, Shuwen; Yong-sheng, Yang; Liu, Chenwei

doi:10.3934/math.2021081

Cited by 16 publications

(6 citation statements)

References 14 publications

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“…To achieve better performance (convergence speed, accuracy, and global optimization ability) compared to individual methods, several hybrid approaches appear in the literature, including DE and PSO ( Hendtlass, 2001 ; Zhang and Xie, 2003 ; Talbi and Batouche, 2004 ; Hao et al, 2007 ; Das et al, 2008 ; Vaisakh et al, 2009 ; Garcia-Guarin et al, 2019 ; Dash et al, 2020 ; Li et al, 2021 ), PSO and GA ( Mousa et al, 2012 ; Esmin and Matwin, 2013 ; Samuel and Rajan, 2015 ; Ali and Tawhid, 2017 ; Dziwiński and Bartczuk, 2019 ; Pu et al, 2019 ; Omidinasab and Goodarzimehr, 2020 ; Fu et al, 2021 ; Goodarzimehr et al, 2023 ), and GA and DE ( Trivedi et al, 2015 , 2016 ; Abidin, 2018 ; Aguitoni et al, 2018 ; Chaudhary et al, 2019 ; Fathy et al, 2020 ) ( Fig. 9 ).…”

Section: Numerical Solution and Calibrationmentioning

confidence: 99%

Building blocks needed for mechanistic modeling of bioprocesses: A critical review based on protein production by CHO cells

González-Hernández,

Perré

2024

Metabolic Engineering Communications

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Section: Numerical Solution and Calibrationmentioning

confidence: 99%

Building blocks needed for mechanistic modeling of bioprocesses: A critical review based on protein production by CHO cells

González-Hernández,

Perré

2024

Metabolic Engineering Communications

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“…The generation of new solutions in the CS algorithm is primarily based on the information difference between individuals and their peers, leading to slow convergence in the later stages of the algorithm and a decrease in optimization accuracy. Information sharing among cuckoo individuals helps alleviate this problem, and previous research [34][35][36][37] has attempted to use information sharing to improve the performance of the CS algorithm, resulting in some new and improved CS algorithms. In order to further strengthen the information sharing among cuckoo individuals, an improved CS based on shared mechanism (ICSABOSM) is proposed, enhancing the collaboration within the population.…”

Section: Improved Cuckoo Search Algorithmmentioning

confidence: 99%

Application of the Improved Cuckoo Algorithm in Differential Equations

Sun

2024

Mathematics

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To address the drawbacks of the slow convergence speed and lack of individual information exchange in the cuckoo search (CS) algorithm, this study proposes an improved cuckoo search algorithm based on a sharing mechanism (ICSABOSM). The enhanced algorithm reinforces information sharing among individuals through the utilization of a sharing mechanism. Additionally, new search strategies are introduced in both the global and local searches of the CS. The results from numerical experiments on four standard test functions indicate that the improved algorithm outperforms the original CS in terms of search capability and performance. Building upon the improved algorithm, this paper introduces a numerical solution approach for differential equations involving the coupling of function approximation and intelligent algorithms. By constructing an approximate function using Fourier series to satisfy the conditions of the given differential equation and boundary conditions with minimal error, the proposed method minimizes errors while satisfying the differential equation and boundary conditions. The problem of solving the differential equation is then transformed into an optimization problem with the coefficients of the approximate function as variables. Furthermore, the improved cuckoo search algorithm is employed to solve this optimization problem. The specific steps of applying the improved algorithm to solve differential equations are illustrated through examples. The research outcomes broaden the application scope of the cuckoo optimization algorithm and provide a new perspective for solving differential equations.

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“…Theorem 2.2. [20] A mixed strategy x * ∈ X is the Nash equilibrium point of a game Γ if and only if x * is an optimal solution to the following optimization problem, and the optimal value is 0:…”

Section: Conclusion 21mentioning

confidence: 99%

“…It means that such algorithms can be considered to solve the Nash equilibria. Pavlidis [25], Boryczka [3], Jia [15], Yang [30], and Li [20] used intelligent algorithms to compute the Nash equilibria of corresponding games. But, most of them dealt with zero sum two-person games or nonzero sum two-person games.…”

Section: Introductionmentioning

confidence: 99%

Improved differential evolution algorithm for solving multi-person noncooperative game

2022

J. Nonlinear Funct. Anal.

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In this paper, the nonzero sum multi-person noncooperative game is considered, and this game can be viewed as a global optimization problem. For solving this problem, an improved differential evolution algorithm is proposed. Our algorithm combines multi-strategy differential operators and crossover operators with a random walk. First, the population is initialized by a set of good points. Second, the single mutation mode is replaced by a multi-mode. Meanwhile, a random walk mechanism is introduced in the crossover process of the differential evolution algorithm. The convergence of the improved algorithm is then proved by using an infinite product method. Finally, the proposed algorithm is illustrated via some numerical examples, and the experimental results show that the proposed new algorithm can solve the multi-person game.

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Differential evolution particle swarm optimization algorithm based on good point set for computing Nash equilibrium of finite noncooperative game

Cited by 16 publications

References 14 publications

Building blocks needed for mechanistic modeling of bioprocesses: A critical review based on protein production by CHO cells

Building blocks needed for mechanistic modeling of bioprocesses: A critical review based on protein production by CHO cells

Application of the Improved Cuckoo Algorithm in Differential Equations

Improved differential evolution algorithm for solving multi-person noncooperative game

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