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Mathematics
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Artificial Intelligence and Game Theory
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Artificial Intelligence and Game Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 20 July 2025 | Viewed by 6055

Special Issue Editors

Dr. Lefeng Cheng

E-Mail Website
Guest Editor
School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China
Interests: artificial intelligence; game theory; smart grid; integrated energy systems; decision optimization theory
Special Issues, Collections and Topics in MDPI journals
Dr. Wentian Lu

E-Mail Website
Guest Editor
School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China
Interests: artificial intelligence; game theory; smart grid; integrated energy systems; decision optimization theory

Special Issue Information

Dear Colleagues,

At present, various countries have formulated a new generation of artificial intelligence development plans to seize the opportunity for a new round of technological changes. Based on this, vigorously developing the application of a new generation of artificial intelligence in smart grids and integrated energy systems will change the entire traditional energy utilization model and further promote the intelligent development of the system. In addition to the above fields, this Special Issue aims to collect research on a new generation of artificial intelligence and game theory-related methods in important engineering fields such as electrical, electronic, mechanical, and computer science. 

Dr. Lefeng Cheng
Dr. Wentian Lu
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • game theory
  • artificial intelligence
  • power system
  • sustainable and renewable energy
  • engineering optimization decision

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Published Papers (6 papers)

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Research

22 pages, 10680 KiB  
Article
A Short-Term Electricity Load Complementary Forecasting Method Based on Bi-Level Decomposition and Complexity Analysis
by Xun Dou and Yu He
Mathematics 2025, 13(7), 1066; https://doi.org/10.3390/math13071066 - 25 Mar 2025
Viewed by 174
Abstract
With the increasing complexity of the power system and the increasing load volatility, accurate load forecasting plays a vital role in ensuring the safety of power supply, optimizing scheduling decisions and resource allocation. However, the traditional single model has limitations in extracting the [...] Read more.
With the increasing complexity of the power system and the increasing load volatility, accurate load forecasting plays a vital role in ensuring the safety of power supply, optimizing scheduling decisions and resource allocation. However, the traditional single model has limitations in extracting the multi-frequency features of load data and processing components with varying complexity. Therefore, this paper proposes a complementary forecasting method based on bi-level decomposition and complexity analysis. In the paper, Pyraformer is used as a complementary model for the Single Channel Enhanced Periodicity Decoupling Framework (SCEPDF). Firstly, a Hodrick Prescott Filter (HP Filter) is used to decompose the electricity data, extracting the trend and periodic components. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is used to further decompose the periodic components to obtain several IMF components. Secondly, based on the sample entropy, spectral entropy, and Lempel–Ziv complexity, a complexity evaluation index system is constructed to comprehensively analyze the complexity of each IMF component. Then, based on the comprehensive complexity of each IMF component, different components are fed into the complementary model. The predicted values of each component are combined to obtain the final result. Finally, the proposed method is tested on the quarterly electrical load dataset. The effectiveness of the proposed method is verified through comparative and ablation experiments. The experimental results show that the proposed method demonstrates excellent performance in short-term electricity load forecasting tasks. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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25 pages, 8250 KiB  
Article
Day-Ahead Economic Dispatch Strategy for Distribution Networks with Multi-Class Distributed Resources Based on Improved MAPPO Algorithm
by Juan Zuo, Qian Ai, Wenbo Wang and Weijian Tao
Mathematics 2024, 12(24), 3993; https://doi.org/10.3390/math12243993 - 19 Dec 2024
Cited by 1 | Viewed by 758
Abstract
In the context of the global response to climate change and the promotion of an energy transition, the Internet of Things (IoT), sensor technologies, and big data analytics have been increasingly used in power systems, contributing to the rapid development of distributed energy [...] Read more.
In the context of the global response to climate change and the promotion of an energy transition, the Internet of Things (IoT), sensor technologies, and big data analytics have been increasingly used in power systems, contributing to the rapid development of distributed energy resources. The integration of a large number of distributed energy resources has led to issues, such as increased volatility and uncertainty in distribution networks, large-scale data, and the complexity and challenges of optimizing security and economic dispatch strategies. To address these problems, this paper proposes a day-ahead scheduling method for distribution networks based on an improved multi-agent proximal policy optimization (MAPPO) reinforcement learning algorithm. This method achieves the coordinated scheduling of multiple types of distributed resources within the distribution network environment, promoting effective interactions between the distributed resources and the grid and coordination among the resources. Firstly, the operational framework and principles of the proposed algorithm are described. To avoid blind trial-and-error and instability in the convergence process during learning, a generalized advantage estimation (GAE) function is introduced to improve the multi-agent proximal policy optimization algorithm, enhancing the stability of policy updates and the speed of convergence during training. Secondly, a day-ahead scheduling model for the power distribution grid containing multiple types of distributed resources is constructed, and based on this model, the environment, actions, states, and reward function are designed. Finally, the effectiveness of the proposed method in solving the day-ahead economic dispatch problem for distribution grids is verified using an improved IEEE 30-bus system example. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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39 pages, 7714 KiB  
Article
Dynamic Evolution Game Strategy of Government, Power Grid, and Users in Electricity Market Demand-Side Management
by Xin Shen, Jianlin Tang, Yijing Zhang, Bin Qian, Jiahao Li, Mi Zhou, Yitao Zhao and Yujun Yin
Mathematics 2024, 12(20), 3249; https://doi.org/10.3390/math12203249 - 17 Oct 2024
Cited by 1 | Viewed by 1067
Abstract
In the process of promoting demand-side management, the core stakeholder groups are government departments, power grid companies, and electricity users. Due to the different positions and conflicting interests of the three parties in the game, intense and complex battles will occur. This paper [...] Read more.
In the process of promoting demand-side management, the core stakeholder groups are government departments, power grid companies, and electricity users. Due to the different positions and conflicting interests of the three parties in the game, intense and complex battles will occur. This paper investigates a tripartite evolutionary game involving government, power grid companies, and electricity users in the context of demand-side management (DSM) and analyzes the dynamic interactions between government departments, power grid companies, and electricity users within the framework of DSM using evolutionary game theory. Using evolutionary game theory, we explore how incentives and strategic interactions among these three stakeholders evolve over time, affecting the stability of DSM policies. The model addresses the asymmetry in the decision-making process and examines the dynamic equilibrium outcomes under various scenarios. The results provide insights into the optimal design of incentive mechanisms to enhance DSM adoption. The findings offer practical recommendations to improve DSM policies, fostering balanced interests between government, grid companies, and users. This research contributes to a deeper understanding of strategic interactions in DSM, revealing how adaptive behaviors can enhance energy efficiency. It also underscores the importance of carefully designed incentive mechanisms in achieving long-term stability and cooperation among key stakeholders. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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20 pages, 3481 KiB  
Article
Short-Term Irradiance Prediction Based on Transformer with Inverted Functional Area Structure
by Zhenyuan Zhuang, Huaizhi Wang and Cilong Yu
Mathematics 2024, 12(20), 3213; https://doi.org/10.3390/math12203213 - 14 Oct 2024
Viewed by 899
Abstract
Solar irradiance prediction is a crucial component in the application of photovoltaic power generation, playing a vital role in optimizing energy production, managing energy storage, and maintaining grid stability. This paper proposes an irradiance prediction method based on a functionally structured inverted transformer [...] Read more.
Solar irradiance prediction is a crucial component in the application of photovoltaic power generation, playing a vital role in optimizing energy production, managing energy storage, and maintaining grid stability. This paper proposes an irradiance prediction method based on a functionally structured inverted transformer network, which maintains the channel independence of each feature in the model input and extracts the correlations between different features through an Attention mechanism, enabling the model to effectively capture the relevant information between various features. After the channel mixing of different features is completed through the Attention mechanism, a linear network is used to predict the irradiance sequence. A data processing method tailored to the prediction model used in this paper is designed, which employs a comprehensive data preprocessing approach combining mutual information, multiple imputation, and median filtering to optimize the raw dataset, enhancing the overall stability and accuracy of the prediction project. Additionally, a Dingo optimization algorithm suitable for the self-tuning of deep learning model hyperparameters is designed, improving the model’s generalization capability and reducing deployment costs. The artificial intelligence (AI) model proposed in this paper demonstrates superior prediction performance compared to existing common prediction models in irradiance data forecasting and can facilitate further applications of photovoltaic power generation in power systems. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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47 pages, 11591 KiB  
Article
Spontaneous Formation of Evolutionary Game Strategies for Long-Term Carbon Emission Reduction Based on Low-Carbon Trading Mechanism
by Zhanggen Zhu, Lefeng Cheng and Teng Shen
Mathematics 2024, 12(19), 3109; https://doi.org/10.3390/math12193109 - 4 Oct 2024
Cited by 5 | Viewed by 1011
Abstract
In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic [...] Read more.
In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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16 pages, 15905 KiB  
Article
Decentralized Stochastic Recursive Gradient Method for Fully Decentralized OPF in Multi-Area Power Systems
by Umair Hussan, Huaizhi Wang, Muhammad Ahsan Ayub, Hamna Rasheed, Muhammad Asghar Majeed, Jianchun Peng and Hui Jiang
Mathematics 2024, 12(19), 3064; https://doi.org/10.3390/math12193064 - 30 Sep 2024
Cited by 7 | Viewed by 1253
Abstract
This paper addresses the critical challenge of optimizing power flow in multi-area power systems while maintaining information privacy and decentralized control. The main objective is to develop a novel decentralized stochastic recursive gradient (DSRG) method for solving the optimal power flow (OPF) problem [...] Read more.
This paper addresses the critical challenge of optimizing power flow in multi-area power systems while maintaining information privacy and decentralized control. The main objective is to develop a novel decentralized stochastic recursive gradient (DSRG) method for solving the optimal power flow (OPF) problem in a fully decentralized manner. Unlike traditional centralized approaches, which require extensive data sharing and centralized control, the DSRG method ensures that each area within the power system can make independent decisions based on local information while still achieving global optimization. Numerical simulations are conducted using MATLAB (Version 24.1.0.2603908) to evaluate the performance of the DSRG method on a 3-area, 9-bus test system. The results demonstrate that the DSRG method converges significantly faster than other decentralized OPF methods, reducing the overall computation time while maintaining cost efficiency and system stability. These findings highlight the DSRG method’s potential to significantly enhance the efficiency and scalability of decentralized OPF in modern power systems. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
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