Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individua...Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individuals.In non-cooperative settings,aggregative games serve as a mathematical framework model for the interdependent optimal decision-making problem among a group of non-cooperative players.In such scenarios,each player's decision is influenced by an aggregation of all players'decisions.Nash equilibrium(NE)seeking in aggregative games has emerged as a vibrant topic driven by applications that harness the aggregation property.This paper presents a comprehensive overview of the current research on aggregative games with a focus on communication topology.A systematic classification is conducted on distributed algorithm research based on communication topologies such as undirected networks,directed networks,and time-varying networks.Furthermore,it sorts out the challenges and compares the algorithms'convergence performance.It also delves into real-world applications of distributed optimization techniques grounded in aggregative games.Finally,it proposes several challenges that can guide future research directions.展开更多
A multi-objective evolutionary optimization method (combining genetic algorithms(GAs)and game theory(GT))is presented for high lift multi-airfoil systems in aerospace engineering.Due to large dimension global op-timiz...A multi-objective evolutionary optimization method (combining genetic algorithms(GAs)and game theory(GT))is presented for high lift multi-airfoil systems in aerospace engineering.Due to large dimension global op-timization problems and the increasing importance of low cost distributed parallel environments,it is a natural idea to replace a globar optimization by decentralized local sub-optimizations using GT which introduces the notion of games associated to an optimization problem.The GT/GAs combined optimization method is used for recon-struction and optimization problems by high lift multi-air-foil desing.Numerical results are favorably compared with single global GAs.The method shows teh promising robustness and efficient parallel properties of coupled GAs with different game scenarios for future advanced multi-disciplinary aerospace techmologies.展开更多
Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the cod...Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.展开更多
In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A ...In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash equilibrium.In our algorithm,each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate,it effectively reduces the amount of computation and calculation time.Moreover,the traditional assumption of stepsize adopted in the existing methods is removed,and the stepsizes in our algorithm are randomized diminishing.Besides,we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm.Finally,a simulation example verifies the validity of our algorithm.展开更多
Real-time train rescheduling plays a vital role in railway transportation as it is crucial for maintaining punctuality and reliability in rail operations.In this paper,we propose a rescheduling model that incorporates...Real-time train rescheduling plays a vital role in railway transportation as it is crucial for maintaining punctuality and reliability in rail operations.In this paper,we propose a rescheduling model that incorporates constraints and objectives generated through human-computer interaction.This approach ensures that the model is aligned with practical requirements and daily operational tasks while facilitating iterative train rescheduling.The dispatcher’s empirical knowledge is integrated into the train rescheduling process using a human-computer interaction framework.We introduce six interfaces to dynamically construct constraints and objectives that capture human intentions.By summarizing rescheduling rules,we devise a rule-based conflict detection-resolution heuristic algorithm to effectively solve the formulated model.A series of numerical experiments are presented,demonstrating strong performance across the entire system.Furthermore,theflexibility of rescheduling is enhanced through secondary analysis-driven solutions derived from the outcomes of humancomputer interactions in the previous step.This proposed interaction method complements existing literature on rescheduling methods involving human-computer interactions.It serves as a tool to aid dispatchers in identifying more feasible solutions in accordance with their empirical rescheduling strategies.展开更多
The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of s...The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.展开更多
Metaheuristic algorithms are one of themost widely used stochastic approaches in solving optimization problems.In this paper,a new metaheuristic algorithm entitled Billiards Optimization Algorithm(BOA)is proposed and ...Metaheuristic algorithms are one of themost widely used stochastic approaches in solving optimization problems.In this paper,a new metaheuristic algorithm entitled Billiards Optimization Algorithm(BOA)is proposed and designed to be used in optimization applications.The fundamental inspiration in BOA design is the behavior of the players and the rules of the billiards game.Various steps of BOA are described and then its mathematical model is thoroughly explained.The efficiency of BOA in dealing with optimization problems is evaluated through optimizing twenty-three standard benchmark functions of different types including unimodal,high-dimensional multimodal,and fixed-dimensionalmultimodal functions.In order to analyze the quality of the results obtained by BOA,the performance of the proposed approach is compared with ten well-known algorithms.The simulation results show that BOA,with its high exploration and exploitation abilities,achieves an impressive performance in providing solutions to objective functions and is superior and far more competitive compared to the ten competitor algorithms.展开更多
Manipuri traditional game Kei-Yen, which originates from the ancient Meitei mythological story, is a mind game between two players of different mindsets, one has the mindset of killing (Kei), whereas the other (Yen) h...Manipuri traditional game Kei-Yen, which originates from the ancient Meitei mythological story, is a mind game between two players of different mindsets, one has the mindset of killing (Kei), whereas the other (Yen) has the mindset of protecting itself and block the moves of Kei. We propose and develop an algorithm of this game by incorporating various possible logical tactics and strategies for a possible computer software of this game. Since this game involves various logical mind games, playing this game can improve our way of thinking, strategies, tricks and other skills related to mind game. In this play there is not the case of draw which means one has to win over the other at the end of the game. This game could become one of most interesting indoor national or international game.展开更多
In on-line role-playing games (RPG), each race holds some attributes and skills. Each skill contains several abilities such as physical damage, hit rate, etc. Parts of the attributes and all the abilities are a functi...In on-line role-playing games (RPG), each race holds some attributes and skills. Each skill contains several abilities such as physical damage, hit rate, etc. Parts of the attributes and all the abilities are a function of the character’s level, which are called Ability-Increasing Functions (AIFs). A well-balanced on-line RPG is characterized by having a set of well-balanced AIFs. In this paper, we propose an evolutionary design method, including integration with an improved Probabilistic Incremental Program Evolution (PIPE) and a Cooperative Coevolutionary Algorithm (CCEA), for on-line RPGs to maintain the game balance. Moreover, we construct a simplest turn-based game model and perform a series of experiments based on it. The results indicate that the proposed method is able to obtain a set of well-balanced AIFs efficiently. They also show that in this case the CCEA outperforms the simple genetic algorithm, and that the capability of PIPE has been significantly improved through the improvement work.展开更多
In the case of on-line action role-playing game, the combat strategies can be divided into three distinct classes, Strategy of Motion(SM), Strategy of Attacking Occasion (SAO) and Strategy of Using Skill (SUS). In thi...In the case of on-line action role-playing game, the combat strategies can be divided into three distinct classes, Strategy of Motion(SM), Strategy of Attacking Occasion (SAO) and Strategy of Using Skill (SUS). In this paper, we analyze such strategies of a basic game model in which the combat is modeled by the discrete competitive Markov decision process. By introducing the chase model and the combat assistant technology, we identify the optimal SM and the optimal SAO, successfully. Also, we propose an evolutionary framework, including integration with competitive coevolution and cooperative coevolution, to search the optimal SUS pair which is regarded as the Nash equilibrium point of the strategy space. Moreover, some experiments are made to demonstrate that the proposed framework has the ability to find the optimal SUS pair. Furthermore, from the results, it is shown that using cooperative coevolutionary algorithm is much more efficient than using simple evolutionary algorithm.展开更多
Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. ...Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. The algorithm uses the minimum cost spanning tree strategy and fuzzy game theory. First, it virtualizes two planes to calculate the multicast tree and the multicast protection tree respectively. Then, it performs a fuzzy game to form a cooperative alliance to optimize the path composition of each multicast tree. Finally, it generates a pair of optimal multicast work tree and multicast protection tree for dynamic multicast services. The time complexity of the algorithm is O(k3 m2 n), where n represents the number of nodes in the networks, k represents the number of dynamic multicast requests, and m represents the number of destination nodes for each multicast request. The experimental results show that the proposed algorithm reduces significantly the blocking rate of dynamic multicast services, and improves the utilization of optical network resources within a certain number of dynamic multicast request ranges.展开更多
In 3D games, a lot of weapons in the movement will drag a ＂follow the shadow＂ effect, which is called the ＂track＂. In this paper, we first analyze the change rule of the ＂track＂, and then put forward a kind of a...In 3D games, a lot of weapons in the movement will drag a ＂follow the shadow＂ effect, which is called the ＂track＂. In this paper, we first analyze the change rule of the ＂track＂, and then put forward a kind of algorithm to realize the ＂track＂. The calculation of this algorithm is small, but the effect is very real, has been successfully applied to a variety of 3D games.展开更多
Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communicatio...Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communication.To this end,a novel distributed robust predefined-time algorithm is proposed,which ensures the precise convergence of agent states to the NE within a settling time that can be directly determined by adjusting one or more parameters.The proposed algorithm employs an integral sliding mode strategy to effectively reject disturbances.Additionally,a consensus-based estimator is designed to overcome the challenge of limited information availability,where each agent can only access information from its directly connected neighbors,which conflicts with the computation of the cost function that requires information from all agents.Finally,a numerical example is provided to demonstrate the algorithm's effectiveness and performance.展开更多
The Roman domination problem is an important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security,considering back...The Roman domination problem is an important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security,considering backups in the face of a dynamic network security requirement.In this paper,firstly,we propose a Roman domination game(RDG)and prove that every Nash equilibrium(NE)of the game corresponds to a strong minimal Roman dominating function(S-RDF),as well as a Pareto-optimal solution.Secondly,we show that RDG is an exact potential game,which guarantees the existence of an NE.Thirdly,we design a game-based synchronous algorithm(GSA),which can be implemented distributively and converge to an NE in O(n)rounds,where n is the number of vertices.In GSA,all players make decisions depending on local information.Furthermore,we enhance GSA to be enhanced GSA(EGSA),which converges to a better NE in O(n2)rounds.Finally,we present numerical simulations to demonstrate that EGSA can obtain a better approximate solution in promising computation time compared with state-of-the-art algorithms.展开更多
With the rapid development of renewable energy,the Microgrid Coalition(MGC)has become an important approach to improving energy utilization efficiency and economic performance.To address the operational optimization p...With the rapid development of renewable energy,the Microgrid Coalition(MGC)has become an important approach to improving energy utilization efficiency and economic performance.To address the operational optimization problem inmulti-microgrid cooperation,a cooperative game strategy based on the Nash bargainingmodel is proposed,aiming to enable collaboration among microgrids to maximize overall benefits while considering energy trading and cost optimization.First,each microgrid is regarded as a game participant,and a multi-microgrid cooperative game model based on Nash bargaining theory is constructed,targeting the minimization of total operational cost under constraints such as power balance and energy storage limits.Second,the Nash bargaining solution is introduced as the benefit allocation scheme to ensure individual rationality and coalition stability.Finally,theAlternating Direction Method of Multipliers(ADMM)is employed to decompose the centralized optimization problem into distributed subproblems for iterative solution,thereby reducing communication burden and protecting privacy.Case studies reveal that the operational costs of the threemicrogrids are reduced by 26.28%,19.00%,and 17.19%,respectively,and the overall renewable energy consumption rate is improved by approximately 66.11%.展开更多
This work investigates quantum speedups for the popular game named Mastermind,in which there are two participants:the codemaker who selects a secret string,and the codebreaker who submits query strings and receives an...This work investigates quantum speedups for the popular game named Mastermind,in which there are two participants:the codemaker who selects a secret string,and the codebreaker who submits query strings and receives answers from the codemaker.The codebreaker's objective is to learn the secret string in as few queries as possible.This work focuses on playing the Mastermind game on quantum computers using different types of codemaker's answers such as black count,l_(p) distance,and separable distance.We show that the codebreaker can learn the secret with certainty by using quantum algorithms which exhibit a sharp reduction in query numbers compared with their classical counterparts.Specifically,our quantum algorithms require O(klog k)black-count queries,O(logk)l_(p)-distance queries,and O(log M)separable-distance queries to learn the secret s∈[k]^(n),respectively,where M is completely determined by k.Thus,the quantum query complexity is independent of the length n of the secret s,as opposed to the query complexity linear in n of classical algorithms.展开更多
A novel quantum algorithm for the Mastermind game was proposed recently by a research team from Sun Yat-sen University to highlight the power of quantum computing.Mastermind is a popular code-breaking game between a c...A novel quantum algorithm for the Mastermind game was proposed recently by a research team from Sun Yat-sen University to highlight the power of quantum computing.Mastermind is a popular code-breaking game between a codemaker and a codebreaker.In the commercial version,the codemaker selects a secret sequence of four colored pegs(positions)from six possible colors.展开更多
基金supported in part by the Fundamental Research Funds for the Central Universities(SWU-XDJH202312)the National Natural Science Foundation of China(62173278)the Chongqing Science Fund for Distinguished Young Scholars(2024NSCQJQX0103).
文摘Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individuals.In non-cooperative settings,aggregative games serve as a mathematical framework model for the interdependent optimal decision-making problem among a group of non-cooperative players.In such scenarios,each player's decision is influenced by an aggregation of all players'decisions.Nash equilibrium(NE)seeking in aggregative games has emerged as a vibrant topic driven by applications that harness the aggregation property.This paper presents a comprehensive overview of the current research on aggregative games with a focus on communication topology.A systematic classification is conducted on distributed algorithm research based on communication topologies such as undirected networks,directed networks,and time-varying networks.Furthermore,it sorts out the challenges and compares the algorithms'convergence performance.It also delves into real-world applications of distributed optimization techniques grounded in aggregative games.Finally,it proposes several challenges that can guide future research directions.
文摘A multi-objective evolutionary optimization method (combining genetic algorithms(GAs)and game theory(GT))is presented for high lift multi-airfoil systems in aerospace engineering.Due to large dimension global op-timization problems and the increasing importance of low cost distributed parallel environments,it is a natural idea to replace a globar optimization by decentralized local sub-optimizations using GT which introduces the notion of games associated to an optimization problem.The GT/GAs combined optimization method is used for recon-struction and optimization problems by high lift multi-air-foil desing.Numerical results are favorably compared with single global GAs.The method shows teh promising robustness and efficient parallel properties of coupled GAs with different game scenarios for future advanced multi-disciplinary aerospace techmologies.
文摘Minimax algorithm and machine learning technologies have been studied for decades to reach an ideal optimization in game areas such as chess and backgammon. In these fields, several generations try to optimize the code for pruning and effectiveness of evaluation function. Thus, there are well-armed algorithms to deal with various sophisticated situations in gaming occasion. However, as a traditional zero-sum game, Connect-4 receives less attention compared with the other members of its zero-sum family using traditional minimax algorithm. In recent years, new generation of heuristics is created to address this problem based on research conclusions, expertise and gaming experiences. However, this paper mainly introduced a self-developed heuristics supported by well-demonstrated result from researches and our own experiences which fighting against the available version of Connect-4 system online. While most previous works focused on winning algorithms and knowledge based approaches, we complement these works with analysis of heuristics. We have conducted three experiments on the relationship among functionality, depth of searching and number of features and doing contrastive test with sample online. Different from the sample based on summarized experience and generalized features, our heuristics have a basic concentration on detailed connection between pieces on board. By analysing the winning percentages when our version fights against the online sample with different searching depths, we find that our heuristics with minimax algorithm is perfect on the early stages of the zero-sum game playing. Because some nodes in the game tree have no influence on the final decision of minimax algorithm, we use alpha-beta pruning to decrease the number of meaningless node which greatly increases the minimax efficiency. During the contrastive experiment with the online sample, this paper also verifies basic characters of the minimax algorithm including depths and quantity of features. According to the experiment, these two characters can both effect the decision for each step and none of them can be absolutely in charge. Besides, we also explore some potential future issues in Connect-4 game optimization such as precise adjustment on heuristic values and inefficiency pruning on the search tree.
文摘In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash equilibrium.In our algorithm,each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate,it effectively reduces the amount of computation and calculation time.Moreover,the traditional assumption of stepsize adopted in the existing methods is removed,and the stepsizes in our algorithm are randomized diminishing.Besides,we prove that all agents converge to Nash equilibrium with probability 1 by our algorithm.Finally,a simulation example verifies the validity of our algorithm.
基金supported by the China Fundamental Research Funds for the Central Universities(2022JBQY006)。
文摘Real-time train rescheduling plays a vital role in railway transportation as it is crucial for maintaining punctuality and reliability in rail operations.In this paper,we propose a rescheduling model that incorporates constraints and objectives generated through human-computer interaction.This approach ensures that the model is aligned with practical requirements and daily operational tasks while facilitating iterative train rescheduling.The dispatcher’s empirical knowledge is integrated into the train rescheduling process using a human-computer interaction framework.We introduce six interfaces to dynamically construct constraints and objectives that capture human intentions.By summarizing rescheduling rules,we devise a rule-based conflict detection-resolution heuristic algorithm to effectively solve the formulated model.A series of numerical experiments are presented,demonstrating strong performance across the entire system.Furthermore,theflexibility of rescheduling is enhanced through secondary analysis-driven solutions derived from the outcomes of humancomputer interactions in the previous step.This proposed interaction method complements existing literature on rescheduling methods involving human-computer interactions.It serves as a tool to aid dispatchers in identifying more feasible solutions in accordance with their empirical rescheduling strategies.
基金Project supported by the National Aeronautics Base Science Foundation of China (No.2000CB080601)the National Defence Key Pre-research Program of China during the 10th Five-Year Plan Period (No.2002BK080602)
文摘The resolution of differential games often concerns the difficult problem of two points border value （TPBV）, then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
基金The research and article are supported by Specific Research project 2022 Faculty of Education,University of Hradec Králové,Czech Republic.
文摘Metaheuristic algorithms are one of themost widely used stochastic approaches in solving optimization problems.In this paper,a new metaheuristic algorithm entitled Billiards Optimization Algorithm(BOA)is proposed and designed to be used in optimization applications.The fundamental inspiration in BOA design is the behavior of the players and the rules of the billiards game.Various steps of BOA are described and then its mathematical model is thoroughly explained.The efficiency of BOA in dealing with optimization problems is evaluated through optimizing twenty-three standard benchmark functions of different types including unimodal,high-dimensional multimodal,and fixed-dimensionalmultimodal functions.In order to analyze the quality of the results obtained by BOA,the performance of the proposed approach is compared with ten well-known algorithms.The simulation results show that BOA,with its high exploration and exploitation abilities,achieves an impressive performance in providing solutions to objective functions and is superior and far more competitive compared to the ten competitor algorithms.
文摘Manipuri traditional game Kei-Yen, which originates from the ancient Meitei mythological story, is a mind game between two players of different mindsets, one has the mindset of killing (Kei), whereas the other (Yen) has the mindset of protecting itself and block the moves of Kei. We propose and develop an algorithm of this game by incorporating various possible logical tactics and strategies for a possible computer software of this game. Since this game involves various logical mind games, playing this game can improve our way of thinking, strategies, tricks and other skills related to mind game. In this play there is not the case of draw which means one has to win over the other at the end of the game. This game could become one of most interesting indoor national or international game.
文摘In on-line role-playing games (RPG), each race holds some attributes and skills. Each skill contains several abilities such as physical damage, hit rate, etc. Parts of the attributes and all the abilities are a function of the character’s level, which are called Ability-Increasing Functions (AIFs). A well-balanced on-line RPG is characterized by having a set of well-balanced AIFs. In this paper, we propose an evolutionary design method, including integration with an improved Probabilistic Incremental Program Evolution (PIPE) and a Cooperative Coevolutionary Algorithm (CCEA), for on-line RPGs to maintain the game balance. Moreover, we construct a simplest turn-based game model and perform a series of experiments based on it. The results indicate that the proposed method is able to obtain a set of well-balanced AIFs efficiently. They also show that in this case the CCEA outperforms the simple genetic algorithm, and that the capability of PIPE has been significantly improved through the improvement work.
文摘In the case of on-line action role-playing game, the combat strategies can be divided into three distinct classes, Strategy of Motion(SM), Strategy of Attacking Occasion (SAO) and Strategy of Using Skill (SUS). In this paper, we analyze such strategies of a basic game model in which the combat is modeled by the discrete competitive Markov decision process. By introducing the chase model and the combat assistant technology, we identify the optimal SM and the optimal SAO, successfully. Also, we propose an evolutionary framework, including integration with competitive coevolution and cooperative coevolution, to search the optimal SUS pair which is regarded as the Nash equilibrium point of the strategy space. Moreover, some experiments are made to demonstrate that the proposed framework has the ability to find the optimal SUS pair. Furthermore, from the results, it is shown that using cooperative coevolutionary algorithm is much more efficient than using simple evolutionary algorithm.
基金supported by the National Natural Science Foundation of China (No.61402529)the Natural Science Basic Research Plan in Shanxi Province of China (No.2020JM-361)+1 种基金the Young and Middle-aged Scientific Research Backbone Projects of Engineering University of PAP (No.KYGG201905)the Basic Researchof Engineering University of PAP (Nos.WJY201920 and WJY202019)。
文摘Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. The algorithm uses the minimum cost spanning tree strategy and fuzzy game theory. First, it virtualizes two planes to calculate the multicast tree and the multicast protection tree respectively. Then, it performs a fuzzy game to form a cooperative alliance to optimize the path composition of each multicast tree. Finally, it generates a pair of optimal multicast work tree and multicast protection tree for dynamic multicast services. The time complexity of the algorithm is O(k3 m2 n), where n represents the number of nodes in the networks, k represents the number of dynamic multicast requests, and m represents the number of destination nodes for each multicast request. The experimental results show that the proposed algorithm reduces significantly the blocking rate of dynamic multicast services, and improves the utilization of optical network resources within a certain number of dynamic multicast request ranges.
文摘In 3D games, a lot of weapons in the movement will drag a ＂follow the shadow＂ effect, which is called the ＂track＂. In this paper, we first analyze the change rule of the ＂track＂, and then put forward a kind of algorithm to realize the ＂track＂. The calculation of this algorithm is small, but the effect is very real, has been successfully applied to a variety of 3D games.
基金supported by the National Natural Science Foundation of China(62373162,U24A20268,624B2055).
文摘Dear Editor,This letter presents a solution to the problem of seeking Nash equilibrium(NE)in a class of non-cooperative games of multi-agent systems(MASs)subject to the input disturbance and the networked communication.To this end,a novel distributed robust predefined-time algorithm is proposed,which ensures the precise convergence of agent states to the NE within a settling time that can be directly determined by adjusting one or more parameters.The proposed algorithm employs an integral sliding mode strategy to effectively reject disturbances.Additionally,a consensus-based estimator is designed to overcome the challenge of limited information availability,where each agent can only access information from its directly connected neighbors,which conflicts with the computation of the cost function that requires information from all agents.Finally,a numerical example is provided to demonstrate the algorithm's effectiveness and performance.
基金supported in part by the National Natural Science Foundation of China(U20A2068)Zhejiang Provincial Natural Science Foundation of China(LD19A010001,LZ24F030009).
文摘The Roman domination problem is an important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security,considering backups in the face of a dynamic network security requirement.In this paper,firstly,we propose a Roman domination game(RDG)and prove that every Nash equilibrium(NE)of the game corresponds to a strong minimal Roman dominating function(S-RDF),as well as a Pareto-optimal solution.Secondly,we show that RDG is an exact potential game,which guarantees the existence of an NE.Thirdly,we design a game-based synchronous algorithm(GSA),which can be implemented distributively and converge to an NE in O(n)rounds,where n is the number of vertices.In GSA,all players make decisions depending on local information.Furthermore,we enhance GSA to be enhanced GSA(EGSA),which converges to a better NE in O(n2)rounds.Finally,we present numerical simulations to demonstrate that EGSA can obtain a better approximate solution in promising computation time compared with state-of-the-art algorithms.
基金funded by StateGrid Beijing Electric PowerCompany Technology Project,grant number 520210230004.
文摘With the rapid development of renewable energy,the Microgrid Coalition(MGC)has become an important approach to improving energy utilization efficiency and economic performance.To address the operational optimization problem inmulti-microgrid cooperation,a cooperative game strategy based on the Nash bargainingmodel is proposed,aiming to enable collaboration among microgrids to maximize overall benefits while considering energy trading and cost optimization.First,each microgrid is regarded as a game participant,and a multi-microgrid cooperative game model based on Nash bargaining theory is constructed,targeting the minimization of total operational cost under constraints such as power balance and energy storage limits.Second,the Nash bargaining solution is introduced as the benefit allocation scheme to ensure individual rationality and coalition stability.Finally,theAlternating Direction Method of Multipliers(ADMM)is employed to decompose the centralized optimization problem into distributed subproblems for iterative solution,thereby reducing communication burden and protecting privacy.Case studies reveal that the operational costs of the threemicrogrids are reduced by 26.28%,19.00%,and 17.19%,respectively,and the overall renewable energy consumption rate is improved by approximately 66.11%.
基金supported by the National Key Research and Development Program of China(Grant No.2024YFB4504004)the National Natural Science Foundation of China(Grant Nos.92465202,62272492,and 12447107)+1 种基金the Guangdong Provincial Quantum Science Strategic Initiative(Grant Nos.GDZX2303007,and GDZX2403001)the Guangzhou Science and Technology Program(Grant No.2024A04J4892)。
文摘This work investigates quantum speedups for the popular game named Mastermind,in which there are two participants:the codemaker who selects a secret string,and the codebreaker who submits query strings and receives answers from the codemaker.The codebreaker's objective is to learn the secret string in as few queries as possible.This work focuses on playing the Mastermind game on quantum computers using different types of codemaker's answers such as black count,l_(p) distance,and separable distance.We show that the codebreaker can learn the secret with certainty by using quantum algorithms which exhibit a sharp reduction in query numbers compared with their classical counterparts.Specifically,our quantum algorithms require O(klog k)black-count queries,O(logk)l_(p)-distance queries,and O(log M)separable-distance queries to learn the secret s∈[k]^(n),respectively,where M is completely determined by k.Thus,the quantum query complexity is independent of the length n of the secret s,as opposed to the query complexity linear in n of classical algorithms.
文摘A novel quantum algorithm for the Mastermind game was proposed recently by a research team from Sun Yat-sen University to highlight the power of quantum computing.Mastermind is a popular code-breaking game between a codemaker and a codebreaker.In the commercial version,the codemaker selects a secret sequence of four colored pegs(positions)from six possible colors.
