Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the co...Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.展开更多
There are currently three different game strategies originated in economics： （1） Cooperative games （Pareto front）, （2） Competitive games （Nash game） and （3） Hierarchical games （Stackelberg game）. Each gam...There are currently three different game strategies originated in economics： （1） Cooperative games （Pareto front）, （2） Competitive games （Nash game） and （3） Hierarchical games （Stackelberg game）. Each game achieves different equilibria with different performance, and their players play different roles in the games. Here, we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multi- criteria aerodynamic optimization problems. The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments. We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method. The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front. Non-dominated Pareto front solutions are obtained, however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.展开更多
The rapid advance of Connected-Automated Vehicles(CAVs)has led to the emergence of diverse delaysensitive and energy-constrained vehicular applications.Given the high dynamics of vehicular networks,unmanned aerial veh...The rapid advance of Connected-Automated Vehicles(CAVs)has led to the emergence of diverse delaysensitive and energy-constrained vehicular applications.Given the high dynamics of vehicular networks,unmanned aerial vehicles-assisted mobile edge computing(UAV-MEC)has gained attention in providing computing resources to vehicles and optimizing system costs.We model the computing offloading problem as a multi-objective optimization challenge aimed at minimizing both task processing delay and energy consumption.We propose a three-stage hybrid offloading scheme called Dynamic Vehicle Clustering Game-based Multi-objective Whale Optimization Algorithm(DVCG-MWOA)to address this problem.A novel dynamic clustering algorithm is designed based on vehiclemobility and task offloading efficiency requirements,where each UAV independently serves as the cluster head for a vehicle cluster and adjusts its position at the end of each timeslot in response to vehiclemovement.Within eachUAV-led cluster,cooperative game theory is applied to allocate computing resourceswhile respecting delay constraints,ensuring efficient resource utilization.To enhance offloading efficiency,we improve the multi-objective whale optimization algorithm(MOWOA),resulting in the MWOA.This enhanced algorithm determines the optimal allocation of pending tasks to different edge computing devices and the resource utilization ratio of each device,ultimately achieving a Pareto-optimal solution set for delay and energy consumption.Experimental results demonstrate that the proposed joint offloading scheme significantly reduces both delay and energy consumption compared to existing approaches,offering superior performance for vehicular networks.展开更多
This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors a...This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors and fuzzy clustering, the design variables are divided into different strategic spaces which belong to each player, then it constructs a payoff function based on the coalition mechanism. Each game player takes its own revenue function as a target and obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. A multi-objective optimization example of the luff mechanism of compensative sheave block shows the effectiveness of the coalition cooperative game method.展开更多
The output uncertainty of high-proportion distributed power generation severely affects the system voltage and frequency.Simultaneously,controllable loads have also annually increased,which markedly improve the capabi...The output uncertainty of high-proportion distributed power generation severely affects the system voltage and frequency.Simultaneously,controllable loads have also annually increased,which markedly improve the capability for nodal-power control.To maintain the system frequency and voltage magnitude around rated values,a new multi-objective optimization model for both voltage and frequency control is proposed.Moreover,a great similarity between the multiobjective optimization and game problems appears.To reduce the strong subjectivity of the traditional methods,the idea and method of the game theory are introduced into the solution.According to the present situational data and analysis of the voltage and frequency sensitivities to nodal-power variations,the design variables involved in the voltage and frequency control are classified into two strategy spaces for players using hierarchical clustering.Finally,the effectiveness and rationality of the proposed control are verified in MATLAB.展开更多
Based on the bimatrix game theory, the network data transmission has been depicted in a game theory way： the actions of the attacker and defender （legitimate users） are depicted within a two-person, non-cooperative...Based on the bimatrix game theory, the network data transmission has been depicted in a game theory way： the actions of the attacker and defender （legitimate users） are depicted within a two-person, non-cooperative and bimatrix game model, this paper proves the existence of the Nash equilibrium theoretically, which is further illustrated by the experimental resuhs.展开更多
This paper deals with rnxn two-person non-zero sum games with interval pay-offs. An analytic method for solving such games is given. A pair of Nash Equilibrium is found by using the method. The analytic method is effe...This paper deals with rnxn two-person non-zero sum games with interval pay-offs. An analytic method for solving such games is given. A pair of Nash Equilibrium is found by using the method. The analytic method is effective to find at least one Nash Equilibrium （N.E） for two-person bimatrix games. Therefore, the analytic method for two-person bimatrix games is adapted to interval bimatrix games.展开更多
When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game ...When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.展开更多
Multi-objective games(MOGs)have received much attention in recent years as a class of games with vector payoffs.Based on the semi-tensor product(STP),this paper discusses the MOG,including the existence,finite-step re...Multi-objective games(MOGs)have received much attention in recent years as a class of games with vector payoffs.Based on the semi-tensor product(STP),this paper discusses the MOG,including the existence,finite-step reachability,and finite-step controllability of Pareto equilibrium of this model,from both static and dynamic perspectives.First,the MOG concept is presented using multi-layer graphs,and STP is used to convert the payoff function into its algebraic form.Then,from the static perspective,two necessary and sufficient conditions are proposed to verify whether all players can meet their expectations and whether the strategy profile is a Pareto equilibrium,separately.Furthermore,from the dynamic perspective,a strategy updating rule is designed to investigate the finite-step reachability of the evolutionary MOG.Finally,the finite-step controllability of the evolutionary MOG is analyzed by adding pseudo-players,and a backward search algorithm is provided to find the shortest evolutionary process and control sequence.展开更多
With the rapid growing of EVs and increasing power loads,the integrated energy systems(IES)in practical operations are facing challenges in balancing safety and economic efficiency,along with the rise of unexpected en...With the rapid growing of EVs and increasing power loads,the integrated energy systems(IES)in practical operations are facing challenges in balancing safety and economic efficiency,along with the rise of unexpected energy usage plans by users.To address these issues,this research proposes a three-layer game-based multi-objective optimization strategy for IES.First,safety performance indexes of the in-tegrated energy network are established using graph theory and the Wiener process.Then,a non-cooperative-Stackelberg-cooperative game framework is constructed,which optimizes safety and eco-nomic indexes while allowing lower-level users to cooperate to maximize their own benefits.Further-more,considering Unexpected Load Deviations(ULDs)during actual operations,a flexible resource margin adjustment-based Adaptive Optimal Strategy and Information Gap Decision Theory(AOS-IGDT)strategy is proposed and embedded in the second stage of rolling optimization.Finally,the proposed strategy is verified using the coupled IEEE 33-bus system and a 17-node thermal network,the results demonstrate its effectiveness in achieving a win-win outcome for system economic and safety perfor-mance while reducing the ULDs and improving the benefits of all stakeholders.展开更多
Aiming at the problem of unstable buffering process of electromagnetic buffer(EMB)under intensive impact load,a three-segment electromagnetic buffer is proposed.The inner tube and air-gap of EMB are divided into three...Aiming at the problem of unstable buffering process of electromagnetic buffer(EMB)under intensive impact load,a three-segment electromagnetic buffer is proposed.The inner tube and air-gap of EMB are divided into three segments.The finite element analysis and impact test results show that the resultant resistance force(RRF)curve has two hump-shaped peaks,which is the reason for the unstable buffering process.In order to stabilize the buffering process,a multi-objective optimization design method of EMB based on Nash game theory is proposed.Firstly,the optimization model is established by taking the two peaks of the RRF curve and the maximum buffer displacement as the optimization objectives.Secondly,the multi-objective optimization model is transformed into a game model by sensitivity analysis and fuzzy clustering.Then,a Nash equilibrium solution strategy of EMB Nash game model based on symmetric elitist information exchange is proposed,which integrates gene expression programming(GEP)surrogate model and genetic algorithm(GA)as an optimization solver.Finally,the Nash equilibrium of the game model is obtained.The results show that the smoothness of the RRF curve has been significantly improved,which proves the effectiveness of the game strategy.展开更多
The interactions between attackers and network administrator are modeled as a non-cooperative non-zero-sum dynamic game with incomplete information, which considers the uncertainty and the special properties of multi-...The interactions between attackers and network administrator are modeled as a non-cooperative non-zero-sum dynamic game with incomplete information, which considers the uncertainty and the special properties of multi-stage attacks. The model is a Fictitious Play approach along a special game tree when the attacker is the leader and the administrator is the follower. Multi-objective optimization methodology is used to predict the attacker’s best actions at each decision node. The administrator also keeps tracking the attacker’s actions and updates his knowledge on the attacker’s behavior and objectives after each detected attack, and uses it to update the prediction of the attacker’s future actions. Instead of searching the entire game tree, appropriate time horizons are dynamically determined to reduce the size of the game tree, leading to a new, fast, adaptive learning algorithm. Numerical experiments show that our algorithm has a significant reduction in the damage of the network and it is also more efficient than other existing algorithms.展开更多
Power flow optimization control,which governs the energy flow among engine,battery,and motor,plays a very important role in plug-in hybrid electric vehicles(PHEVs).Its performance directly affects the fuel economy of ...Power flow optimization control,which governs the energy flow among engine,battery,and motor,plays a very important role in plug-in hybrid electric vehicles(PHEVs).Its performance directly affects the fuel economy of PHEVs.For the purpose of improving fuel economy,the electric system including battery and motor will be frequently scheduled,which would affect battery life.Therefore,a multi-objective optimization mechanism taking fuel economy and battery life into account is necessary,which is also a research focus in field of hybrid vehicles.Motivated by this issue,this paper proposes a multi-objective power flow optimization control strategy for a power split PHEV using game theory.Firstly,since the demand power of driver which is necessary for the power flow optimization control,cannot be known in advance,the demand power of driver can be modelled using a Markov chain to obtain predicted demand power.Secondly,based on the predicted demand power,the multi-objective optimization control problem is transformed into a game problem.A novel non-cooperative game model between engine and battery is established,and the benefit function with fuel economy and battery life as the optimization objective is proposed.Thirdly,under the premise of satisfying various constraints,the participants of the above game maximize their own benefit function to obtain the Nash equilibrium,which comprises of optimal power split scheme.Finally,the proposed strategy is verified compared with two baseline strategies,and results show that the proposed strategy can reduce equivalent fuel consumption by about 15%compared with baseline strategy 1,and achieve similar fuel economy while greatly extend battery life simultaneously compared with baseline strategy 2.展开更多
To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to ...To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to the individual welfare functions,we transform the multi–objective game into a single-objective game and define its bargaining equilibrium,which is a Nash equilibrium of the single-objective game.And then,based on certain continuity and concavity of the multi-objective game's payoff function,we proof the bargaining equilibrium still exists and is also a weakly Pareto-Nash equilibrium.Moreover,we analyze several special bargaining equilibria,and compare them in a few examples.展开更多
The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective t...The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.展开更多
文摘Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each “player” is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.
基金The project supported by the National Natural Science Foundation of China (10372040)Scientific Research Foundation (SRF) for Returned Oversea's Chinese Scholars (ROCS) (2003-091). The English text was polished by Yunming Chen
文摘There are currently three different game strategies originated in economics： （1） Cooperative games （Pareto front）, （2） Competitive games （Nash game） and （3） Hierarchical games （Stackelberg game）. Each game achieves different equilibria with different performance, and their players play different roles in the games. Here, we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multi- criteria aerodynamic optimization problems. The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments. We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method. The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front. Non-dominated Pareto front solutions are obtained, however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
基金funded by Shandong University of Technology Doctoral Program in Science and Technology,grant number 4041422007.
文摘The rapid advance of Connected-Automated Vehicles(CAVs)has led to the emergence of diverse delaysensitive and energy-constrained vehicular applications.Given the high dynamics of vehicular networks,unmanned aerial vehicles-assisted mobile edge computing(UAV-MEC)has gained attention in providing computing resources to vehicles and optimizing system costs.We model the computing offloading problem as a multi-objective optimization challenge aimed at minimizing both task processing delay and energy consumption.We propose a three-stage hybrid offloading scheme called Dynamic Vehicle Clustering Game-based Multi-objective Whale Optimization Algorithm(DVCG-MWOA)to address this problem.A novel dynamic clustering algorithm is designed based on vehiclemobility and task offloading efficiency requirements,where each UAV independently serves as the cluster head for a vehicle cluster and adjusts its position at the end of each timeslot in response to vehiclemovement.Within eachUAV-led cluster,cooperative game theory is applied to allocate computing resourceswhile respecting delay constraints,ensuring efficient resource utilization.To enhance offloading efficiency,we improve the multi-objective whale optimization algorithm(MOWOA),resulting in the MWOA.This enhanced algorithm determines the optimal allocation of pending tasks to different edge computing devices and the resource utilization ratio of each device,ultimately achieving a Pareto-optimal solution set for delay and energy consumption.Experimental results demonstrate that the proposed joint offloading scheme significantly reduces both delay and energy consumption compared to existing approaches,offering superior performance for vehicular networks.
文摘This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors and fuzzy clustering, the design variables are divided into different strategic spaces which belong to each player, then it constructs a payoff function based on the coalition mechanism. Each game player takes its own revenue function as a target and obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. A multi-objective optimization example of the luff mechanism of compensative sheave block shows the effectiveness of the coalition cooperative game method.
基金the National Key Research and Development Program of China(Basic Research Class)(No.2017YFB0903000)the National Natural Science Foundation of China(No.U1909201).
文摘The output uncertainty of high-proportion distributed power generation severely affects the system voltage and frequency.Simultaneously,controllable loads have also annually increased,which markedly improve the capability for nodal-power control.To maintain the system frequency and voltage magnitude around rated values,a new multi-objective optimization model for both voltage and frequency control is proposed.Moreover,a great similarity between the multiobjective optimization and game problems appears.To reduce the strong subjectivity of the traditional methods,the idea and method of the game theory are introduced into the solution.According to the present situational data and analysis of the voltage and frequency sensitivities to nodal-power variations,the design variables involved in the voltage and frequency control are classified into two strategy spaces for players using hierarchical clustering.Finally,the effectiveness and rationality of the proposed control are verified in MATLAB.
基金Supported bythe National Nature Science Founda-tion of China (90104029) the Specialized Research Fund for theDoctoral Programof Higher Education (20050487046)
文摘Based on the bimatrix game theory, the network data transmission has been depicted in a game theory way： the actions of the attacker and defender （legitimate users） are depicted within a two-person, non-cooperative and bimatrix game model, this paper proves the existence of the Nash equilibrium theoretically, which is further illustrated by the experimental resuhs.
文摘This paper deals with rnxn two-person non-zero sum games with interval pay-offs. An analytic method for solving such games is given. A pair of Nash Equilibrium is found by using the method. The analytic method is effective to find at least one Nash Equilibrium （N.E） for two-person bimatrix games. Therefore, the analytic method for two-person bimatrix games is adapted to interval bimatrix games.
基金National Natural Science Foundation of China(NSFC61773142,NSFC62303136)。
文摘When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
基金Project supported by the National Natural Science Foundation of China(Nos.62273201 and 62350037)the Taishan Scholar Project of Shandong Province of China(No.TSTP20221103)。
文摘Multi-objective games(MOGs)have received much attention in recent years as a class of games with vector payoffs.Based on the semi-tensor product(STP),this paper discusses the MOG,including the existence,finite-step reachability,and finite-step controllability of Pareto equilibrium of this model,from both static and dynamic perspectives.First,the MOG concept is presented using multi-layer graphs,and STP is used to convert the payoff function into its algebraic form.Then,from the static perspective,two necessary and sufficient conditions are proposed to verify whether all players can meet their expectations and whether the strategy profile is a Pareto equilibrium,separately.Furthermore,from the dynamic perspective,a strategy updating rule is designed to investigate the finite-step reachability of the evolutionary MOG.Finally,the finite-step controllability of the evolutionary MOG is analyzed by adding pseudo-players,and a backward search algorithm is provided to find the shortest evolutionary process and control sequence.
基金supported by the Key Laboratory of Smart Grid in Shaanxi Province.
文摘With the rapid growing of EVs and increasing power loads,the integrated energy systems(IES)in practical operations are facing challenges in balancing safety and economic efficiency,along with the rise of unexpected energy usage plans by users.To address these issues,this research proposes a three-layer game-based multi-objective optimization strategy for IES.First,safety performance indexes of the in-tegrated energy network are established using graph theory and the Wiener process.Then,a non-cooperative-Stackelberg-cooperative game framework is constructed,which optimizes safety and eco-nomic indexes while allowing lower-level users to cooperate to maximize their own benefits.Further-more,considering Unexpected Load Deviations(ULDs)during actual operations,a flexible resource margin adjustment-based Adaptive Optimal Strategy and Information Gap Decision Theory(AOS-IGDT)strategy is proposed and embedded in the second stage of rolling optimization.Finally,the proposed strategy is verified using the coupled IEEE 33-bus system and a 17-node thermal network,the results demonstrate its effectiveness in achieving a win-win outcome for system economic and safety perfor-mance while reducing the ULDs and improving the benefits of all stakeholders.
基金supported by the China Postdoctoral Science Foundation(Grant No.BX2021126).
文摘Aiming at the problem of unstable buffering process of electromagnetic buffer(EMB)under intensive impact load,a three-segment electromagnetic buffer is proposed.The inner tube and air-gap of EMB are divided into three segments.The finite element analysis and impact test results show that the resultant resistance force(RRF)curve has two hump-shaped peaks,which is the reason for the unstable buffering process.In order to stabilize the buffering process,a multi-objective optimization design method of EMB based on Nash game theory is proposed.Firstly,the optimization model is established by taking the two peaks of the RRF curve and the maximum buffer displacement as the optimization objectives.Secondly,the multi-objective optimization model is transformed into a game model by sensitivity analysis and fuzzy clustering.Then,a Nash equilibrium solution strategy of EMB Nash game model based on symmetric elitist information exchange is proposed,which integrates gene expression programming(GEP)surrogate model and genetic algorithm(GA)as an optimization solver.Finally,the Nash equilibrium of the game model is obtained.The results show that the smoothness of the RRF curve has been significantly improved,which proves the effectiveness of the game strategy.
文摘The interactions between attackers and network administrator are modeled as a non-cooperative non-zero-sum dynamic game with incomplete information, which considers the uncertainty and the special properties of multi-stage attacks. The model is a Fictitious Play approach along a special game tree when the attacker is the leader and the administrator is the follower. Multi-objective optimization methodology is used to predict the attacker’s best actions at each decision node. The administrator also keeps tracking the attacker’s actions and updates his knowledge on the attacker’s behavior and objectives after each detected attack, and uses it to update the prediction of the attacker’s future actions. Instead of searching the entire game tree, appropriate time horizons are dynamically determined to reduce the size of the game tree, leading to a new, fast, adaptive learning algorithm. Numerical experiments show that our algorithm has a significant reduction in the damage of the network and it is also more efficient than other existing algorithms.
基金the National Natural Science Foundation of China(Grant Nos.51975048,U1764257 and 51705480)the Beijing Institute of Technology Research Fund Program for Young Scholars。
文摘Power flow optimization control,which governs the energy flow among engine,battery,and motor,plays a very important role in plug-in hybrid electric vehicles(PHEVs).Its performance directly affects the fuel economy of PHEVs.For the purpose of improving fuel economy,the electric system including battery and motor will be frequently scheduled,which would affect battery life.Therefore,a multi-objective optimization mechanism taking fuel economy and battery life into account is necessary,which is also a research focus in field of hybrid vehicles.Motivated by this issue,this paper proposes a multi-objective power flow optimization control strategy for a power split PHEV using game theory.Firstly,since the demand power of driver which is necessary for the power flow optimization control,cannot be known in advance,the demand power of driver can be modelled using a Markov chain to obtain predicted demand power.Secondly,based on the predicted demand power,the multi-objective optimization control problem is transformed into a game problem.A novel non-cooperative game model between engine and battery is established,and the benefit function with fuel economy and battery life as the optimization objective is proposed.Thirdly,under the premise of satisfying various constraints,the participants of the above game maximize their own benefit function to obtain the Nash equilibrium,which comprises of optimal power split scheme.Finally,the proposed strategy is verified compared with two baseline strategies,and results show that the proposed strategy can reduce equivalent fuel consumption by about 15%compared with baseline strategy 1,and achieve similar fuel economy while greatly extend battery life simultaneously compared with baseline strategy 2.
基金supported by the National Natural Science Foundation of China(No.11271098)by the Science and Technology Fund Program of Guizhou Province(No.7425)。
文摘To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to the individual welfare functions,we transform the multi–objective game into a single-objective game and define its bargaining equilibrium,which is a Nash equilibrium of the single-objective game.And then,based on certain continuity and concavity of the multi-objective game's payoff function,we proof the bargaining equilibrium still exists and is also a weakly Pareto-Nash equilibrium.Moreover,we analyze several special bargaining equilibria,and compare them in a few examples.
文摘The intuitionistic fuzzy set(I-fuzzy set)plays an effective role in game theory when players face‘neither this nor that’situation to set their goals.This study presents a maxmin–minmax solution to multi-objective two person zero-sum matrix games with I-fuzzy goals.In this article,a class of piecewise linear membership and non-membership functions for I-fuzzy goals is constructed.These functions are more effective in real games because marginal rate of increase(decrease)of such membership functions(non-membership functions)is different in different intervals of tolerance errors.Finally,one numerical example is given to examine the effectiveness and advantages of the proposed results.
