Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance.A non-cooperative game model is established,considering the competition and self-interest behavior of jobs from different customers for machine resources.The job from different customers is mapped to the players in the game model,the corresponding optional processing machine and location are mapped to the strategy set,and the makespan of the job is mapped to the payoff.Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model.A Nash equilibrium solution algorithm based on the genetic algorithm(NEGA)is designed,and the effective solution of approximate Nash equilibrium for the game model is realized.The fitness function,single-point crossover operator,and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium.Rules are also designed to avoid the generation of invalid offspring chromosomes.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.Compared with other algorithms such as heuristic algorithms(FCFS,SPT,and LPT),the simulated annealing algorithm(SA),and the particle swarm optimization algorithm(PSO),experimental results show that the proposed NE-GA algorithm has obvious performance advantages.

Peer-to-Peer Energy Trading Method of Multi-Virtual Power Plants Based on Non-Cooperative Game

The current electricity market fails to consider the energy consumption characteristics of transaction subjects such as virtual power plants.Besides,the game relationship between transaction subjects needs to be further explored.This paper proposes a Peer-to-Peer energy trading method for multi-virtual power plants based on a non-cooperative game.Firstly,a coordinated control model of public buildings is incorporated into the scheduling framework of the virtual power plant,considering the energy consumption characteristics of users.Secondly,the utility functions of multiple virtual power plants are analyzed,and a non-cooperative game model is established to explore the game relationship between electricity sellers in the Peer-to-Peer transaction process.Finally,the influence of user energy consumption characteristics on the virtual power plant operation and the Peer-to-Peer transaction process is analyzed by case studies.Furthermore,the effect of different parameters on the Nash equilibrium point is explored,and the influence factors of Peer-to-Peer transactions between virtual power plants are summarized.According to the obtained results,compared with the central air conditioning set as constant temperature control strategy,the flexible control strategy proposed in this paper improves the market power of each VPP and the overall revenue of the VPPs.In addition,the upper limit of the service quotation of the market operator have a great impact on the transaction mode of VPPs.When the service quotation decreases gradually,the P2P transaction between VPPs is more likely to occur.

Coordinated Scheduling of Two-Agent Production and Transportation Based on Non-Cooperative Game

A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average.

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

Resource Allocation for Network Security Risk Assessment：A Non-Cooperative Differential Game Based Approach

In this paper, we propose a non-cooperative differential game theory based resource allocation approach for the network security risk assessment. For the risk assessment, the resource will be used for risk assess, including response cost and response negative cost. The whole assessment process is considered as a differential game for optimal resource control. The proposed scheme can be obtained through the Nash Equilibrium. It is proved that the game theory based algorithm is applicable and the optimal resource level can be achieved based on the proposed algorithm.

Bi-matrix Games with Fuzzy Strategies and Fuzzy Payoffs and Their Mathematical Programming Equivalents

A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.

QoS awared power and admission controls based on non-cooperative game theory in wireless networks

In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative game where the users adjust their transmit powers to maximize the utility, thus restraining the interferences. By using adaptive utility functions and tunable pricing parameters according to QoS levels, this algorithm can well meet different QoS requirements and improve system capacity compared with those that ignore the QoS differences.

An Optimized Resource Scheduling Strategy for Hadoop Speculative Execution Based on Non-cooperative Game Schemes

Hadoop is a well-known parallel computing system for distributed computing and large-scale data processes.“Straggling”tasks,however,have a serious impact on task allocation and scheduling in a Hadoop system.Speculative Execution(SE)is an efficient method of processing“Straggling”Tasks by monitoring real-time running status of tasks and then selectively backing up“Stragglers”in another node to increase the chance to complete the entire mission early.Present speculative execution strategies meet challenges on misjudgement of“Straggling”tasks and improper selection of backup nodes,which leads to inefficient implementation of speculative executive processes.This paper has proposed an Optimized Resource Scheduling strategy for Speculative Execution(ORSE)by introducing non-cooperative game schemes.The ORSE transforms the resource scheduling of backup tasks into a multi-party non-cooperative game problem,where the tasks are regarded as game participants,whilst total task execution time of the entire cluster as the utility function.In that case,the most benefit strategy can be implemented in each computing node when the game reaches a Nash equilibrium point,i.e.,the final resource scheduling scheme to be obtained.The strategy has been implemented in Hadoop-2.x.Experimental results depict that the ORSE can maintain the efficiency of speculative executive processes and improve fault-tolerant and computation performance under the circumstances of Normal Load,Busy Load and Busy Load with Skewed Data.

Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games

In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.

Non-cooperative game for network access selection in heterogeneous integrated networks

The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access network to obtain the most desired service.A kind of unified quantification model of non-monotone quality of service(QoS) and a model of non-cooperative game between users and networks are proposed for heterogeneous network access selection.An optimal network pricing mechanism could be formulated by using a novel strategy which is used in this non-cooperative game model to balance the interests of both the users and the networks.This access network selection mechanism could select the most suitable network for users,and it also could provide the basis when formulating QoS standards in heterogeneous integrated networks.The simulation results show that this network selection decision-making algorithm can meet the users' demand for different levels service in different scenes and it can also avoid network congestion caused by unbalanced load.

Excess Benefit Allocation in Shared Savings Based on Non-cooperative Game Theory

Energy saving income distribution mode is of great significance to the energy industry.With the continuous application of new technologies,the problem of excess energy saving income distribution has become one of the obstacles to the appreciation of energy performance.At present,the distribution of risk and income is mainly based on the contribution of risk and income,which has some limitations.The benefit distribution of energy saving negotiation between energy saving service companies and clients can be regarded as a bargaining process where an effective range satisfying both parties can be obtained.This provides a new perspective in solving the problem of excess energy saving income distribution in energy management contract projects.

MADRL-based UAV swarm non-cooperative game under incomplete information

Unmanned Aerial Vehicles(UAVs)play increasing important role in modern battlefield.In this paper,considering the incomplete observation information of individual UAV in complex combat environment,we put forward an UAV swarm non-cooperative game model based on Multi-Agent Deep Reinforcement Learning(MADRL),where the state space and action space are constructed to adapt the real features of UAV swarm air-to-air combat.The multi-agent particle environment is employed to generate an UAV combat scene with continuous observation space.Some recently popular MADRL methods are compared extensively in the UAV swarm noncooperative game model,the results indicate that the performance of Multi-Agent Soft Actor-Critic(MASAC)is better than that of other MADRL methods by a large margin.UAV swarm employing MASAC can learn more effective policies,and obtain much higher hit rate and win rate.Simulations under different swarm sizes and UAV physical parameters are also performed,which implies that MASAC owns a well generalization effect.Furthermore,the practicability and convergence of MASAC are addressed by investigating the loss value of Q-value networks with respect to individual UAV,the results demonstrate that MASAC is of good practicability and the Nash equilibrium of the UAV swarm non-cooperative game under incomplete information can be reached.

Non-cooperative Game Based Optimal Dispatch Model for Integrated Energy Systems

In order to improve the efficiency of energy utilization,the integrated energy system(IES)has emerged.The IES typically acts as a whole system during operations,the subsystems are separated,and the interests of each system are independent.In this paper,considering the relationship between the various energy systems,non-cooperative game theory is used to establish the optimal dispatch model.The proposed model mainly relies on the relationship between the cooperation and competition among various subsystems to obtain the maximum benefit they can accept.Furthermore,the basic definition is combined with the particle swarm optimization algorithm to solve the problem.The results show that the optimization strategy proposed in this paper can operate safely and reliably,and effectively distribute the benefits of each energy system.

Fuzzy mathematics and game theory based D2D multicast network construction

Device to device(D2 D) multi-hop communication in multicast networks solves the contradiction between high speed requirements and limited bandwidth in regional data sharing communication services. However, most networking models demand a large control overhead in eNodeB. Moreover, the topology should be calculated again due to the mobility of terminals, which causes the long delay. In this work, we model multicast network construction in D2 D communication through a fuzzy mathematics and game theory based algorithm. In resource allocation, we assume that user equipment(UE) can detect the available frequency and the fuzzy mathematics is introduced to describe an uncertain relationship between the resource and UE distributedly, which diminishes the time delay. For forming structure, a distributed myopic best response dynamics formation algorithm derived from a novel concept from the coalitional game theory is proposed, in which every UE can self-organize into stable structure without the control from eNodeB to improve its utilities in terms of rate and bit error rate(BER) while accounting for a link maintenance cost, and adapt this topology to environmental changes such as mobility while converging to a Nash equilibrium fast. Simulation results show that the proposed architecture converges to a tree network quickly and presents significant gains in terms of average rate utility reaching up to 50% compared to the star topology where all of the UE is directly connected to eNodeB.

A DNN based trajectory optimization method for intercepting non-cooperative maneuvering spacecraft

Current successes in artificial intelligence domain have revitalized interest in neural networks and demonstrated their potential in solving spacecraft trajectory optimization problems. This paper presents a data-free deep neural network(DNN) based trajectory optimization method for intercepting noncooperative maneuvering spacecraft, in a continuous low-thrust scenario. Firstly, the problem is formulated as a standard constrained optimization problem through differential game theory and minimax principle. Secondly, a new DNN is designed to integrate interception dynamic model into the network and involve it in the process of gradient descent, which makes the network endowed with the knowledge of physical constraints and reduces the learning burden of the network. Thus, a DNN based method is proposed, which completely eliminates the demand of training datasets and improves the generalization capacity. Finally, numerical results demonstrate the feasibility and efficiency of our proposed method.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

On Dynamics and Nash Equilibriums of Networked Games

Networked noncooperative games are investigated,where each player(or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors current information to decide its next strategy. By using sub-neighborhood, the dynamics of the evolution is obtained. Then a method for calculating Nash equilibriums from mixed strategies of multi-players is proposed.The relationship between local Nash equilibriums based on individual neighborhoods and global Nash equilibriums of overall network is revealed. Then a technique is proposed to construct Nash equilibriums of an evolutionary game from its one step static Nash equilibriums. The basic tool of this approach is the semi-tensor product of matrices, which converts strategies into logical matrices and payoffs into pseudo-Boolean functions, then networked evolutionary games become discrete time dynamic systems.

No-cooperative games for multiple emergency locations in resource scheduling

When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model and an algorithm for scheduling of relief resources are presented. In the model, the players correspond to the multiple emergency locations, strategies correspond to all resources scheduling and the payoff of each emergency location corresponds to the reciprocal of its scheduling cost. Thus, the optimal results are determined by the Nash equilibrium point of this game. Then the iterative algorithm is introduced to seek the Nash equilibrium point. Simulation and analysis are given to demonstrate the feasibility and availability of the model.