Task strategy generation method and device based on vector value game matrix, and medium
By constructing a vector-valued game matrix and Nash equilibrium theory, and combining it with a multi-objective heuristic solution algorithm, a Pareto-Nash equilibrium solution set is generated. This solves the problem of insufficient performance representation in multi-objective game decision-making, improves the flexibility and adaptability of decision-making, and realizes efficient multi-objective game decision-making.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- 10TH RES INST OF CETC
- Filing Date
- 2026-04-29
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies are insufficient to fully characterize the adversarial effectiveness of both sides in multi-objective game decision-making under multiple objective dimensions. The models lack adaptability and flexibility, making it difficult to generate decision schemes that take into account multi-objective optimization.
By constructing a vector-valued game matrix and combining Nash equilibrium theory with a multi-objective heuristic solution algorithm, a Pareto-Nash equilibrium solution set is generated. Through multi-dimensional performance evaluation and resource-constrained optimization models, the flexibility and adaptability of decision-making are improved.
It achieves more accurate multi-dimensional performance representation, improves decision quality and execution efficiency, and can provide multiple decision-making options in dynamically changing game scenarios to meet the strategy selection needs of different scenarios.
Smart Images
Figure CN122154945A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent decision-making technology in game theory, and in particular to a method, device and medium for generating task strategies based on vector-valued game matrices. Background Technology
[0002] Currently, in complex scenarios involving multi-agent collaborative decision-making and multi-platform intelligent interaction, how to formulate efficient decision-making strategies in a multi-party game environment has become a key research focus in related fields. Game theory, as an important theoretical tool, is widely used in the construction of various decision-making models.
[0003] In games, the decisions made by one player are influenced by the decisions made by the other players, and the decisions made by one player also affect the decisions made by the other players. John von Neumann and Morganstein's book, *Game Theory and Economic Behavior*, summarizes previous work on game theory and economic mathematics, proposes fundamental axioms of games, and lays the foundation for the basic analytical framework of games.
[0004] For most games, it's impossible to find the optimal solution by repeatedly eliminating inferior strategies. Therefore, scholars proposed the concept of Nash equilibrium, a crucial concept in game theory. When a strategy combination satisfies the meaning of Nash equilibrium, no single player can unilaterally change their decision and increase their own benefit. Nash equilibrium is essentially a non-cooperative game, and a game may have more than one Nash equilibrium solution.
[0005] Currently, game theory in practical applications is often a macroscopic, complex, multi-dimensional comprehensive game process. Players need to compare and weigh the payoffs of multiple objective dimensions in order to arrive at a decent and stable decision. Traditional single-objective game theory methods cannot meet the needs of modeling and solving such complex problems, and it is difficult to weigh the payoffs of each objective dimension to generate a global strategy.
[0006] Patent CN112612300B discloses a multi-objective game theory method and apparatus for multi-platform intelligent decision-making. The multi-objective game theory method includes: S1, obtaining the total strategy space of the two opposing sides; S2, setting at least one optimization objective based on preferences; S3, transforming the optimization objective into at least one sub-optimization objective, and setting a corresponding payoff function based on each sub-optimization objective; S4, constructing high-dimensional matrices for evaluating the total strategy space of the two opposing sides based on the payoff functions; S5, outputting the hybrid strategy Nash equilibrium solution based on the high-dimensional matrices of the two opposing sides using a multi-objective hybrid strategy Nash equilibrium solution algorithm.
[0007] Furthermore, patent CN114819316B discloses a complex optimization method for multi-agent task planning. This method is based on Markov decision theory and game theory, and includes multi-objective task allocation and multi-agent path planning. The multi-objective task allocation employs a bidirectional bidding strategy, i.e., a cyclic bidding strategy where agents bid for target tasks and target tasks bid for agents. The multi-agent interaction module includes a correlation ranking unit and a cyclic interaction unit connected sequentially. The correlation ranking unit performs correlation ranking, and the cyclic interaction unit uses a cyclic recursive structure to reduce the dimensionality of the state variables output by the correlation ranking unit, obtaining interaction information whose data dimension is independent of the number of agents.
[0008] While these technologies offer insights into multi-objective game decision-making, they still have certain shortcomings and limitations. First, the high-dimensional matrices constructed by these multi-objective game methods often rely on single-dimensional payoff function mappings, making it difficult to fully represent the adversarial effectiveness of both sides across multiple objective dimensions, and resulting in insufficient comprehensive evaluation of multi-dimensional effectiveness. Second, the interactive information processing flow of these task planning methods is relatively complex, and the combination of correlation ranking and iterative recursion requires improvement in the adaptability and flexibility of the model when facing dynamically changing game scenarios. Third, the equilibrium solution-solving process of existing technologies mostly focuses on specific Nash equilibrium types, and the generated decision schemes have limitations in their multi-objective optimization capabilities, making it difficult to meet the actual needs of decision-makers to flexibly choose strategies across multiple dimensions. Summary of the Invention
[0009] To address the challenge of efficiently solving the vector-valued game matrix for both sides in generating adversarial strategies for traditional large-scale complex games, this invention proposes a task strategy generation method, device, and medium based on the vector-valued game matrix. This method can improve the availability and adaptability of game models in highly dynamic and adversarial environments. This invention is applicable to various decision-making systems that involve multi-dimensional complex games with opponents.
[0010] The technical solution adopted in this invention is as follows: A task strategy generation method based on vector-valued game matrices includes: Based on the multidimensional performance evaluation results of the mutual confrontation between various feasible task strategies of the two sides in the game, a vector value game matrix is constructed. Based on the vector value game matrix and various resource constraints of both sides, a multi-objective optimization model of the vector value game matrix is constructed by combining Nash equilibrium theory. A multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector value game matrix, generate the Pareto-Nash equilibrium solution set of the vector value game matrix, and output the corresponding task strategy.
[0011] Furthermore, the construction of the vector-valued game matrix based on the multi-dimensional effectiveness evaluation results of the mutual adversarial interaction between various feasible task strategies of both sides includes: combining the opponent's feasible strategy set. And our feasible strategy set The multidimensional performance evaluation results under adversarial conditions are calculated to dynamically determine and adjust the value of each element in the vector-valued game matrix; where, m The number of feasible strategies for the opponent. n This represents the number of feasible strategies available to us.
[0012] Furthermore, the strategies in the opponent's feasible strategy set and our feasible strategy set are multivariate arrays:
[0013] in, Resource elements representing strategies The target elements of the strategy are represented. The elements of a strategy representation method The time element of the strategy, Spatial elements representing strategies.
[0014] Furthermore, in the vector-valued game matrix, each element is a one-dimensional vector, representing the performance evaluation results of multiple optimization objective dimensions when our feasible strategy confronts the opponent's feasible strategy. These optimization objective dimensions include task payoffs. Failure and loss Resource consumption The time spent fighting .
[0015] Furthermore, the construction of a multi-objective optimization model for the vector-valued game matrix based on the vector-valued game matrix and various resource constraints of both sides of the game, combined with Nash equilibrium theory, includes: based on the vector-valued game matrix of both sides of the game, comprehensively considering the mutual constraints of multiple optimization objectives and the dynamic change constraints of the importance of each optimization objective, and constructing a multi-objective optimization model for the vector-valued game matrix in combination with Nash equilibrium theory.
[0016] Furthermore, the expression for the multi-objective optimization model of the vector-valued game matrix includes:
[0017] in, This indicates that we adopt the first... The probability of a feasible strategy. This represents a possible solution for us, which is the probability distribution of each feasible strategy we can adopt. ; Indicates that the opponent adopted the first The probability of a feasible strategy. A feasible solution for an opponent is represented by the probability distribution of the opponent adopting each feasible strategy. ; This indicates that we have adopted the proposed solution. Adopting a solution with the opponent When engaging in confrontation, k Evaluation results for each optimization objective dimension; Indicates the first The and the first There are constraints between the optimization objectives. .
[0018] Furthermore, the multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector-valued game matrix to generate the Pareto-Nash equilibrium solution set of the vector-valued game matrix. This includes: analyzing the mean fitness of each dimension of the optimal subset, i.e., the Pareto front; comprehensively considering the dominance of each feasible solution in the multiple optimization objective dimensions; and giving a horizontal ranking of the points contained in the Pareto front that are in equilibrium, thereby generating the Pareto-Nash equilibrium solution set of the vector-valued game matrix.
[0019] Furthermore, the multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector-valued game matrix to generate the Pareto-Nash equilibrium solution set of the vector-valued game matrix. Specifically, this includes: taking the average fitness of the optimal solution set of each optimization objective dimension as the score of the corresponding optimization objective in the sense of Nash equilibrium; the closer the average fitness is to zero, the higher the score, and the easier it is to reach Nash equilibrium; based on the relationship between the optimization objective dimensions represented by the average fitness of each optimization objective dimension, the level ranking of the points contained in the Pareto front that are in equilibrium is given; and by comprehensively considering the dominance relationship of each feasible solution in each optimization objective dimension, the Pareto-Nash equilibrium solution set of the vector-valued game matrix is generated, thereby generating the probability of adopting different strategies within our feasible strategy set.
[0020] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the task strategy generation method based on a vector value game matrix.
[0021] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the task strategy generation method based on a vector value game matrix.
[0022] The beneficial effects of this invention are as follows: This invention constructs a vector-valued game matrix, builds a multi-objective optimization model, and uses a heuristic solution algorithm to generate a Pareto-Nash equilibrium solution set. This effectively meets the decision-making needs of both sides in a multi-objective adversarial game, significantly improving decision quality and execution efficiency in multi-objective game scenarios. Compared to existing technologies, this invention has the following significant advantages.
[0023] 1. Enhanced multi-dimensional performance representation capability. This invention constructs a vector-valued game matrix based on the performance evaluation results of the multi-objective dimensions of the game, which can more accurately and comprehensively cover the adversarial effects of multiple objectives and avoid performance evaluation bias caused by dimension mapping.
[0024] 2. Superior Model Adaptability and Flexibility. This invention combines various resource constraints of both sides in the game to construct a multi-objective optimization model. It eliminates the need for complex correlation ranking and iterative dimensionality reduction operations. In dynamically changing multi-objective continuous game scenarios, it can better adapt to strategy adjustments and resource changes, thereby improving the flexibility of decision-making.
[0025] 3. The decision-making schemes are more practical. The Pareto-Nash equilibrium solution set generated by this invention takes into account both Pareto optimality in multi-objective dimensions and Nash equilibrium in game adversarial situations. It can provide decision-makers with multiple decision-making schemes to meet the strategy selection needs in different scenarios and improve task efficiency in multi-objective game situations.
[0026] In summary, this invention addresses the need for generating decision-making solutions in multi-dimensional game adversarial scenarios between two players. Based on the evaluation results of various feasible adversarial scenarios across different objective dimensions, it constructs a vector-valued game matrix for both players, designs a multi-objective optimization model for the vector-valued game matrix, and implements a heuristic solution algorithm. This enables efficient generation of Pareto-Nash equilibrium solution sets for the vector-valued game matrix, allowing decision-makers to make more flexible choices among multiple decision options and improving task efficiency and flexibility in multi-objective game scenarios. This invention is applicable to various decision-making systems involving complex multi-dimensional games with opponents and has broad application prospects. Attached Figure Description
[0027] Figure 1 This is a flowchart of a task strategy generation method based on a vector-valued game matrix according to Embodiment 1 of the present invention.
[0028] Figure 2 This is a schematic diagram of the task strategy in Embodiment 2 of the present invention.
[0029] Figure 3 This is a flowchart of the multi-objective heuristic solution algorithm of Embodiment 2 of the present invention.
[0030] Figure 4 This is a fitness change graph of the three target dimensions during the iteration process of Embodiment 2 of the present invention.
[0031] Figure 5 This is a three-dimensional visualization result of the fitness of the Pareto-Nash equilibrium solution set in three objective dimensions according to Embodiment 2 of the present invention. Detailed Implementation
[0032] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0033] Example 1 like Figure 1 As shown, this embodiment provides a task strategy generation method based on a vector-valued game matrix, including: Based on the multidimensional performance evaluation results of the mutual confrontation between various feasible task strategies of the two sides in the game, a vector value game matrix is constructed. Based on the vector value game matrix and various resource constraints of both sides, a multi-objective optimization model of the vector value game matrix is constructed by combining Nash equilibrium theory. A multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector value game matrix, generate the Pareto-Nash equilibrium solution set of the vector value game matrix, and output the corresponding task strategy.
[0034] It should be noted that Pareto optimality is a core concept in multi-objective optimization problems. It refers to the fact that changing it to any other solution that makes at least one objective dimension better will necessarily make at least one other objective dimension worse. The set of all Pareto optimal solutions is called the Pareto solution set.
[0035] Specifically, the task strategy generation method in this embodiment can be implemented using the following steps: S1. Based on the multidimensional effectiveness evaluation results of the mutual confrontation between various feasible task strategies of the two sides, construct the vector value game matrix of the confrontation between the two sides. S2. Based on the vector-valued game matrix of the two sides, combined with theories such as Nash equilibrium, and comprehensively considering multiple optimization objectives (e.g., task benefits). Failure and loss Resource consumption The time spent fighting A multi-objective optimization model based on vector value game matrix is constructed, which is constrained by mutual constraints and dynamic changes in the importance of each optimization objective. S3. The solution of the multi-objective optimization model of vector value game matrix is transformed into a multi-objective optimization problem, and the solution is obtained by multi-objective heuristic algorithm to obtain the final task strategy.
[0036] In step S1, our feasible strategy set is as follows: The opponent's feasible strategy set is ;in, m The number of feasible strategies for the opponent. n This represents the number of feasible strategies available to our side. It should be noted that a task strategy is a plan prepared and implemented by both sides in a game to accomplish a task. It specifies the purpose, content, methods, steps, time, and requirements for completing the task. Its essence lies in identifying and analyzing the capabilities, background, and environment of the opposing parties in the game, integrating the decision-makers' skills, knowledge, creativity, and judgment to clearly analyze dangers, threats, consequences, destruction, and risks, thereby achieving the task objective.
[0037] A strategy mainly describes five elements in the execution of a task: 1) Who to do, describing the subject of the strategy; 2) Do what, describing the goal of the strategy; 3) By what, describing the method of the strategy; 4) When to do it, describing the time attribute of the strategy; and 5) Where to do it, describing the spatial attribute of the strategy.
[0038] Preferably, in this embodiment, the strategy is modeled as a multivariate array according to its elements:
[0039] in, The resource elements representing a strategy, such as the entity that executes the strategy; It represents the target elements of a strategy, such as the desired effect of the strategy; The methodological elements representing a strategy, such as the techniques and means used in executing the strategy; The time elements of the strategy are represented, such as key time points for executing the strategy and time windows; Spatial elements representing a strategy, such as key spatial locations and routes for execution. The resources, objectives, methods, space, and time elements of a strategy are interdependent and mutually restrictive, permeating the entire task process. (Refer to...) Figure 2 .
[0040] Decision-makers need to fully evaluate the benefits, risks, and costs of a strategy to find the optimal strategy to achieve the task objective. In this scenario, both sides have multiple available strategies. This embodiment constructs a vector-valued game matrix based on the available strategies of both sides. Each element in the vector-valued game matrix is a one-dimensional vector, representing the task payoff when our feasible strategies compete against the opponent's feasible strategies. Failure and loss Resource consumption Combat takes time The performance evaluation results are presented across multiple objective dimensions. Specifically, the vector-valued game matrix is shown in Table 1.
[0041] Table 1 - Vector Value Game Matrix of Example 1
[0042] The above vector-valued game matrix indicates that our side has A feasible strategy, the opponent has A feasible strategy, both parties in The game involves a multi-dimensional objective, where each element in the matrix is a one-dimensional vector. The subscript of each value in the vector represents the feasible strategy number of our side and the feasible strategy number of the opponent, respectively, and the superscript of each value in the vector represents the objective dimension being evaluated.
[0043] Preferably, task rewards Failure and loss Resource consumption Combat takes time Calculations were performed using dimensionless normalization and based on performance extrema. and performance value Unify the performance value to Interval:
[0044] in, Through the above methods, one can obtain a key element in the game theory confrontation. The vector-valued game matrix.
[0045] In step S2, the vector-valued game problem involved is a complex multi-objective game problem, in which the two players need to compete on multiple different objective dimensions. Preferably, the multi-objective optimization model of the vector-valued game matrix in this embodiment can be expressed as:
[0046] in, This indicates that we adopt the first... The probability of a feasible strategy. This represents a possible solution for us, which is the probability distribution of each feasible strategy we can adopt. Similarly, Indicates that the opponent adopted the first The probability of a feasible strategy. A feasible solution for an opponent is represented by the probability distribution of the opponent adopting each feasible strategy. . Indicates the first The and the first There are constraints between the optimization objectives. .
[0047] In the multi-objective optimization model of vector-valued game matrix, our optimization objective is to achieve dominance in as many game dimensions as possible. Therefore, the optimization objective of the model is set as follows: ,in, This indicates that we have adopted the proposed solution. Adopting a solution with the opponent When engaging in confrontation, k The evaluation results for each objective dimension can be expressed as:
[0048] Based on the evaluation results of each objective dimension, the optimization objective function is designed as follows:
[0049] The optimization function for each objective dimension is as follows:
[0050] The above formula indicates that, in the dimension of benefit-oriented goals such as task effectiveness, the optimization goal is the reciprocal of the performance evaluation result in that dimension, and in the dimension of failure losses... Resource consumption Combat takes time In the equivalent cost type of objective dimension, the optimization objective is the performance evaluation result in that dimension.
[0051] In the multi-objective optimization model of vector-valued game matrix, the first constraint condition and the second constraint This indicates that the probability distribution of each strategy in our feasible solution is between 0 and 1, and the sum of the probabilities is 1; the third constraint... and the fourth constraint This indicates that the probability distribution of each strategy among the opponent's feasible options is between 0 and 1, and the sum of the probabilities is 1; the fifth constraint. Indicates the first The and the first There are constraints between the optimization objectives. .
[0052] If it exists satisfy ,and ,but This is a Nash equilibrium solution for the model.
[0053] In step S3, the multi-objective optimization problem consists of multiple conflicting and influencing objectives. These objectives cannot simultaneously reach their optimal state; therefore, it is generally recommended to try to ensure that these objectives reach their optimal state within a certain region. In a multi-objective optimization problem, if a solution... At least one objective is better than another solution. Okay, and the solution No objective is better than another solution If the difference is such that it is called a solution, then it is called a solution. Dominant Solution .
[0054] Preferably, the two solutions of the vector-valued game matrix multi-objective optimization model are considered. ,untie Dominant Solution (recorded as) The judgment condition for ) is:
[0055] For a solution in a vector-valued game matrix multi-objective optimization model, if no other solution can dominate it, then the solution is called a non-dominated solution.
[0056] In a solution set of a vector-valued game matrix multi-objective optimization model, the Pareto rank of a non-dominated solution is defined as 1. After removing non-dominated solutions from the solution set, a new set of non-dominated solutions is found, and its Pareto rank is incremented by 1. This process is repeated until the solution set is empty, yielding the Pareto ranks of all solutions in the set. Individuals with a Pareto rank of 1, being undominated by other individuals, are called Pareto optimal solutions, and the solution set of all Pareto optimal solutions is called the Pareto optimal solution set. Therefore, solving the vector-valued game matrix multi-objective optimization model is equivalent to finding the Pareto Nash equilibrium solution set of the model.
[0057] See Figure 3 This embodiment provides a multi-objective heuristic algorithm for solving Pareto Nash equilibrium solution sets in vector-valued games, including the following steps: 1) Initialize the solution set and external archive set: Randomly generate multiple solutions within the constraints of the solution to form the initial solution set, and initialize the archive set to empty; 2) Add non-dominated solutions from the initial solution set to the Archive set: By calculating the dominance relationships between solutions in the initial solution set, add the non-dominated solutions to the Archive set; 3) Calculate the density information of each solution in the Archive set:
[0058] in, Represents the Archive set; Indicates the first number in Archive collection One solution. Represents the solutions in Archive. and solution The distance between them This represents the distance threshold between solutions. Representing Archive set and solution The set of all solutions whose distance is less than a distance threshold. This indicates the number of elements in the set.
[0059] 4) Selecting the global optimal solution and the individual optimal solution: Based on the density information of each solution in the Archive set, the solution with the smallest density information in the current iteration is selected as the global optimal solution. For each remaining solution, if it is dominated by the global optimum of the previous iteration, it is updated to the global optimum of the previous iteration with a certain probability, ultimately forming the individual optimum of the current iteration. .
[0060] 5) Update Archive: Update the Archive based on the global optimal solution and individual optimal solution of the current round.
[0061] 6) Determine if the iteration termination condition is met: When the iteration round reaches the maximum iteration round, or the global optimal solution of the current round is consistent with the global optimal solution of the previous round, output the non-dominated solution and the process ends; otherwise, go to step 3) and start the relevant calculations for the next round.
[0062] Preferably, in step 5), the method for updating the Archive set based on the global optimal solution and the individual optimal solution of the current round includes:
[0063] in, For the current round of Archive collection Each solution and its rate of change in the current round For the next round of Archive, the first Each solution and its rate of change in the next round; Indicates the contraction factor; c1 represents the weight decay factor; c2 and c3 represent the individual learning factor and the social learning factor, respectively, which characterize the degree to which the individual and global optima are approached. Indicates uniform distribution to An interval is used to introduce appropriate randomness into the update process.
[0064] Example 2 This embodiment is based on embodiment 1: In this embodiment, we have three feasible strategies. The opponent has four feasible strategies. Task benefits in three target dimensions Failure and loss and resource consumption The game results of our side and the opponent were evaluated, and the vector value game matrix was constructed as shown in Table 2.
[0065] Table 2 - Vector Value Game Matrix of Example 2
[0066] Specifically, the relevant parameter settings for the multi-objective heuristic algorithm in this embodiment are shown in Table 3.
[0067] Table 3 - Parameter settings for multi-objective heuristic algorithms
[0068] Based on the above algorithm parameter settings, the vector value game matrix is solved. During the iteration process, the fitness changes of the three objective dimensions are as follows: Figure 4 As shown, fitness is dimensionless; the three-dimensional visualization of the fitness of the Pareto-Nash equilibrium solution set in the three objective dimensions is as follows. Figure 5 As shown, the subgraphs are: (a) the mapping of the Pareto front to optimization objectives 1 and 2, (b) the mapping of the Pareto front to optimization objectives 1 and 3, (c) the mapping of the Pareto front to optimization objectives 2 and 3, (d) the left-hand view, (e) the right-hand view, and (f) the top-hand view. The mean fitness values of each dimension of the optimal subset (i.e., the Pareto front) are analyzed, as shown in Table 4.
[0069] Table 4 - Mean fitness values for each optimization direction
[0070] The fitness of the average value across each optimization objective dimension corresponds to the partial order of the objective across multiple optimization dimensions. Since the final Pareto solution set is a frontier that does not consider the weights of each optimization objective dimension, there is no partial order among the particles in the solution set. However, from the perspective of the objective dimensions, according to the definition of particle fitness, each optimization dimension has an optimal fitness value; the closer it is to 0, the closer it is to Nash equilibrium. Therefore, the average fitness of the optimal solution set for each optimization dimension can be seen as the score of that objective based on Nash equilibrium; the closer it is to 0, the higher the score, and the easier it is to reach Nash equilibrium.
[0071] Higher-scoring objective dimensions are more valuable in the task, indicating that the objective in that dimension is easier for both parties to achieve equilibrium. The chosen solution is likely to satisfy the objective well. Therefore, in subsequent task progression, more effort should be invested in considering objectives with lower scores to ensure that objectives in all dimensions can be effectively addressed. The partial order relationship between optimization dimensions can also illustrate the essential differences in payoff matrices for different optimization objectives. Since some payoff matrices are difficult to reach Nash equilibrium, the partial order relationship can also provide decision-makers with a reference between different tasks.
[0072] By observing the relationship between the three sets of optimization objectives in the fitness mean table of each optimization direction, the Pareto front contains a set of points at an equilibrium level where resource consumption > failure loss > task gain. This indicates that the strategy adopted by our side in the current scenario can make the type of gain more likely to approach Nash equilibrium.
[0073] After 60 iterations, the global optimal solution in the Archive set converges in terms of fitness across the three objective dimensions, generating a Pareto-Nash equilibrium solution set containing a vector-valued game matrix with 60 different solutions, as shown in Table 5.
[0074] Table 5 - Pareto-Nash Equilibrium Solution Sets for Vector-Valued Game Matrices
[0075] Finally, the adoption probabilities of different options within our strategy set were generated. That is, the probability of adopting strategy 1 is 74.92%, the probability of adopting strategy 2 is 17.43%, and the probability of adopting strategy 3 is 7.64%, which can support decision-makers to make more flexible choices among multiple solutions under the guidance of different objective dimensions.
[0076] Example 3 This embodiment is based on embodiment 1: This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the task strategy generation method based on vector value game matrix of Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form.
[0077] Example 4 This embodiment is based on embodiment 1: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the task strategy generation method based on a vector-valued game matrix as described in Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.
[0078] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.
[0079] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.
Claims
1. A method for generating task strategies based on vector-valued game matrices, characterized in that, include: Based on the multidimensional performance evaluation results of the mutual confrontation between various feasible task strategies of the two sides in the game, a vector value game matrix is constructed. Based on the vector value game matrix and various resource constraints of both sides, a multi-objective optimization model of the vector value game matrix is constructed by combining Nash equilibrium theory. A multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector value game matrix, generate the Pareto-Nash equilibrium solution set of the vector value game matrix, and output the corresponding task strategy.
2. The task strategy generation method based on vector-valued game matrix according to claim 1, characterized in that, The vector-valued game matrix is constructed based on the multi-dimensional performance evaluation results of the mutual adversarial interaction between various feasible task strategies of both sides in the game, including: Combine with the opponent's feasible strategy set And our feasible strategy set The multidimensional performance evaluation results under adversarial conditions are calculated to dynamically determine and adjust the value of each element in the vector-valued game matrix; where, m The number of feasible strategies for the opponent. n This represents the number of feasible strategies available to us.
3. The task strategy generation method based on vector-valued game matrix according to claim 2, characterized in that, The strategies in the opponent's feasible strategy set and our feasible strategy set are multi-variable arrays: in, Resource elements representing strategies The target elements of the strategy are represented. The elements of a strategy representation method The time element of the strategy, Spatial elements representing strategies.
4. The task strategy generation method based on vector-valued game matrix according to claim 2, characterized in that, In the vector-valued game matrix, each element is a one-dimensional vector, representing the performance evaluation results of multiple optimization objective dimensions when our feasible strategies compete against the opponent's feasible strategies. These optimization objective dimensions include task payoffs. Failure and loss Resource consumption The time spent fighting .
5. The task strategy generation method based on vector-valued game matrix according to claim 4, characterized in that, The multi-objective optimization model for vector-valued game matrices, constructed based on vector-valued game matrices and various resource constraints for both sides, combined with Nash equilibrium theory, includes: Based on the vector-valued game matrix of the two sides, a multi-objective optimization model of the vector-valued game matrix is constructed by comprehensively considering the mutual constraints of multiple optimization objectives and the dynamic changes in the importance of each optimization objective, and combining Nash equilibrium theory.
6. The task strategy generation method based on vector-valued game matrix according to claim 5, characterized in that, The expression for the vector-valued game matrix multi-objective optimization model includes: in, This indicates that we adopt the first... The probability of a feasible strategy. This represents a possible solution for us, which is the probability distribution of each feasible strategy we can adopt. ; Indicates that the opponent adopted the first The probability of a feasible strategy. A feasible solution for an opponent is represented by the probability distribution of the opponent adopting each feasible strategy. ; This indicates that we have adopted the proposed solution. Adopting a solution with the opponent When engaging in confrontation, k Evaluation results for each optimization objective dimension; Indicates the first The and the first There are constraints between the optimization objectives. .
7. The task strategy generation method based on vector-valued game matrix according to claim 1, characterized in that, The multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector-valued game matrix, generating a Pareto-Nash equilibrium solution set for the vector-valued game matrix, including: By analyzing the mean fitness of the optimization directions of the optimal subset, i.e. the Pareto front, and comprehensively considering the dominance of each feasible solution in multiple optimization objective dimensions, we give the level ranking of the points contained in the Pareto front that are in equilibrium, thereby generating the Pareto-Nash equilibrium solution set of the vector value game matrix.
8. The task strategy generation method based on vector-valued game matrix according to claim 7, characterized in that, The multi-objective heuristic solution algorithm is used to solve the multi-objective optimization model of the vector-valued game matrix, generating a Pareto-Nash equilibrium solution set for the vector-valued game matrix, specifically including: The average fitness of the optimal solution set for each optimization objective dimension is regarded as the score of the corresponding optimization objective in the sense of Nash equilibrium. The closer the average fitness is to zero, the higher the score and the easier it is to reach Nash equilibrium. Based on the relationship between the optimization objective dimensions represented by the average fitness of each objective dimension, the equilibrium level of the point set contained in the Pareto front is given. By combining the dominance relationship of each feasible solution in each optimization objective dimension, the Pareto-Nash equilibrium solution set of the vector value game matrix is generated, thereby generating the probability of adopting different strategies within our feasible strategy set.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the task strategy generation method based on vector value game matrix as described in any one of claims 1-8.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the task strategy generation method based on the vector value game matrix as described in any one of claims 1-8.