Maritime air defense countermeasure situation analysis method and device, electronic equipment and storage medium

Abstract

The application discloses a maritime air defense confrontation situation analysis method and device, electronic equipment and a storage medium. The method comprises the following steps: solving a leader problem optimization model to obtain a plurality of groups of leader optimal solutions; solving a follower problem optimization model for each group of leader optimal solutions to obtain a plurality of groups of follower optimal solutions corresponding to each group of leader optimal solutions; determining a decision subject, a decision space and an utility function, thereby determining a Stackelberg game model; solving the Stackelberg game model to obtain a pair of game equilibrium solutions of an attack side and a defense side in the decision space when the game is in equilibrium, so as to obtain a pair of attack and defense schemes when the game of the confrontation sides in the maritime air defense confrontation scene is in equilibrium. According to the method provided by the application, the real scene that the decision of the attack sides is not carried out at the same time and always changes according to the strategy of the other side can be simulated, and an analysis basis with fewer vulnerabilities and smaller risks for the decision in the actual scene is provided.

Description

Technical Field

[0001] This invention belongs to the field of auxiliary decision-making technology, specifically relating to a method and device for analyzing maritime air defense confrontation situations, electronic equipment, and storage medium. Background Technology

[0002] In modern defense and confrontation problems, the need for continuous innovation and optimization of decision analysis methods is crucial to cope with complex and ever-changing environments. Current methods for analyzing defense and confrontation situations lack adaptability and flexibility in complex environments, and fail to provide clear modeling and description of the decision-making problems of both sides, thus affecting decision-making effectiveness. Taking air defense confrontation as an example, current confrontation simulation technologies typically focus only on the situation optimization analysis of one side in air defense confrontation, failing to consider the sequential nature of decisions made by both sides. This leads to decisions that are detached from reality and lack a comprehensive consideration of the overall situation for both sides; consequently, the resulting decision solutions may also be detached from reality and lack a comprehensive consideration of the overall situation for both sides. When users implement such potentially flawed solutions, they may be exploited by the opponent, ultimately impacting the effectiveness of the confrontation. Summary of the Invention

[0003] This invention provides a method for analyzing maritime air defense confrontation situations, which can solve the problem that current confrontation scheme generation methods consider relatively simple factors and are detached from reality, resulting in low effectiveness of the generated confrontation schemes.

[0004] In a first aspect, embodiments of the present invention provide a method for analyzing maritime air defense confrontation situations, the method comprising:

[0005] Solving the leader problem optimization model yields multiple optimal solutions for the leader;

[0006] For each group of leader optimal solutions, the follower problem optimization model is solved to obtain multiple groups of follower optimal solutions corresponding to each group of leader optimal solutions. Here, the leader is one of the attacker and the defender, and the follower is the other of the attacker and the defender.

[0007] Based on the leader problem optimization model, the follower problem optimization model, the leader's optimal solution and the follower's optimal solution corresponding to the leader's optimal solution, the decision subject, decision space and utility function are determined, thereby determining the Stackelberg game model;

[0008] Solving the Stackelberg game model yields a pair of game equilibrium solutions for the attacker and defender in the decision space, thus providing a pair of attack and defense strategies for the opposing sides in a maritime air defense confrontation scenario.

[0009] In one possible implementation of the first aspect, if the leader is the defender, the leader problem optimization model can satisfy the following formula:

[0010]

[0011]

[0012]

[0013] Among them, f d1 The first leader's utility value, maxf d1 An optimization objective of the leader problem optimization model is to maximize the effective defense distance from all angles. e A is the termination angle of the defense zone. s The starting angle of the defense zone, depth i (θ) represents the effective defense distance of the i-th defense unit at angle θ; f d2 The second leader's utility value, maxf d2 Another optimization objective of the leader problem optimization model is to maximize the breadth of key defense angles, α i The key deployment angle; st represents the constraint condition, x i y i Let be the deployment coordinates of the i-th defense unit, max_dis be the farthest distance between the defense unit and the center of the defense zone, and min_dis be the shortest distance between the defense units.

[0014] In one possible implementation of the first aspect, if the follower is the attacker, the follower problem optimization model can satisfy the following formula:

[0015]

[0016]

[0017]

[0018] A s ≤θ j ≤A e

[0019] Among them, f a For follower utility value, maxf a This indicates that the optimization objective of the follower problem optimization model is to maximize the expected return of a breakthrough, m j,k p indicates whether to order the j-th attacking unit to attack the k-th target. j Let e ​​be the probability that the j-th attacking unit successfully breaks through the defense. j,k To achieve the expected hit return, c jw Let w represent the countermeasures device model of the j-th attacking unit, and θ represent the countermeasures device model of the j-th attacking unit. j Let A be the attack azimuth angle of the j-th attacking unit. eA is the termination angle of the defense zone. s The starting angle of the defense zone.

[0020] In one possible implementation of the first aspect, multiple optimal solutions for leaders can be obtained by solving the leader problem optimization model using a non-dominated sorting genetic algorithm.

[0021] In one possible implementation of the first aspect, for each group of leader optimal solutions, the optimal solutions for multiple groups of followers corresponding to each group of leader optimal solutions can be obtained by solving the follower problem optimization model using the tabu search algorithm.

[0022] In one possible implementation of the first aspect, the attacker and defender can be regarded as decision-making entities, and the utility function of the decision-making entities can be determined according to the optimization objectives of the leader problem optimization model and the follower problem optimization model; the decision space can be determined according to the leader's optimal solution and the follower's optimal solution corresponding to the leader's optimal solution, thus obtaining the Stackelberg game model; each set of leader's optimal solutions can be regarded as the upper-level nodes of the game tree; the follower's optimal solutions corresponding to the leader's optimal solutions can be regarded as the leaf nodes corresponding to the upper-level nodes where the leader's optimal solutions are located, thus obtaining the game tree in the Stackelberg game model.

[0023] In one possible implementation of the first aspect, based on the max-min criterion, other leaf nodes with lower follower utility values ​​can be pruned at the same upper-level node, while retaining the leaf node with the highest follower utility value to obtain the game tree after initial pruning. The optimal follower solution and the optimal leader solution corresponding to the optimal leaf node and the optimal upper-level node in the game tree after initial pruning are determined as the game equilibrium solution.

[0024] For example, in the game tree after initial pruning, the optimal leaf node is the leaf node corresponding to the optimal parent node; the follower utility value of the optimal leaf node is the worst in the game tree after initial pruning, and the game equilibrium solution is in the decision space.

[0025] Secondly, embodiments of the present invention provide a maritime air defense confrontation situation analysis device, the device comprising a processing unit; the processing unit is used for:

[0026] Solving the leader problem optimization model yields multiple optimal solutions for the leader;

[0027] For each group of leader optimal solutions, the follower problem optimization model is solved to obtain multiple groups of follower optimal solutions corresponding to each group of leader optimal solutions. Here, the leader is one of the attacker and the defender, and the follower is the other of the attacker and the defender.

[0028] Based on the leader problem optimization model, the follower problem optimization model, the leader's optimal solution and the follower's optimal solution corresponding to the leader's optimal solution, the decision subject, decision space and utility function are determined, thereby determining the Stackelberg game model;

[0029] Solving the Stackelberg game model yields a pair of game equilibrium solutions for the attacker and defender in the decision space, thus providing a pair of attack and defense strategies for the opposing sides in a maritime air defense confrontation scenario.

[0030] Thirdly, embodiments of the present invention provide an electronic device, including a processor and a memory, wherein the memory is used to store a computer program; the processor can be used to execute a calculator program (instructions) stored in the memory to implement the method of the first aspect described above.

[0031] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program that, when executed, can implement the method described in the first aspect above.

[0032] The beneficial effects of the embodiments of the present invention compared with the prior art are as follows: According to the method provided by the present invention, the order and dominance of decision-making are determined by the leader-follower form, which can simulate the real scenario where the decisions of the attacking parties are not made simultaneously and always change according to the strategy of the other party; by solving the attack and defense plans of the attacking and defending parties through the Stackelberg game model, the game process of both parties can be simulated at the same time, and the optimal strategy plan of the rational opposing parties under the given goals and constraints can be obtained, thereby providing a less flawed and less risky analytical basis for decision-making in real-world scenarios. Attached Figure Description

[0033] Figure 1 A flowchart illustrating a method for analyzing maritime air defense confrontation situations, provided in an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of the structure of a Stackelberg game model provided in an embodiment of the present invention;

[0035] Figure 3 A schematic diagram of the structure of a Stackelberg game model after preliminary pruning, provided in an embodiment of the present invention;

[0036] Figure 4 A flowchart illustrating a maritime air defense confrontation situation analysis method provided by the present invention;

[0037] Figure 5 A schematic diagram illustrating an effective defense distance provided in an embodiment of the present invention;

[0038] Figure 6This is a flowchart illustrating a method for solving an optimization model for the leader problem and an optimization model for the follower problem, provided in an embodiment of the present invention.

[0039] Figure 7 This is a schematic diagram of a maritime air defense confrontation situation analysis device provided in an embodiment of the present invention.

[0040] Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0042] The Stackelberg model, a game theory model widely used in economics and decision theory, is suitable for describing and analyzing the strategic interactions between attackers and defenders in adversarial defense due to its leader-follower hierarchical structure. By simulating the decision-making process between attackers and defenders, Stackelberg games can help reveal optimal defensive strategies and potential attack strategies.

[0043] Therefore, the attacker can be considered the leader in a Stackelberg game, and the defender the follower; or the defender can be considered the leader, and the attacker the leader. Then, a Stackelberg model is constructed based on the different solutions for the leader and follower. Solving this model yields a pair of equilibrium solutions at game equilibrium, i.e., a pair of attack and defense strategies at game equilibrium.

[0044] The maritime air defense confrontation situation analysis method provided in this embodiment of the invention can be applied to electronic devices such as mobile terminals, personal laptops, and supercomputers. This embodiment of the invention does not impose any restrictions on the specific type of electronic device.

[0045] Figure 1 The diagram shown illustrates a method for analyzing maritime air defense confrontation situations according to an embodiment of the present invention. As an example and not a limitation, method 100 can be applied to the aforementioned electronic equipment. Method 100 may include steps S101-S104, which are described below.

[0046] S101, Solve the leader problem optimization model to obtain multiple optimal solutions for the leader.

[0047] In some embodiments, since the basic elements in the decision space of the Stackelberg model are the offensive or defensive strategies of the leader and followers, rather than directly obtainable parameters of the leader and followers, the Stackelberg model can be constructed by first building a leader problem optimization model based on the leader's parameters and a follower problem optimization model based on the followers' parameters. These two models are then solved sequentially to obtain the offensive and defensive strategies of the leader and followers; finally, the Stackelberg model is constructed based on these strategies.

[0048] For example, a solution to the leader problem optimization model is an offensive or defensive strategy.

[0049] In one possible implementation, the leader can be one of the attackers and defenders. Correspondingly, the follower is the other of the attackers and defenders.

[0050] In one example, in a scenario like a maritime air defense confrontation in a game, where the attacking and defending sides' attacking and defending equipment can change their set positions and parameters at any time, both the attacking and defending sides can act as leaders.

[0051] In another example, in general, in an attack-defense scenario where the location of the defender's defensive equipment deployment is already determined, since the defender's equipment deployment cannot be changed with the change of the attack plan, the defender can be regarded as the leader and the attacker as the follower to construct the Stackelberg model.

[0052] S102, Solve the follower problem optimization model for the optimal solution of each group of leaders to obtain the optimal solutions of multiple groups of followers corresponding to the optimal solutions of each group of leaders.

[0053] Similarly, a solution to the follower problem optimization model is either an offensive or defensive plan for the follower. Whether it's an offensive or defensive plan depends on the follower's role.

[0054] Since each solution of the followers is determined under the specific circumstances of knowing the leader's solution, this can simulate the situation in real decision-making scenarios where the decision-making order of the attacking and defending sides is sequential, making the determined solution closer to the actual situation.

[0055] S103. Based on the leader problem optimization model, the follower problem optimization model, the leader's optimal solution, and the follower's optimal solution corresponding to the leader's optimal solution, determine the decision subject, decision space, and utility function, thereby determining the Stackelberg game model.

[0056] In one possible implementation, the attacker and defender can be considered as decision-makers. The leader's decision space is determined based on the leader's optimal solution, and the follower's decision space is determined based on the follower's optimal solution. The follower's and leader's decision spaces together constitute the decision space in the Stackelberg game model. This combines the separate optimization problems of the two problems into a single game problem. Simultaneously, utility functions are assigned to the leader and follower based on the optimization objectives of the leader and follower optimization models, respectively, resulting in the Stackelberg game model. Then, the game tree in the Stackelberg game model is constructed. Thus, when solving the Stackelberg game model, the pair of solutions with the maximum or minimum utility functions within the decision space can be found to obtain the game equilibrium solution.

[0057] For example, see Figure 2 An optimal solution for the leader can be used as a higher-level node in the game tree (see [link]). Figure 2 (See 201 in the text), and then the optimal solution of the followers corresponding to the optimal solution of the leader is used as the leaf node corresponding to the upper-level node (see 201 in the text). Figure 2 (202 in the middle); After setting all the upper-level nodes and leaf nodes in this way, the game tree in the Stackelberg game model can be obtained (see 202 in the middle); Figure 2 (200 in the middle).

[0058] S104 solves the Stackelberg game model to obtain a pair of game equilibrium solutions for the attacker and defender in the decision space, so as to obtain a pair of attack and defense schemes when the opposing sides are in game equilibrium in the maritime air defense confrontation scenario.

[0059] In one possible implementation, when the utility functions of both the leader and followers are proportional to the performance of the solution, and their optimization objective is to maximize their utility functions, the Stackelberg game model can be solved in the decision space using backward induction to obtain the game equilibrium solution.

[0060] In one example, based on the max-min game framework, other leaf nodes with lower follower utility values ​​can be pruned at the same upper-level node, retaining the leaf node with the highest follower utility value to obtain the game tree after initial pruning (see...). Figure 3 (301 in the text). This preserves the best-performing follower optimal solution. The optimal upper-level node in the game tree after initial pruning, and the pair of leader and follower optimal solutions corresponding to the optimal leaf node, are determined as the game equilibrium solution (see [reference]). Figure 3 (302 in the middle).

[0061] For example, in the game tree after initial pruning, the optimal leaf node is the leaf node corresponding to the optimal parent node; the follower utility value of the optimal leaf node is the worst. This indicates that the leader solution corresponding to the optimal parent node has good performance.

[0062] According to the method provided by the present invention, the order and dominance of decision-making are determined by the leader-follower form, which can simulate a real scenario in which the decisions of the attacking parties are not made simultaneously and always change according to the strategy of the other party. By solving the attack and defense plans of the attacking and defending parties through the Stackelberg game model, the game process of both parties can be simulated at the same time, and the optimal strategy plan of the rational opposing parties under the given goals and constraints can be obtained, thereby providing a less flawed and less risky analytical basis for decision-making in real-world scenarios.

[0063] Figure 4 The diagram shown illustrates a flowchart of a maritime air defense confrontation situation analysis method provided by the present invention. As an example and not a limitation, method 400 is a possible specific implementation of method 100. Method 400 may include steps S401-S406. In method 400, the defending party can be considered the leader, and the attacking party the follower. The steps are described below.

[0064] S401, Construct a leader problem optimization model.

[0065] In one possible implementation, since the defender has no information about the attacker in the scenario, the goal of defense is to cover the danger zone as much as possible. Therefore, the optimization objective of the leader problem optimization model can be twofold: one is to maximize the effective defense distance for each possible angle of attack when deploying defensive equipment; the other is to maximize the coverage of key defense angles. Unlike current methods that generate defense plans based on known attack scenarios, such as deployments to intercept incoming targets with known trajectories, or escort deployments based on known enemy launch sites and formations, this invention sets the defender's follow-through utility value based on scenarios with unknown attack plans, which is closer to real-world combat scenarios.

[0066] In one example, the leader problem optimization model can satisfy the following formula:

[0067]

[0068]

[0069]

[0070] Among them, f d1 The first leader's utility value, maxf d1An optimization objective of the leader problem optimization model is to maximize the effective defense distance from all angles. e A is the termination angle of the defense zone. s The starting angle of the defense zone, depth i (θ) represents the effective defense distance of the i-th defense unit at angle θ; f d2 The second leader's utility value, maxf d2 Another optimization objective of the leader problem optimization model is to maximize the breadth of key defense angles, α i The key deployment angle; st represents the constraint condition, x i y i Let be the deployment coordinates of the i-th defense unit, max_dis be the farthest distance between the defense unit and the center of the defense zone, and min_dis be the shortest distance between the defense units.

[0071] in:

[0072]

[0073] γ is the angle of the key deployment center of the i-th defensive unit, ω i This represents the maximum range of key defensive angles for the i-th defensive unit.

[0074] For example, the effective defense distance of the i-th defense unit at angle θ can be the path length of an incoming target in the θ direction through the defense area of ​​the i-th defense unit.

[0075] Optionally, the position of the i-th defensive unit and the distance d between the incoming target in the θ direction and the defense center can be determined first. i,θ Then through the discriminant p i,θ To determine whether an incoming target in the θ direction passes through the defense zone of the i-th defense unit, the result of the determination and the distance d are used. i,θ Determine the effective defense distance of the i-th defense unit at angle θ.

[0076] For example, distance d i,θ The following formula can be satisfied:

[0077] d i,θ =|cos(θ)|·|-tan(θ)·x i +y i |

[0078] For example, the discriminant p i,θ The following formula can be satisfied:

[0079]

[0080] Where: R iLet be the effective defense radius of the i-th defense unit.

[0081] For example, the effective defense distance of the i-th defense unit at angle θ can satisfy the following formula:

[0082]

[0083] in:

[0084]

[0085] For example, see Figure 5 The three defense units were deployed in, for example, Figure 5 The deployment coordinates at points O1, O2, and O3 are (x1, y1), (x2, y2), and (x3, y3), respectively, with effective defense radii of R1, R2, and R3. The straight line connecting the incoming target in the θ direction to the defense center is... Figure 5 The red line in the diagram. We can first determine the distance d from the three points to the red line. 1,θ d 2,θ d 3,θ Then, based on this distance, determine the discriminant p of the three. i,θ The value of θ is then determined. Finally, the effective defense distance of the three angles (θ, θ, and θ) is determined. See [link / reference]. Figure 5 The effective defensive distance of defensive unit O2 at angle θ is the distance between A2 and B2, the effective defensive distance of defensive unit O1 at angle θ is the distance between A1 and O, and the effective defensive distance of defensive unit O3 at angle θ is the distance between A3 and O.

[0086] S402, solve the leader problem optimization model to obtain multiple optimal solutions for leaders.

[0087] In one possible implementation, the leader problem optimization model can be solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to obtain multiple optimal solutions for the leader.

[0088] Specifically, see Figure 6 The leader problem optimization model can be solved by following these steps:

[0089] Step 1: Initialize the population and perform non-dominated ranking on the individuals in the population. The specific steps are as follows: First, calculate the function value of each individual on all objective functions (i.e., the first follower effect value and the second follower effect value), then calculate the dominance relationship between pairs of individuals, and finally divide the individuals into different non-dominated levels.

[0090] Step 2: Generate the offspring population using operators such as selection, crossover, and mutation;

[0091] Step 3: Increment the iteration count by one to obtain the parent and child populations, and determine whether a new parent population has been generated. If so, proceed to step 4; otherwise, proceed to step 5.

[0092] Step 4: Generate offspring population using operators such as selection, crossover, and mutation. If the termination condition is met, the process ends and the optimal solution set is output; otherwise, return to step 3.

[0093] Step 5: Perform fast non-dominated sorting on the merged population, using the same method as in Step 1;

[0094] Step 6: Calculate the crowding level, then select suitable individuals to enter the next generation, and return to Step 3.

[0095] For example, in multi-objective optimization problems, a Pareto front can be used to describe a set of solutions such that each solution in the set is a non-dominated solution. The NSGA-II algorithm, through iteration, can fit an approximate Pareto front in which each non-dominated solution is a leader-optimal solution in a set.

[0096] S403, Construct an optimization model for the follower problem.

[0097] In some embodiments, a follower problem optimization model can be constructed first based on the parameters of the attacker. Then, the leader optimal solution can be obtained in the above-mentioned Pareto front by uniform sampling and substituted into the follower problem optimization model. Solving the model generates multiple sets of follower optimal solutions corresponding to the leader optimal solution.

[0098] In one possible implementation, since the attacker has a clear understanding of the attack plan, a targeted attack plan needs to be formulated. Therefore, the optimization objective of the follower problem optimization model can be to maximize the expected benefit of penetration. Unlike the current weapon-target allocation model that generates attack decisions, this invention also takes into account the attack angle issue, enabling a more realistic simulation of the adversarial scenario.

[0099] In one example, the optimization model for the follower problem can satisfy the following formula:

[0100]

[0101]

[0102]

[0103] A s ≤θ j ≤A e

[0104] Among them, f a For follower utility value, maxf a This indicates that the optimization objective of the follower problem optimization model is to maximize the expected return of a breakthrough, m j,k p indicates whether to order the j-th attacking unit to attack the k-th target. j Let e ​​be the probability that the j-th attacking unit successfully breaks through the defense. j,k To achieve the expected hit return, c jw Let w represent the countermeasures device model of the j-th attacking unit, and θ represent the countermeasures device model of the j-th attacking unit. j Let A be the attack azimuth angle of the j-th attacking unit. e A is the termination angle of the defense zone. s The starting angle of the defense zone.

[0105] For example, the decision variable in the follower problem optimization model is m. j,k θ j c j Among them, m j,k It is a binary decision variable, c j Indicates the selection of countermeasures equipment; c j =[c j1 ,...,c jw ].

[0106] For example, the probability of the j-th attacking unit successfully breaking through the defense can be satisfied by the following formula:

[0107]

[0108] in, Let represent the probability that the i-th defensive unit successfully intercepts the j-th attacking unit, which satisfies:

[0109]

[0110] Among them, s i,j The base defense success rate of the i-th defensive unit against the j-th attacking unit; t i d represents the time required for the i-th defensive unit to achieve maximum defensive efficiency at the optimal angle and distance. t θ t Let t0 and t1 represent the distance between the attack target launched by the j-th attacking unit and the i-th defending unit at a certain time t, and the angle of the target's direction of attack, respectively; t0 and t1 represent the times when the attack target launched by the j-th attacking unit enters and leaves the defending area, respectively; f(d) and g(θ) represent the distribution functions of the influence of distance and angle on the unit's defense efficiency, respectively, which can be approximated by a non-standard normal distribution function.

[0111] For example, the distribution function of the effect of distance on unit defense efficiency can satisfy the following formula:

[0112]

[0113] Where, r min The efficiency after the maximum attenuation caused by distance (within the effective defense range) is determined by the equipment model, and the same applies to g(θ).

[0114] For example, the expected hit payoff can satisfy the following formula:

[0115]

[0116] Among them, dmg j,k h represents the expected damage dealt by the j-th attacking unit to the k-th attacking target. k v represents the damage threshold at which the k-th target is destroyed. k This represents the battlefield value of the k-th attack target.

[0117] S404: Solve the follower problem optimization model for each group of leader optimal solutions to obtain multiple follower optimal solutions corresponding to each group of leader optimal solutions.

[0118] In one possible implementation, the optimal solutions for multiple groups of followers corresponding to the optimal solutions for each group of leaders can be obtained by solving the follower problem optimization model using the tabu search algorithm.

[0119] Specifically, see Figure 6 The process involves initializing parameters and an initial solution, and emptying the tabu list. It then checks if the current solution meets convergence conditions, such as the maximum number of iterations or when the follower utility value stabilizes. If the termination condition is met, iteration stops, and the optimal follower solution determined in previous iterations is output. If the termination condition is not met, neighborhood solutions are generated based on the current solution, and candidate solutions are generated based on the neighborhood solutions. Next, it checks if the candidate solutions satisfy the contempt criterion. If they do, the candidate solution is used as the next current solution and added to the tabu list, updating the global optimal state to the state parameters of this solution. If the contempt criterion is not met, the current solution replaces the earliest entry into the tabu list, and the best solution of the non-tabu object is used as the next current solution. This iterative process continues.

[0120] For example, the contempt criterion is specifically the contempt for taboo criteria. For instance, a solution may be taboo, but if it meets certain conditions, such as being better than the current solution (this needs to be set according to the specific situation), then the solution can be accepted.

[0121] For example, non-taboo objects are not in the taboo list.

[0122] S405. Based on the leader problem optimization model, the follower problem optimization model, the leader's optimal solution, and the follower's optimal solution corresponding to the leader's optimal solution, the decision-making subject, decision space, and utility function are determined, thereby determining the Stackelberg game model.

[0123] In one possible implementation, the decision-making agents, decision space, and utility function can be defined before constructing the Stackelberg game model.

[0124] For example, the participants in the game (i.e. decision-makers) can be the defender L as the leader and the attacker F as the follower.

[0125] In one example, the leader's decision space can satisfy: S L =X×Y×Γ, where S L Let X, Y, and Γ represent the leader's decision space, where X, Y, and Γ represent the sub-decision space of the possible horizontal and vertical coordinates of defensive units and the set of angles representing the key defensive deployment centers, respectively. For example, x = {x1, x2, ...}, x ∈ X. x represents a set of possible horizontal coordinate deployments for all defensive units. i Let x be the x-coordinate of the i-th defensive unit.

[0126] The decision space of followers can satisfy: S F =M×Θ×C, where S F For the follower's decision space, M, Θ, and C represent the sub-decision spaces of allocation scheme, angle of attack, and selection of countermeasures equipment, respectively.

[0127] In one example, corresponding to the optimization objective of the leader problem model, the leader's utility function, i.e., the payoff function, can satisfy:

[0128] u L 1 (s L ,s F )=f d1

[0129] u L 2 (s L ,s F )=f d2

[0130] Among them, u L 1 u L 2 Let s represent the utility functions of the first leader and the second leader, respectively. L Let s represent a solution within the leader's decision space. F This represents a solution within the follower's decision space.

[0131] Accordingly, the leader's objective in the game is:

[0132]

[0133]

[0134] in, The optimal response function for followers can satisfy:

[0135]

[0136] Corresponding to the optimization objective of the follower problem model, the follower's utility function, i.e., the payoff function, can satisfy:

[0137] u F (s L ,s F )=f a

[0138] Among them, u F This represents the follower utility function.

[0139] S406 solves the Stackelberg game model to obtain a pair of game equilibrium solutions for the attacker and defender in the decision space, so as to obtain a pair of attack and defense schemes when the opposing sides are in game equilibrium in the maritime air defense confrontation scenario.

[0140] For example, steps S405 and S406 of method 400 are the same as steps S103 and S104 of method 100. For details, please refer to the relevant description of steps S103 and S104 in method 100, which will not be repeated here.

[0141] According to the method provided by this invention, the order and dominance of decision-making are determined through a leader-follower model, which can simulate a real scenario where the decisions of the attacking parties are not simultaneous and always change according to the other party's strategy. By solving the attack and defense schemes of both sides using the Stackelberg game model, the game process of both sides can be simulated simultaneously, obtaining the optimal strategy schemes of the rational opposing parties under given objectives and constraints, thus providing a less flawed and less risky analytical basis for decision-making in real-world scenarios. Furthermore, since the attacking and defending parties have different known information, this invention sets different optimization objectives for the leader problem optimization model and the follower problem optimization model for this scenario; simultaneously, setting different utility values ​​for the attacking parties can fully consider the different payoff evaluations of both sides; this can further simulate real decision-making scenarios, reduce the flaws and risks of the final generated adversarial scheme, and improve the performance of the scheme. By using a hybrid algorithm of NSGA-II and tabu search to solve for an approximate game equilibrium solution instead of a theoretical game equilibrium solution, the computational complexity can be reduced.

[0142] Figure 7 The diagram illustrates a structural schematic of a maritime air defense confrontation situation analysis device provided in an embodiment of the present invention. As an example and not a limitation, the device 700 may include a processing unit 710.

[0143] Processing unit 710 can be used for:

[0144] Solving the leader problem optimization model yields multiple optimal solutions for the leader;

[0145] For each group of leader optimal solutions, the follower problem optimization model is solved to obtain multiple groups of follower optimal solutions corresponding to each group of leader optimal solutions. Here, the leader is one of the attacker and the defender, and the follower is the other of the attacker and the defender.

[0146] Based on the leader problem optimization model, the follower problem optimization model, the leader's optimal solution and the follower's optimal solution corresponding to the leader's optimal solution, the decision subject, decision space and utility function are determined, thereby determining the Stackelberg game model;

[0147] Solving the Stackelberg game model yields a pair of game equilibrium solutions for the attacker and defender in the decision space, thus providing a pair of attack and defense strategies for the opposing sides in a maritime air defense confrontation scenario.

[0148] According to the device provided by the present invention, the order and dominance of decision-making are determined by a leader-follower approach, which can simulate a real scenario where the decisions of the attacking parties are not made simultaneously and always change according to the strategy of the other party. By solving the attack and defense plans of the attacking and defending parties through the Stackelberg game model, the game process of both parties can be simulated simultaneously, and the optimal strategy plan of the rational opposing parties under given goals and constraints can be obtained, thereby providing a less flawed and less risky analytical basis for decision-making in real-world scenarios.

[0149] Figure 8 The diagram shown is a structural schematic of an electronic device provided in an embodiment of the present invention. Figure 8 The illustrated electronic device 800 may include: at least one processor 810 ( Figure 8 The diagram shows only one processor, a memory 820, and a computer program 830 stored in the memory 820 and executable on the at least one processor 810, wherein the processor 810 executes the computer program 830 to implement the steps in any of the above method embodiments.

[0150] The electronic device 800 may be a robot or other processing device capable of implementing the above methods. This embodiment of the invention does not impose any restrictions on the specific type of electronic device.

[0151] Those skilled in the art will understand that Figure 8 This is merely an example of electronic device 800 and does not constitute a limitation on the electronic device. It may include more or fewer components than shown, or combine certain components, or use different components. For example, the electronic device 800 may also include input / output interfaces.

[0152] The processor 810 may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASTCs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0153] In some embodiments, the memory 820 may be an internal storage unit, such as a hard disk or RAM. In other embodiments, the memory 820 may be an external storage device, such as a plug-in hard disk, a smart memory card (SMC), a secure digital card (SD), or a flash card. Furthermore, the memory 820 may include both internal and external storage units. The memory 820 is used to store the operating system, applications, a boot loader, data, and other programs, such as the program code of the computer program. The memory 820 can also be used to temporarily store data that has been output or will be output.

[0154] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0155] Those skilled in the art will understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the functions described above can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0156] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0157] This invention provides a computer program product that, when run on an electronic device, enables the electronic device to perform the steps described in the various method embodiments above.

[0158] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographing device / terminal device, 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. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0159] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0160] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

Claims

1. A method for analyzing maritime air defense confrontation situations, characterized in that, include: Solving the leader problem optimization model yields multiple optimal solutions for the leader; For each set of optimal leader solutions, the follower problem optimization model is solved to obtain multiple sets of optimal follower solutions corresponding to each set of optimal leader solutions, where the leader is one of the attacker and the defender, and the follower is the other of the attacker and the defender. Based on the leader problem optimization model, the follower problem optimization model, the leader optimal solution and the follower optimal solution corresponding to the leader optimal solution, the decision subject, decision space and utility function are determined, thereby determining the Stackelberg game model; Solving the Stackelberg game model yields a pair of game equilibrium solutions for the attacker and defender in the decision space, thus obtaining a pair of attack and defense schemes when the opposing sides are in game equilibrium in a maritime air defense confrontation scenario. The leader is the defender, and the leader problem optimization model satisfies the following formula: in, The utility value of the first leader. The optimization objective of the aforementioned leader problem optimization model is to maximize the effective defense distance from all angles. The termination angle of the defense zone, The starting angle of the defense zone, For the first One defensive unit Effective defensive distance at an angle; The utility value of the second leader. Another optimization objective of the aforementioned leader problem optimization model is to maximize the breadth of key defense angles. The key deployment angles; Indicates constraints. , For the first The deployment coordinates of each defensive unit. The furthest distance between the defending unit and the center of the defense zone. This is the closest distance between the defensive units; The follower is the attacker, and the optimization model for the follower problem satisfies the following formula: in, For follower utility value, This indicates that the optimization objective of the aforementioned follower problem optimization model is to maximize the expected return from a breakthrough. Indicate whether to make the first j The attacking unit attacked the first k One target of attack, For the first j The probability of an attacking unit successfully breaking through the defense. In order to achieve the expected profit, Indicates the first j The countermeasures equipment model for each attacking unit is w , For the first j The attack azimuth of each attacking unit. The termination angle of the defense zone, The starting angle of the defense zone.

2. The method according to claim 1, characterized in that, The optimization model for the leader problem yields multiple optimal solutions for the leader, including: The leader problem optimization model is solved using a non-dominated sorting genetic algorithm to obtain multiple optimal solutions for the leader.

3. The method according to claim 2, characterized in that, The process of solving the follower problem optimization model for each set of leader optimal solutions yields multiple sets of follower optimal solutions corresponding to each set of leader optimal solutions, including: For each group of optimal leader solutions, the follower problem optimization model is solved using the tabu search algorithm to obtain multiple groups of optimal follower solutions corresponding to each group of optimal leader solutions.

4. The method according to claim 1, characterized in that, The leader problem optimization model, the follower problem optimization model, the leader's optimal solution, and the follower's optimal solution corresponding to the leader's optimal solution determine the decision-making agent, decision space, and utility function, thereby determining the Stackelberg game model, including: The attacker and defender are taken as the decision-making entities, and the utility function of the decision-making entities is determined according to the optimization objectives of the leader problem optimization model and the follower problem optimization model. The decision space is determined based on the leader's optimal solution and the follower's optimal solution corresponding to the leader's optimal solution, thus obtaining the Stackelberg game model; The optimal solution for each leader is taken as the upper-level node of the game tree; The optimal solutions of the followers corresponding to the optimal solutions of the leader are taken as the leaf nodes of the upper-level nodes where the optimal solutions of the leader are located, thus obtaining the game tree in the Stackelberg game model.

5. The method according to claim 4, characterized in that, Solving the Stackelberg game model to obtain a pair of game equilibrium solutions for the attacker and the defender in the decision space at game equilibrium includes: Based on the max-min criterion, other leaf nodes with lower follower utility values ​​are pruned at the same upper-level node, and the leaf node with the highest follower utility value is retained to obtain the game tree after initial pruning. The optimal solution of the follower and the optimal solution of the leader corresponding to the optimal leaf node and the optimal upper-level node in the game tree after the initial pruning are determined as the game equilibrium solution. In the game tree after initial pruning, the optimal leaf node is the leaf node corresponding to the optimal upper-level node; the follower utility value of the optimal leaf node is the worst in the game tree after initial pruning, and the game equilibrium solution is within the decision space.

6. A maritime air defense confrontation situation analysis device, characterized in that, The device includes a processing unit, the processing unit being used for: Solving the leader problem optimization model yields multiple optimal solutions for the leader; For each set of optimal leader solutions, the follower problem optimization model is solved to obtain multiple sets of optimal follower solutions corresponding to each set of optimal leader solutions, where the leader is one of the attacker and the defender, and the follower is the other of the attacker and the defender. Based on the leader problem optimization model, the follower problem optimization model, the leader optimal solution and the follower optimal solution corresponding to the leader optimal solution, the decision subject, decision space and utility function are determined, thereby determining the Stackelberg game model; Solving the Stackelberg game model yields a pair of game equilibrium solutions for the attacker and defender in the decision space, thus obtaining a pair of attack and defense schemes for the opposing sides in the maritime air defense confrontation scenario when the game is at equilibrium. The leader is the defender, and the leader problem optimization model satisfies the following formula: in, The utility value of the first leader. The optimization objective of the aforementioned leader problem optimization model is to maximize the effective defense distance from all angles. The termination angle of the defense zone, The starting angle of the defense zone, For the first One defensive unit Effective defensive distance at an angle; The utility value of the second leader. Another optimization objective of the aforementioned leader problem optimization model is to maximize the breadth of key defense angles. The key deployment angles; Indicates constraints. , For the first The deployment coordinates of each defensive unit. The furthest distance between the defending unit and the center of the defense zone. This is the closest distance between the defensive units; The follower is the attacker, and the optimization model for the follower problem satisfies the following formula: in, For follower utility value, This indicates that the optimization objective of the aforementioned follower problem optimization model is to maximize the expected return from a breakthrough. Indicate whether to make the first j The attacking unit attacked the first k One target of attack, For the first j The probability of an attacking unit successfully breaking through the defense. In order to achieve the expected profit, Indicates the first j The countermeasures equipment model for each attacking unit is w , For the first j The attack azimuth of each attacking unit. The termination angle of the defense zone, The starting angle of the defense zone.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed, it implements the method as described in any one of claims 1-5.

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