A collaborative defense method based on Tian Ji's horse racing strategy

Abstract

This invention discloses a collaborative defense method based on the Tian Ji horse racing strategy, applicable to collaborative defense of surface boats. By initializing two horse groups, defining attributes and calculating average mass in a graded manner, comparing the speeds of the fast and slow horses of both sides to select five suitable strategies, updating the attributes of the participating horses and iterating, taking into account both population diversity and search balance, and outputting the global optimal solution after the iteration reaches the target, effectively avoiding local optima and improving the accuracy of defense resource allocation and combat effectiveness.

Description

Technical Field

[0001] This invention belongs to the field of surface vessel collaborative defense and intelligent optimization technology, and relates to collaborative defense optimization methods, particularly a collaborative defense method based on the Tian Ji horse racing strategy. Background Technology

[0002] With the continuous increase in the demand for maritime security protection, the requirements for optimization accuracy, global search capability, and dynamic adaptability in surface vessel collaborative defense are becoming increasingly stringent. Existing collaborative defense optimization algorithms often suffer from problems such as being prone to getting trapped in local optima, an imbalance between exploration and development, and insufficient adaptability to complex adversarial scenarios, resulting in inefficient allocation of defense resources and poor accuracy in risk prevention and control.

[0003] This invention proposes a collaborative defense method based on the Tian Ji horse racing strategy. This method avoids the local optima of traditional algorithms through dynamic competition between two populations and adaptive selection of multiple strategies, and provides an efficient and flexible global optimization solution for collaborative defense of surface vessels. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a collaborative defense method based on the Tian Ji horse racing strategy, offering the following technical solution:

[0005] A collaborative defense method based on the Tian Ji horse racing strategy, the method comprising the following steps:

[0006] S1. Initialize Tian Ji's horse herd and Qi Wang's horse herd, clarify the horse attributes and fitness definitions, sort and classify them by speed, determine the horse level and average quality of the herd, and build the basic framework for optimization; S2. Compare the speed relationship between the slowest and fastest horses of both sides, determine the applicable scenario based on the speed difference, and select a matching cooperative defense optimization strategy from 5 competitive strategies; S3. Execute the selected competitive strategy, update the corresponding participating horse attributes, take into account the diversity of the herd and the balance between local and global search, and complete a single round of optimization iteration; S4. Repeat steps S2-S3 until the preset number of iterations or optimization accuracy requirements are reached, terminate the iteration and output the global optimal solution, and achieve the cooperative defense optimization goal.

[0007] Preferably, the specific content of S1 is as follows:

[0008] Suppose there are two groups of horses: one is Tian Ji's herd, and the other is the King of Qi's herd, each with n horses. Tian Ji's herd can be represented as...

[0009]

[0010] Where, x Ti It is the i-th horse in Tian Ji's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse.

[0011] The King of Qi's herd of horses can be represented as

[0012]

[0013] Where, x Ki It is the i-th horse in the King of Qi's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse.

[0014] Preferably, the specific content of S2 is as follows:

[0015] Each iteration will consist of n rounds of competition. After each round, the horses of both sides will be removed from the current population. The following 5 competition strategies will be used.

[0016] Strategy 1: When Tian Ji's slowest horse is faster than King Qi's slowest horse, Tian Ji's slowest horse will race against King Qi's slowest horse, and Tian Ji will win. The formula for updating Tian Ji's slowest horse is as follows:

[0017]

[0018] α=1+round(0.5×(0.5+rand))×n1

[0019] β=round(0.5×(1+rand))×n2

[0020]

[0021] R = L × B

[0022]

[0023] B = (b1, ..., b) k , ..., b d )

[0024]

[0025] g = randperm(d)

[0026]

[0027] Where, x Tsi (t) is Tian Ji's slowest horse at present, T si Let n1, n2, u, and v be the numbers of Tian Ji's slowest horses, and let x be a number. Tf (t) is the fastest horse in Tian Ji's herd. and Γ represents the average mass of Tian Ji's and King Qi's horse herds, respectively, p is the weight, Γ is the standard Gamma function, b = 1.5, R is the running factor, and β is a variation term.

[0028] Meanwhile, King Qi's slowest horse is trying to catch up with Tian Ji's slowest horse. Therefore, the algorithm will update King Qi's slowest horse based on Tian Ji's slowest horse. The updated slowest horse for King Qi is...

[0029]

[0030] Where, x Ksi (t) is Tian Ji's slowest horse at present, x Tsi (t) is Tian Ji's slowest horse at present, K si This is the number of Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0031] Strategy 2: When Tian Ji's slowest horse is slower than King Qi's slowest horse, Tian Ji will use his slowest horse to race against King Qi's fastest horse. Although Tian Ji will lose this round, he is using his weakest horse to neutralize King Qi's fastest horse. In this round, since Tian Ji knows that his slowest horse is slower than any other horse in King Qi's current herd, the algorithm will update Tian Ji's slowest horse based on a randomly selected horse from all of Tian Ji's horses. The update formula for Tian Ji's slowest horse is as follows:

[0032]

[0033] Where, x Tsi (t) is Tian Ji's slowest horse at present, T si It is the number of Tian Ji's slowest horse, x Tr1 The horses were randomly selected from Tian Ji's herd. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0034] The current fastest horse update formula for King Qi is:

[0035]

[0036] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0037] Strategy 3: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is faster than the King of Qi's fastest horse, Tian Ji's fastest horse races against the King of Qi's fastest horse, and Tian Ji wins. Therefore, in this round, to maintain Tian Ji's horse's leading position as much as possible, the algorithm updates Tian Ji's fastest horse based on the fastest horse in Tian Ji's herd. The update formula is as follows:

[0038]

[0039] Where Tfi is the number of Tian Ji's fastest horse at present, x Tf (t) is the fastest horse in Tian Ji's herd. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0040] The fastest current formula for King Qi's horse is as follows:

[0041]

[0042] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0043] Strategy 4: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is slower than the King of Qi's fastest horse, in order to neutralize the King of Qi's strongest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji's slowest horse will be updated by randomly selecting a horse from his herd. The update formula is as follows:

[0044]

[0045] Where Tsi is the number of Tian Ji's slowest horse, x Tr2 The horse was randomly selected from Tian Ji's herd, x Tsi (t) is Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0046] The fastest horse in King Qi's herd will be updated to indicate the current fastest horse in King Qi's herd. The update formula is as follows:

[0047]

[0048] Where, xKf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0049] Strategy 5: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse has the same speed as the King of Qi's fastest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji will lose. The formula for updating Tian Ji's slowest horse is as follows:

[0050]

[0051] Where Tsi is the number of Tian Ji's slowest horse, x Tr3 It was a horse randomly selected from Tian Ji's herd. Tsi (t) is Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0052] The fastest horse update formula for King Qi is as follows:

[0053]

[0054] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0055] Preferably, the specific content of S3 is as follows:

[0056] Execute the selected competitive strategy, update the attributes of the participating horses according to the strategy-specific rules, remove the participating horses in this round after the update, and complete the single-round collaborative defense optimization iteration.

[0057] Preferably, the specific content of S4 is as follows:

[0058] The S2-S3 steps are executed iteratively, with the optimization effect dynamically monitored during the iteration process. The strategy execution intensity is adjusted based on the average quality difference of the population. When the preset iteration threshold is reached or the optimization accuracy error meets the requirements, the iteration process is terminated, and the globally optimal solution is output for application in surface vessel collaborative defense.

[0059] Implementing the embodiments of this invention will have the following beneficial effects: This invention discloses a collaborative defense method based on the Tian Ji horse racing strategy, applicable to surface vessel collaborative defense scenarios. The method first initializes two horse groups, one for Tian Ji and one for the King of Qi, clarifying horse attributes and fitness definitions, classifying them by speed, and calculating the average mass of the population to build an optimization framework. Then, it compares the current speed relationship between the fast and slow horses of both sides, adaptively selecting suitable scenarios from five competitive strategies. Next, it executes the selected strategy, updating the attributes of the participating horses according to specific rules, balancing population diversity and search balance, and removing participating horses to complete a single round of iteration. Finally, it iterates until a preset number of iterations or accuracy requirements are reached, terminating and outputting the globally optimal solution. Through dynamic competition between two populations and multi-strategy adaptation, it effectively avoids local optima, improving the accuracy of collaborative defense resource allocation and practical effectiveness. Attached Figure Description

[0060] To more clearly understand the embodiments of the present invention or the solutions of the prior art, the relevant drawings will be briefly described below. These drawings illustrate specific implementations of the present invention and are intended to provide necessary information to those skilled in the art, enabling them to obtain the relevant content without additional creative thinking. The drawings visually illustrate the structure, composition, and workflow of the present invention, helping to deeply understand the detailed aspects of the embodiments. The specific content is as follows:

[0061] Figure 1 A flowchart of a collaborative defense method based on Tian Ji's horse racing strategy;

[0062] Figure 2 This is a simulation result diagram of the collaborative defense described in one embodiment. Detailed Implementation

[0063] Next, the technical solutions will be described in detail with reference to the accompanying drawings of the embodiments of the present invention. It should be particularly noted that the embodiments described are merely examples of the present invention and do not cover all possible implementations. Any other implementations derived by those skilled in the art from the embodiments of the present invention without creative thinking should be considered within the scope of protection of the present invention. Specific methods are shown below; see details below. Figures 1-2 The method includes:

[0064] S1. Initialize Tian Ji's horse herd and Qi Wang's horse herd, clarify the horse attributes and fitness definitions, sort and classify them by speed, determine the horse level and average quality of the herd, and build the basic framework for optimization; S2. Compare the speed relationship between the slowest and fastest horses of both sides, determine the applicable scenario based on the speed difference, and select a matching cooperative defense optimization strategy from 5 competitive strategies; S3. Execute the selected competitive strategy, update the corresponding participating horse attributes, take into account the diversity of the herd and the balance between local and global search, and complete a single round of optimization iteration; S4. Repeat steps S2-S3 until the preset number of iterations or optimization accuracy requirements are reached, terminate the iteration and output the global optimal solution, and achieve the cooperative defense optimization goal.

[0065] In some specific embodiments, the specific content of S1 is as follows:

[0066] Suppose there are two groups of horses: one is Tian Ji's herd, and the other is the King of Qi's herd, each with n horses. Tian Ji's herd can be represented as...

[0067]

[0068] Where, x Ti It is the i-th horse in Tian Ji's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse.

[0069] The King of Qi's herd of horses can be represented as

[0070]

[0071] Where, x Ki It is the i-th horse in the King of Qi's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse.

[0072] In some specific embodiments, the specific content of S2 is as follows:

[0073] Each iteration will consist of n rounds of competition. After each round, the horses of both sides will be removed from the current population. The following 5 competition strategies will be used.

[0074] Strategy 1: When Tian Ji's slowest horse is faster than King Qi's slowest horse, Tian Ji's slowest horse will race against King Qi's slowest horse, and Tian Ji will win. The formula for updating Tian Ji's slowest horse is as follows:

[0075]

[0076] α=1+round(0.5×(0.5+rand))×n1

[0077] β=round(0.5×(1+rand))×n2

[0078]

[0079] R = L × B

[0080]

[0081] B = (b1, ..., b) k , ..., b d )

[0082]

[0083] g = randperm(d)

[0084]

[0085] Where, x Tsi (t) is Tian Ji's slowest horse at present, T si Let n1, n2, u, and v be the numbers of Tian Ji's slowest horses, and let x be a number. Tf (t) is the fastest horse in Tian Ji's herd. and Γ represents the average mass of Tian Ji's and King Qi's horse herds, respectively, p is the weight, Γ is the standard Gamma function, b = 1.5, R is the running factor, and β is a variation term.

[0086] Meanwhile, King Qi's slowest horse is trying to catch up with Tian Ji's slowest horse. Therefore, the algorithm will update King Qi's slowest horse based on Tian Ji's slowest horse. The updated slowest horse for King Qi is...

[0087]

[0088] Where, x Ksi (t) is Tian Ji's slowest horse at present, x Tsi (t) is Tian Ji's slowest horse at present, K si This is the number of Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0089] Strategy 2: When Tian Ji's slowest horse is slower than King Qi's slowest horse, Tian Ji will use his slowest horse to race against King Qi's fastest horse. Although Tian Ji will lose this round, he is using his weakest horse to neutralize King Qi's fastest horse. In this round, since Tian Ji knows that his slowest horse is slower than any other horse in King Qi's current herd, the algorithm will update Tian Ji's slowest horse based on a randomly selected horse from all of Tian Ji's horses. The update formula for Tian Ji's slowest horse is as follows:

[0090]

[0091] Where, x Tsi (t) is Tian Ji's slowest horse at present, T si It is the number of Tian Ji's slowest horse, x Tr1 The horses were randomly selected from Tian Ji's herd. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0092] The current fastest horse update formula for King Qi is:

[0093]

[0094] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0095] Strategy 3: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is faster than the King of Qi's fastest horse, Tian Ji's fastest horse races against the King of Qi's fastest horse, and Tian Ji wins. Therefore, in this round, to maintain Tian Ji's horse's leading position as much as possible, the algorithm updates Tian Ji's fastest horse based on the fastest horse in Tian Ji's herd. The update formula is as follows:

[0096]

[0097] Where Tfi is the number of Tian Ji's fastest horse at present, x Tf (t) is the fastest horse in Tian Ji's herd. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0098] The fastest current formula for King Qi's horse is as follows:

[0099]

[0100] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0101] Strategy 4: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is slower than the King of Qi's fastest horse, in order to neutralize the King of Qi's strongest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji's slowest horse will be updated by randomly selecting a horse from his herd. The update formula is as follows:

[0102]

[0103] Where Tsi is the number of Tian Ji's slowest horse, x Tr2 The horse was randomly selected from Tian Ji's herd, x Tsi (t) is Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0104] The fastest horse in King Qi's herd will be updated to indicate the current fastest horse in King Qi's herd. The update formula is as follows:

[0105]

[0106] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0107] Strategy 5: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse has the same speed as the King of Qi's fastest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji will lose. The formula for updating Tian Ji's slowest horse is as follows:

[0108]

[0109] Where Tsi is the number of Tian Ji's slowest horse, x Tr3 It was a horse randomly selected from Tian Ji's herd. Tsi (t) is Tian Ji's slowest horse at present. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0110] The fastest horse update formula for King Qi is as follows:

[0111]

[0112] Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

[0113] In some specific embodiments, the specific content of S3 is as follows:

[0114] Execute the selected competitive strategy, update the attributes of the participating horses according to the strategy-specific rules, remove the participating horses in this round after the update, and complete the single-round collaborative defense optimization iteration.

[0115] In some specific embodiments, the specific content of S4 is as follows:

[0116] The S2-S3 steps are executed iteratively, with the optimization effect dynamically monitored during the iteration process. The strategy execution intensity is adjusted based on the average quality difference of the population. When the preset iteration threshold is reached or the optimization accuracy error meets the requirements, the iteration process is terminated, and the globally optimal solution is output for application in surface vessel collaborative defense.

[0117] Figure 2 This is a simulation result diagram of the pursuit-escape game described in one embodiment. The simulation conditions are as follows: the center coordinates of the defense circle are (300, 300), the radius is 20 meters, there are 5 obstacles with a radius of 10 meters, there are 4 defense boats, and their initial positions are evenly distributed along the edge of the defense circle. The destruction radius is 10 meters. There are 7 attack boats, and their initial positions are evenly distributed along the edge of the circle 200 meters away from the center of the defense circle. The game duration is 100 seconds, and the time step is 1 second. The solid gray circles represent obstacles, the hollow gray circles represent the defense circle, the solid black lines represent the trajectories of the defense boats, the solid black circles represent the positions of the defense boats, the dashed black lines represent the trajectories of the attack boats, and the hollow black pentagrams represent the positions of the destroyed attack boats.

[0118] This invention addresses the problems of existing collaborative defense optimization algorithms, such as getting trapped in local optima, imbalance between exploration and development, and insufficient adaptability to complex adversarial scenarios, leading to inefficient resource allocation and poor precision in defense. It provides a collaborative defense method based on the Tian Ji horse racing strategy. This method first initializes two horse groups, one for Tian Ji and one for the King of Qi, defining horse attributes and fitness, and calculating the average population quality according to speed. Then, it selects five suitable competitive strategies by comparing the current speed relationship between the fast and slow horses of both sides. The strategy is then executed to update the attributes of the participating horses and remove participating horses to complete a single round of iteration. After iterating to a preset number of times or a required accuracy, the globally optimal solution is output and applied to collaborative defense of surface vessels, balancing population diversity and search balance.

[0119] The above description is merely a preferred embodiment of the present invention in the field of pursuit and escape game theory, and is not intended to limit its scope of application. In fact, the scope of protection of the present invention covers various implementation forms and technical solutions. The technical solutions disclosed herein are merely specific manifestations based on the core principles of the present invention, and not the only implementation methods. It should be clarified that improvements, adjustments, extended applications, and other implementation forms of the technical solutions guided by the core principles of the present invention should all be included within the scope of protection of the present invention. Therefore, all modifications and changes that do not depart from the core ideas of the present invention should be considered as part of the present invention.

Claims

1. A collaborative defense method based on Tian Ji's horse racing strategy, characterized in that... It includes the following steps: S1. Initialize Tian Ji's horse herd and Qi Wang's horse herd, clarify the horse attributes and fitness definitions, sort and classify them according to speed, determine the horse grade and average quality of the herd, and build an optimization framework. S2. Compare the speed relationship between the slowest and fastest horses of both sides, determine the applicable scenario based on the speed difference, and select a matching collaborative defense optimization strategy from 5 competitive strategies. S3. Execute the selected competition strategy, update the corresponding horse attributes, take into account population diversity and local-global search balance, and complete a single round of optimization iteration; S4. Repeat steps S2-S3 until the preset number of iterations or optimization accuracy requirements are reached, then terminate the iteration and output the global optimal solution to achieve the collaborative defense optimization goal.

2. The collaborative defense method based on Tian Ji's horse racing strategy according to claim 1, characterized in that: The specific content of S1 is as follows: Suppose there are two groups of horses: one is Tian Ji's herd, and the other is the King of Qi's herd, each with n horses. Tian Ji's herd can be represented as... Where, x Ti It is the i-th horse in Tian Ji's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse. The King of Qi's herd of horses can be represented as Where, x Ki It is the i-th horse in the King of Qi's herd. Let d represent the j-th attribute of the i-th horse, and d be the number of attributes of the horse.

3. The collaborative defense method based on Tian Ji's horse racing strategy according to claim 1, characterized in that: The specific content of S2 is as follows: Each iteration will consist of n rounds of competition. After each round, the horses of both sides will be removed from the current population. The following 5 competition strategies will be adopted. Strategy 1: When Tian Ji's slowest horse is faster than King Qi's slowest horse, Tian Ji's slowest horse will race against King Qi's slowest horse, and Tian Ji will win. The formula for updating Tian Ji's slowest horse is as follows: α=1+round(0.5×(0.5+rand))×n1 β=round(0.5×(1+rand))×n2 R = L × B B=(b1,...,b k ,...,b d ) g = randperm(d) Where, x Tsi (t) is Tian Ji's slowest horse at present, T si Let n1, n2, u, and v be the numbers of Tian Ji's slowest horses, and let x be a number. Tf (t) is the fastest horse in Tian Ji's herd. and Γ represents the average mass of Tian Ji's and Qi King's horse herds, respectively, p is the weight, Γ is the standard Gamma function, b = 1.5, R is the running factor, and β is a variation term; Meanwhile, King Qi's slowest horse is trying to catch up with Tian Ji's slowest horse. Therefore, the algorithm will update King Qi's slowest horse based on Tian Ji's slowest horse. The updated slowest horse for King Qi is... Where, x Ksi (t) is Tian Ji's slowest horse at present, x Tsi (t) is Tian Ji's slowest horse at present, K si This is the number of Tian Ji's slowest horse at present. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. Strategy 2: When Tian Ji's slowest horse is slower than King Qi's slowest horse, Tian Ji will use his slowest horse to race against King Qi's fastest horse. Although Tian Ji will lose this round, he is using his weakest horse to neutralize King Qi's fastest horse. In this round, since Tian Ji knows that his slowest horse is slower than any other horse in King Qi's current herd, the algorithm will update Tian Ji's slowest horse based on a randomly selected horse from all of Tian Ji's horses. The update formula for Tian Ji's slowest horse is as follows: Where, x Tsi (t) is Tian Ji's slowest horse at present, T si It is the number of Tian Ji's slowest horse, x Tr1 The horses were randomly selected from Tian Ji's herd. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. The current fastest horse update formula for King Qi is: Where, x Kf It was the fastest horse in the Qi King's herd, K fi It is the number of the fastest horse currently owned by the King of Qi. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. Strategy 3: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is faster than the King of Qi's fastest horse, Tian Ji's fastest horse races against the King of Qi's fastest horse, and Tian Ji wins. Therefore, in this round, to maintain Tian Ji's horse's leading position as much as possible, the algorithm updates Tian Ji's fastest horse based on the fastest horse in Tian Ji's herd. The update formula is as follows: Where Tfi is the number of Tian Ji's fastest horse at present, x Tf (t) is the fastest horse in Tian Ji's herd. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. The fastest current formula for King Qi's horse is as follows: Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. Strategy 4: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse is slower than the King of Qi's fastest horse, in order to neutralize the King of Qi's strongest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji's slowest horse will be updated by randomly selecting a horse from his herd. The update formula is as follows: Where Tsi is the number of Tian Ji's slowest horse, x Tr2 The horse was randomly selected from Tian Ji's herd, x Tsi (t) is Tian Ji's slowest horse at present. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. The fastest horse in King Qi's herd will be updated to indicate the current fastest horse in King Qi's herd. The update formula is as follows: Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. Strategy 5: When Tian Ji's slowest horse has the same speed as the King of Qi's slowest horse, and Tian Ji's fastest horse has the same speed as the King of Qi's fastest horse, Tian Ji will race his slowest horse against the King of Qi's fastest horse. Tian Ji will lose. The formula for updating Tian Ji's slowest horse is as follows: Where Tsi is the number of Tian Ji's slowest horse, x Tr3 It was a horse randomly selected from Tian Ji's herd. Tsi (t) is Tian Ji's slowest horse at present. and These are the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable. The fastest horse update formula for King Qi is as follows: Where, x Kf It is the fastest horse in King Qi's herd, and Kfi is the current fastest horse's number. and ρ represents the average quality of Tian Ji's and King Qi's horse herds, respectively. p is the weight, R is the running factor, and β is a variable.

4. The collaborative defense method based on Tian Ji's horse racing strategy according to claim 1, characterized in that: The specific content of S3 is as follows: Execute the selected competitive strategy, update the attributes of the participating horses according to the strategy-specific rules, remove the participating horses in this round after the update, and complete the single-round collaborative defense optimization iteration.

5. A collaborative defense method based on Tian Ji's horse racing strategy according to claim 1, characterized in that: The specific content of S4 is as follows: The S2-S3 steps are executed iteratively, with the optimization effect dynamically monitored during the iteration process. The strategy execution intensity is adjusted based on the average quality difference of the population. When the preset iteration threshold is reached or the optimization accuracy error meets the requirements, the iteration process is terminated, and the globally optimal solution is output for application in surface vessel collaborative defense.

Images