Airport target firepower distribution method based on improved Hemma optimization algorithm

Abstract

The invention discloses an airport target firepower distribution method based on an improved Hemma optimization algorithm, and belongs to the field of firepower distribution. The method comprises the following steps: firstly, comprehensively considering factors such as spatial distribution characteristics of an airport, an initial position of a fighter, target characteristics and a missile-target matching damage effect, constructing a mathematical model of airport target firepower distribution, introducing firepower resource constraint and damage constraint conditions, and carrying out quantitative evaluation on a firepower distribution scheme through a target function; and a firepower distribution solution is optimized by using the swarm intelligence behavior of the Hemma optimization algorithm. In order to improve the performance of the algorithm, an SPM chaotic mapping technology is adopted, and an adaptive weight position updating mechanism, a reverse learning strategy and a neighbor dimension cross optimization strategy are introduced. According to the improved algorithm, the convergence speed of a firepower allocation result can be remarkably increased, and falling into a local optimal solution is effectively avoided, so that efficient allocation of firepower resources is realized in a complex battlefield environment.

Description

Technical Field

[0001] The invention belongs to the field of airport firepower distribution, and specifically discloses an airport target firepower distribution method based on a Hippo optimization algorithm. Background Art

[0002] As crucial infrastructure in modern military and civil aviation, the proper functioning of airports is directly linked to the smooth execution of aviation missions. In military operations, targets within airports are often considered crucial strategic targets. Effective firepower strikes against these targets can significantly weaken enemy aviation capabilities and even have a decisive impact on the overall battle situation. Therefore, the scientific and rational allocation of firepower against military targets within airports has become a research topic of great military significance.

[0003] In practice, firepower allocation against military targets within an airport involves a variety of complex factors, including target characteristics, the number and performance of missiles or ammunition, the choice of attack aiming point, the influence of environmental factors such as wind speed, and the optimal allocation of combat resources. The comprehensive consideration of these factors requires that firepower allocation not only maximize damage effects but also achieve optimal firepower effectiveness within limited combat resources.

[0004] With the increasing complexity of modern warfare and the advancement of precision strike technology, traditional firepower allocation methods are increasingly unable to meet the demands of efficient and accurate combat. Optimization techniques combined with intelligent algorithms, such as the Hippo optimization algorithm, can effectively handle complex, high-dimensional, multi-constrained optimization problems, providing a new solution for airfield firepower allocation. These algorithms can find optimal solutions for multi-dimensional parameters such as the number of missiles, attack sequence, and attack targets, thereby improving the effectiveness of firepower strikes, reducing resource waste, and maximizing the achievement of combat objectives.

[0005] Existing technologies have many limitations in the allocation of firepower to airport targets. Traditional firepower allocation methods are often based on simplified assumptions and are difficult to adapt to complex and changing combat environments. They are not capable of handling high-dimensional, multi-constrained optimization problems, which can easily lead to waste of resources or low combat effectiveness, and perform poorly in multi-objective optimization and task adaptability. Although the Hippo optimization algorithm has certain global search capabilities, it is prone to falling into local optimality under complex constraints, is sensitive to the initial population and parameter settings, and its computational efficiency needs to be improved. In addition, the multi-task allocation model has difficulties in handling complex constraints and multi-objective optimization, lacks dynamic adaptability, and has difficulty in quickly responding to changes in the battlefield environment. These shortcomings make existing technologies unable to meet the needs of modern warfare for efficient, accurate, and dynamic adjustment of firepower allocation to airport targets, limiting the full realization of combat effectiveness.

[0006] In-depth research on the firepower allocation of military targets in airports is not only of great value to the military field, but also can provide a reference for other similar target damage optimization problems and has broad application prospects. However, the existing airport target firepower allocation method still needs to be improved in terms of global search capability, allocation efficiency, accuracy, dynamic performance, allocation problem solution speed and result quality, algorithm solution efficiency and result quality. Summary of the Invention

[0007] The purpose of the present invention is to overcome the above-mentioned defects in the background technology, propose a method for allocating firepower to airport targets based on the improved Hippo optimization algorithm, establish a multi-constraint and multi-task task allocation model for airport military targets, and propose to use the SPM chaotic mapping method for initialization, adopt an adaptive weight mechanism, a reverse learning strategy, and a neighboring dimension cross-optimization strategy to update the population position, so as to avoid the algorithm from falling into local optimality and improve the optimization ability.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] A method for allocating firepower to airport targets based on an improved Hippo optimization algorithm comprises the following steps:

[0010] Step S1: Taking an airport as a target, analyzing typical targets within the airport and the relationships between them, and performing target damage. The typical targets include: airport runways, aprons, reinforced fortifications, and ammunition depots. Aiming points within the airport runways are coupled, and damage is performed by striking all aiming points on a group of runway runways.

[0011] Step S2: determining the constraints of the firepower allocation model based on the analysis results of step S1 on the typical targets within the airport and the relationships between the typical targets, and constructing the objective function of the firepower allocation model based on the distance between the target point and the fighter, that is, the total mission time fitness function, the distance between the target points, and the damage effectiveness fitness function;

[0012] Step S3, an improved Hippo optimization algorithm is obtained by combining the spatial pyramid chaotic mapping (SPM chaotic mapping), the adaptive weight position update mechanism, the reverse learning strategy, and the neighborhood dimension cross optimization strategy with the Hippo optimization algorithm, specifically:

[0013] Determine the encoding form of the population individuals in the Hippo algorithm according to the target number, initialize the population individuals of the Hippo algorithm through the SPM chaotic mapping, and uniformly generate the initial firepower distribution solution within the solution space under the constraints of the step S2, and judge the quality of the firepower distribution solution according to the objective function of step S2;

[0014] After generating the initial firepower allocation solution, the adaptive weight position update mechanism and reverse learning strategy are used as the exploration phase of the improved Hippo optimization algorithm to search for the firepower allocation solution;

[0015] Finally, when updating the position of each generation, a neighborhood dimension cross optimization strategy is used to retain the good genes of the previous generation;

[0016] Step S4: Perform iterative optimization calculations on the firepower allocation solution according to the improved Hippo optimization algorithm of step S3 until the iteration stop condition is met.

[0017] Furthermore, the implementation process of step S1 is as follows:

[0018] The h typical targets in the airport are represented by T = {T1, T2, ..., T h} indicates that the typical targets include the following types: fortifications, airport runways, aprons, and ammunition depots; among them, the typical targets belonging to the airport runway type are coupled with each other, and the typical targets with coupling relationships are divided into a group. Targets in the same group indicate that all targets in the group should be hit when the attack is carried out, and the attack is considered to be effective. Let m be the number of target groups, and the matrix B is the target group, denoted as B1, B2,…, B m When B1 = {T1, T2, T3}, it means that targets T1, T2, and T3 belong to the same group. When a military strike is carried out against them, all three targets need to be struck.

[0019] Furthermore, the constraints of the firepower allocation model in step S2 are specifically:

[0020] According to the different amount of ammunition carried by each fighter, and the total number of tasks performed by the fighter cannot exceed its ammunition capacity, the constraint condition is obtained

[0021]

[0022] R ij The mission performed by the fighter, the number of our fighters is n F ,use Indicates the starting position of the fighter, and the amount of ammunition carried is represented by matrix C i express, Indicates the amount of ammunition carried by each aircraft. Each aircraft is assigned at least one mission.

[0023]

[0024] Each task is executed only once or not at all

[0025]

[0026] Where N jIndicates the number of times the jth goal is executed.

[0027] Furthermore, the objective function of the firepower allocation model in step S2 is composed of the mission total time fitness function T(R) and the damage effectiveness fitness function E(R), and is normalized by the minimum-maximum normalization method, specifically:

[0028] f(R)=ω1T(R)+ω2E(R)

[0029] Where ω1 and ω2 are the weight coefficients corresponding to the total mission time fitness function and the damage effectiveness fitness function respectively;

[0030] The minimum-maximum normalization method performs normalization processing as follows:

[0031]

[0032] Where, d min is the minimum value in the data, d max is the maximum value in the data, d norm The data are normalized.

[0033] Furthermore, the total mission time fitness function T(R) takes the straight-line distance from the starting point to each target point as a quantitative indicator of time. The position information of the fighter and the target are both known, then:

[0034]

[0035] Where T(R) is the distance fitness value, For fighter U i location, Target T j location, Target T j-1 Position, D i For fighter U i The fitness value within the execution task sequence.

[0036] Furthermore, the damage effectiveness fitness function is:

[0037]

[0038] Where E(R) is the fitness value of the damage effect, represents the target number of group i, Indicates whether the jth target in the i-th group is selected to be attacked, ξ i represents the weight coefficient of group i.

[0039] Furthermore, the improved Hippo optimization algorithm described in step S3 is implemented as follows:

[0040] Step S3-1, determine the encoding form of the population individuals in the Hippo algorithm, use the number of targets as the dimension of the solution space, and the number of fighters as the range of the solution in the solution space. When the number of targets is n F When , the encoding form of the population individuals in the Hippo algorithm is:

[0041] X i ={x ij |j=1,2…h}

[0042] Where, X i The i-th individual in the population, x ij represents the code of the jth position of the i-th individual, x ij ∈{0,1,…,n F};

[0043] Step S3-2: Decode the code of the population individual in the Hippo algorithm, and fill in the corresponding code by judging the code number at any position in the solution. and described R is the matrix storing the tasks performed by fighters in task allocation. ij =1 means fighter i attacks target j, It is a grouping matrix, marking the attack situation of the fighter jets on the group. Indicates target group B i The lth target is hit, and the specific decoding method is:

[0044]

[0045] Where, is the code of the jth position of the kth individual. This formula indicates that by judging whether the value of the solution is equal to the number of the fighter, if it is equal, the position of the corresponding aircraft in the mission matrix is ​​set to 1, otherwise it is set to 0;

[0046] Step S3-3: Generate a corresponding initial firepower allocation solution based on the typical targets and the number of fighters, use the SPM chaotic mapping method to generate chaotic values ​​in the solution space, discretize the chaotic values ​​into the solution space according to the encoding form, and randomly initialize the population of the Hippo algorithm under the constraints of step S2 to generate an initial Hippo population, i.e., the initial firepower allocation solution;

[0047] Step S3-4, after generating the initial firepower allocation solution, the firepower allocation solution is searched through the adaptive weight position update mechanism and the reverse learning strategy as the exploration phase of the improved Hippopotamus optimization algorithm; specifically, according to the exploration phase 1 of the improved Hippopotamus optimization algorithm, the position of the hippopotamus population is updated to obtain the firepower allocation solution; through the exploration phase 2, the safe position of the hippopotamus population is explored to calculate the candidate solution of the firepower allocation solution; the firepower allocation solution is updated by fusing the reverse learning strategy with the original search strategy of the development phase to obtain a better solution and a better potential solution;

[0048] Step S3-5: Compare the differences in different dimensions between the best individuals of two adjacent generations of the hippo population, i.e., the current generation and the previous generation, through the adjacent generation dimension crossover optimization strategy, and select the dimension with the largest difference for crossover operation. If the fitness value of the individual after crossover is better than that of the original individual, the crossover result is retained; otherwise, the original individual is kept unchanged;

[0049] Step S3-6: Continuously update and iterate the population through the algorithms of step S3-4 and step S3-5 until the iteration stop condition is met, and finally output the final firepower allocation result.

[0050] Furthermore, the SPM chaotic mapping method is specifically as follows:

[0051]

[0052] Where x i represents the i-th chaotic value that satisfies the SPM chaotic mapping, x i+1 represents the i+1th chaotic value, mod() represents the remainder function, rand() represents a random number between the interval [0,1], and η and μ are factors related to the chaotic state.

[0053] Furthermore, the step S3-4 is specifically as follows:

[0054] Exploration Phase 1: In the improved Hippopotamus optimization algorithm, the hippopotamus updates its position in this phase. The following formula represents the position of the male hippopotamus:

[0055]

[0056]

[0057] Where, represents the position of the male hippopotamus, that is, the firepower allocation solution represented by the individual, D represents the position of the dominant hippopotamus, that is, the solution corresponding to the firepower allocation scheme with the best fitness in the current iteration number, r1 represents a random number in the interval [0,1], I1 represents a random number in the interval [1,2], ω(t) represents the weight coefficient that changes with time, T represents the maximum number of iterations, and t represents the current iteration number;

[0058] When the juvenile hippopotamus moves away from the female hippopotamus, the position update formula of the male hippopotamus, female hippopotamus and juvenile hippopotamus in the group is:

[0059]

[0060] Where, represents the position of female hippopotamus and juvenile hippopotamus in the group, i.e., the solution of firepower distribution, r2 represents the random vector; MG i represents the average value of randomly selected hippos, T represents the selection probability, and I2 represents a random number between the interval [1,2];

[0061] Exploration Phase 2: When attacked by predators or other creatures, the hippopotamus will react defensively. When predators or other creatures invade, the hippopotamus's position is:

[0062]

[0063] Where, Indicates the location of predators and other creatures invading the hippopotamus's territory, which is a candidate solution for the firepower allocation solution. represents a random vector with Levy distribution, which describes the position mutation of the predator when attacking the hippopotamus. j represents the position of the predator in the search space, represents the distance between the i-th hippopotamus and the predator. b, c, d, and g all represent uniformly distributed random numbers, but their value ranges are different. The value range of b is [2, 4], the value range of c is [1, 1.5], the value range of d is [2, 3], and the value range of g is [2, 4]. r3 represents a random number uniformly distributed in the interval [-1, 1]. Factors that cause hippos to adopt defensive behaviors to protect themselves from predators, F i represents the objective function value;

[0064] Development stage: The original search strategy in the unimproved Hippo optimization algorithm is used to integrate reverse learning to update the location and find the nearest safe place. The updated location is:

[0065]

[0066] Where, represents the location of the hippopotamus that is being searched for the nearest safe place, i.e., the better solution or potential better solution in the current firepower allocation solution, X max (i) and X min (i) represents the upper and lower limits of the solution of the i-th hippopotamus in the solution space, r 41 Represents a random number uniformly distributed in the interval [0,1], r 42Represents a random number that conforms to the normal distribution, t is the current number of iterations, and λ represents a random number uniformly distributed in the interval [0,1]. The above formula indicates that when λ>0.5, the first method is used to update the position, and when λ≤0.5, the reverse learning strategy is used to update the position.

[0067] Furthermore, the specific mathematical expression of the adjacent generation dimension cross optimization strategy is as follows:

[0068]

[0069] Where, represents the position of the i-th hippopotamus when the number of iterations is t, Indicates the j-th dimension value of the optimal hippopotamus when the number of iterations is t-1, is the position after the cross dimension, f(·) is the fitness calculation function, for each hippopotamus i, according to the dimension difference Δ i,j Sort from large to small and select the dimension with the largest difference for crossover.

[0070] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0071] (1) The present invention provides an airport target firepower allocation method based on the improved Hippo optimization algorithm. By initializing the population using SPM chaotic mapping and introducing a position update mechanism of adaptive weights, a reverse learning strategy, and a neighboring dimension cross optimization strategy, a more efficient and accurate firepower allocation algorithm is constructed, which effectively improves the solution speed and result quality of the firepower allocation problem.

[0072] (2) The present invention provides an airport target firepower allocation method based on the improved Hippo optimization algorithm, which has outstanding performance in multi-constraint optimization modeling and improves the algorithm's solution efficiency and result quality.

[0073] (3) The present invention provides an airport target firepower allocation method based on an improved Hippopotamus optimization algorithm. By simulating the behavior of a hippopotamus group, the improved Hippopotamus algorithm can efficiently search the solution space under complex constraints, avoid local optimal solutions, and quickly converge to a near-optimal solution, effectively avoiding the risk of falling into a local optimal solution.

[0074] (4) The present invention provides an airport target firepower allocation method based on the improved Hippo optimization algorithm, which can flexibly respond to multi-objective optimization problems, such as maximizing strike effectiveness, minimizing resource waste, etc. It has strong adaptability and can adjust strategies according to different mission requirements.

[0075] (5) The present invention provides an airport target firepower distribution method based on the improved Hippo optimization algorithm. By adaptively adjusting and optimizing parameters, the method reduces the dependence on initial conditions, improves the computational efficiency and solution accuracy, and thus provides an efficient and intelligent optimization solution for airport target firepower distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The present invention is a flow chart of the airport runway firepower allocation method based on the improved Hippo optimization algorithm. DETAILED DESCRIPTION

[0077] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0078] like Figure 1 As shown, a method for allocating firepower to airport targets based on an improved Hippo optimization algorithm comprises the following steps:

[0079] Step S1: Taking an airport as a target, analyzing typical targets within the airport and the relationships between them, and performing target damage. The typical targets include: airport runways, aprons, reinforced fortifications, and ammunition depots. Aiming points within the airport runways are coupled, and damage is performed by striking all aiming points on a group of runway runways.

[0080] Step S2: determining the constraints of the firepower allocation model based on the analysis results of step S1 on the typical targets within the airport and the relationships between the typical targets, and constructing the objective function of the firepower allocation model based on the distance between the target point and the fighter, that is, the total mission time fitness function, the distance between the target points, and the damage effectiveness fitness function;

[0081] Step S3, an improved Hippo optimization algorithm is obtained by combining the spatial pyramid chaotic mapping (SPM chaotic mapping), the adaptive weight position update mechanism, the reverse learning strategy, and the neighborhood dimension cross optimization strategy with the Hippo optimization algorithm, specifically:

[0082] Determine the encoding form of the population individuals in the Hippo algorithm according to the target number, initialize the population individuals of the Hippo algorithm through the SPM chaotic mapping, and uniformly generate the initial firepower distribution solution within the solution space under the constraints of the step S2, and judge the quality of the firepower distribution solution according to the objective function of step S2;

[0083] After generating the initial firepower allocation solution, the adaptive weight position update mechanism and reverse learning strategy are used as the exploration phase of the improved Hippo optimization algorithm to search for the firepower allocation solution;

[0084] Finally, when updating the position of each generation, a neighborhood dimension cross optimization strategy is used to retain the good genes of the previous generation;

[0085] Step S4: Perform iterative optimization calculations on the firepower allocation solution according to the improved Hippo optimization algorithm of step S3 until the iteration stop condition is met.

[0086] Furthermore, the implementation process of step S1 is as follows:

[0087] The h typical targets in the airport are represented by T = {T1, T2, ..., T h} indicates that the typical targets include the following types: fortifications, airport runways, aprons, and ammunition depots; among them, the typical targets belonging to the airport runway type are coupled with each other, and the typical targets with coupling relationships are divided into a group. Targets in the same group indicate that all targets in the group should be hit when the attack is carried out, and the attack is considered to be effective. Let m be the number of target groups, and the matrix B is the target group, denoted as B1, B2,…, B m When B1 = {T1, T2, T3}, it means that targets T1, T2, and T3 belong to the same group. When a military strike is carried out against them, all three targets need to be struck.

[0088] Furthermore, the constraints of the firepower allocation model in step S2 are specifically:

[0089] According to the different amount of ammunition carried by each fighter, and the total number of tasks performed by the fighter cannot exceed its ammunition capacity, the constraint condition is obtained

[0090]

[0091] R ij The mission performed by the fighter, the number of our fighters is n F ,use Indicates the starting position of the fighter, and the amount of ammunition carried is represented by matrix C i express, Indicates the amount of ammunition carried by each aircraft. Each aircraft is assigned at least one mission.

[0092]

[0093] Each task is executed only once or not at all

[0094]

[0095] Where N jIndicates the number of times the jth goal is executed.

[0096] Furthermore, the objective function of the firepower allocation model in step S2 is composed of the mission total time fitness function T(R) and the damage effectiveness fitness function E(R), and is normalized by the minimum-maximum normalization method, specifically:

[0097] f(R)=ω1T(R)+ω2E(R)

[0098] Where ω1 and ω2 are the weight coefficients corresponding to the total mission time fitness function and the damage effectiveness fitness function respectively;

[0099] The minimum-maximum normalization method performs normalization processing as follows:

[0100]

[0101] Where, d min is the minimum value in the data, d max is the maximum value in the data, d norm The data are normalized.

[0102] Furthermore, the total mission time fitness function T(R) takes the straight-line distance from the starting point to each target point as a quantitative indicator of time. The position information of the fighter and the target are both known, then:

[0103]

[0104] Where T(R) is the distance fitness value, For fighter U i location, Target T j location, Target T j-1 Position, D i For fighter U i The fitness value within the execution task sequence.

[0105] Furthermore, the damage effectiveness fitness function is:

[0106]

[0107]

[0108] Where E(R) is the fitness value of the damage effect, represents the target number of group i, Indicates whether the jth target in the i-th group is selected to be attacked, ξ i represents the weight coefficient of group i.

[0109] Furthermore, the improved Hippo optimization algorithm described in step S3 is implemented as follows:

[0110] Step S3-1, determine the encoding form of the population individuals in the Hippo algorithm, use the number of targets as the dimension of the solution space, and the number of fighters as the range of the solution in the solution space. When the number of targets is n F When , the encoding form of the population individuals in the Hippo algorithm is:

[0111] X i ={x ij |j=1,2…h}

[0112] Where, X i The i-th individual in the population, x ij represents the code of the jth position of the i-th individual, x ij ∈{0,1,…,n F};

[0113] Step S3-2: Decode the code of the population individual in the Hippo algorithm, and fill in the corresponding code by judging the code number at any position in the solution. and described R is the matrix storing the tasks performed by fighters in task allocation. ij =1 means fighter i attacks target j, It is a grouping matrix, marking the attack situation of the fighter jets on the group. Indicates target group B i The lth target is hit, and the specific decoding method is:

[0114]

[0115] Where x kj is the code of the jth position of the kth individual. This formula indicates that by judging whether the value of the solution is equal to the number of the fighter, if they are equal, the position of the corresponding aircraft in the mission matrix is ​​set to 1, otherwise it is set to 0.

[0116] Step S3-3: Generate a corresponding initial firepower allocation solution based on the typical targets and the number of fighters, use the SPM chaotic mapping method to generate chaotic values ​​in the solution space, discretize the chaotic values ​​into the solution space according to the encoding form, and randomly initialize the population of the Hippo algorithm under the constraints of step S2 to generate an initial Hippo population, i.e., the initial firepower allocation solution;

[0117] Step S3-4, after generating the initial firepower allocation solution, the firepower allocation solution is searched through the adaptive weight position update mechanism and the reverse learning strategy as the exploration phase of the improved Hippopotamus optimization algorithm; specifically, according to the exploration phase 1 of the improved Hippopotamus optimization algorithm, the position of the hippopotamus population is updated to obtain the firepower allocation solution; through the exploration phase 2, the safe position of the hippopotamus population is explored to calculate the candidate solution of the firepower allocation solution; the firepower allocation solution is updated by fusing the reverse learning strategy with the original search strategy of the development phase to obtain a better solution and a better potential solution;

[0118] Step S3-5: Compare the differences in different dimensions between the best individuals of two adjacent generations of the hippo population, i.e., the current generation and the previous generation, through the adjacent generation dimension crossover optimization strategy, and select the dimension with the largest difference for crossover operation. If the fitness value of the individual after crossover is better than that of the original individual, the crossover result is retained; otherwise, the original individual is kept unchanged;

[0119] Step S3-6: The population is continuously updated and iterated through the algorithms of step S3-4 and step S3-5 until the iteration stop condition is met, and finally the final firepower allocation result is output.

[0120] Furthermore, the SPM chaotic mapping method is specifically as follows:

[0121]

[0122] Where x i represents the i-th chaotic value that satisfies the SPM chaotic mapping, x i+1 represents the i+1th chaotic value, mod() represents the remainder function, rand() represents a random number between the interval [0,1], and η and μ are factors related to the chaotic state.

[0123] Furthermore, the step S3-4 is specifically as follows:

[0124] Exploration Phase 1: In the improved Hippopotamus optimization algorithm, the hippopotamus updates its position in this phase. The following formula represents the position of the male hippopotamus:

[0125]

[0126]

[0127] Where, represents the position of the male hippopotamus, that is, the firepower allocation solution represented by the individual, D represents the position of the dominant hippopotamus, that is, the solution corresponding to the firepower allocation scheme with the best fitness in the current iteration number, r1 represents a random number in the interval [0,1], I1 represents a random number in the interval [1,2], ω(t) represents the weight coefficient that changes with time, T represents the maximum number of iterations, and t represents the current iteration number;

[0128] When the juvenile hippopotamus moves away from the female hippopotamus, the position update formula of the male hippopotamus, female hippopotamus and juvenile hippopotamus in the group is:

[0129]

[0130] Where, represents the position of female hippopotamus and juvenile hippopotamus in the group, i.e., the solution of firepower distribution, r2 represents the random vector; MG i represents the average value of randomly selected hippos, T represents the selection probability, and I2 represents a random number between the interval [1,2];

[0131] Exploration Phase 2: When attacked by predators or other creatures, the hippopotamus will react defensively. When predators or other creatures invade, the hippopotamus's position is:

[0132]

[0133] Where, Indicates the location of predators and other creatures invading the hippopotamus's territory, which is a candidate solution for the firepower allocation solution. represents a random vector with Levy distribution, which describes the position mutation of the predator when attacking the hippopotamus. j represents the position of the predator in the search space, represents the distance between the i-th hippopotamus and the predator. b, c, d, and g all represent uniformly distributed random numbers, but their value ranges are different. The value range of b is [2, 4], the value range of c is [1, 1.5], the value range of d is [2, 3], and the value range of g is [2, 4]. r3 represents a random number uniformly distributed in the interval [-1, 1]. Factors that cause hippos to adopt defensive behaviors to protect themselves from predators, F i represents the objective function value;

[0134] Development stage: The original search strategy in the unimproved Hippo optimization algorithm is used to integrate reverse learning to update the location and find the nearest safe place. The updated location is:

[0135]

[0136] Where, represents the location of the hippopotamus that is being searched for the nearest safe place, i.e., the better solution or potential better solution in the current firepower allocation solution, X max (i) and X min (i) represents the upper and lower limits of the solution of the i-th hippopotamus in the solution space, r 41 Represents a random number uniformly distributed in the interval [0,1], r 42Represents a random number that conforms to the normal distribution, t is the current number of iterations, and λ represents a random number uniformly distributed in the interval [0,1]. The above formula indicates that when λ>0.5, the first method is used to update the position, and when λ≤0.5, the reverse learning strategy is used to update the position.

[0137] Furthermore, the specific mathematical expression of the adjacent generation dimension cross optimization strategy is as follows:

[0138]

[0139]

[0140] Where, and represents the position of the i-th hippopotamus at iterations t-1 and t, Indicates the j-th dimension value of the optimal hippopotamus when the number of iterations is t-1, is the position after the cross dimension, f(·) is the fitness calculation function, for each hippopotamus i, according to the dimension difference Δ i,j Sort from large to small, select the h dimensions with the largest difference for crossover, and the dimension difference calculation formula is: h=1,2,…,|R cross ×d|, where R cross is the cross ratio.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for allocating firepower to airport targets based on an improved Hippo optimization algorithm, characterized in that: The following steps are involved: Step S1: Taking an airport as a target, analyzing typical targets within the airport and the relationships between them, and performing target damage. The typical targets include: airport runways, aprons, reinforced fortifications, and ammunition depots. Aiming points within the airport runways are coupled, and damage is performed by striking all aiming points on a group of runway runways. Step S2: determining the constraints of the firepower allocation model based on the analysis results of step S1 on the typical targets within the airport and the relationships between the typical targets, and constructing the objective function of the firepower allocation model based on the distance between the target point and the fighter, that is, the total mission time fitness function, the distance between the target points, and the damage effectiveness fitness function; Step S3, an improved Hippo optimization algorithm is obtained by combining the spatial pyramid chaotic mapping (SPM chaotic mapping), the adaptive weight position update mechanism, the reverse learning strategy, and the neighborhood dimension cross optimization strategy with the Hippo optimization algorithm, specifically: Determine the encoding form of the population individuals in the Hippo algorithm according to the target number, initialize the population individuals of the Hippo algorithm through the SPM chaotic mapping, and uniformly generate the initial firepower distribution solution within the solution space under the constraints of the step S2, and judge the quality of the firepower distribution solution according to the objective function of step S2; After generating the initial firepower allocation solution, the adaptive weight position update mechanism and reverse learning strategy are used as the exploration phase of the improved Hippo optimization algorithm to search for the firepower allocation solution; Finally, when updating the position of each generation, a neighborhood dimension cross optimization strategy is used to retain the good genes of the previous generation; Step S4: Perform iterative optimization calculations on the firepower allocation solution according to the improved Hippo optimization algorithm of step S3 until the iteration stop condition is met.

2. The method for allocating firepower to airport targets based on the improved Hippo optimization algorithm according to claim 1, characterized in that: The implementation process of step S1 is as follows: The h typical targets in the airport are represented by T = {T1, T2, ..., T h } indicates that the typical targets include the following types: fortifications, airport runways, aprons, and ammunition depots; among them, the typical targets belonging to the airport runway type are coupled with each other, and the typical targets with coupling relationships are divided into a group. Targets in the same group mean that all targets in the group should be hit when the attack is carried out, and the attack is considered to be effective. Let m be the number of target groups, and the matrix B is the target group, denoted as B1, B2,…, B m When B1 = {T1, T2, T3}, it means that targets T1, T2, and T3 belong to the same group. When a military strike is carried out against them, all three targets need to be struck.

3. The airport target firepower distribution method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: The constraints of the firepower allocation model in step S2 are specifically: According to the different amount of ammunition carried by each fighter, and the total number of tasks performed by the fighter cannot exceed its ammunition capacity, the constraint condition is obtained R ij The mission performed by the fighter, the number of our fighters is n F ,use Indicates the starting position of the fighter, and the amount of ammunition carried is represented by matrix C i express, Indicates the amount of ammunition carried by each aircraft, Each fighter is assigned at least one mission Each task is executed only once or not at all Where N j Indicates the number of times the jth goal is executed.

4. The airport target firepower distribution method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: The objective function of the firepower allocation model in step S2 is composed of the total mission time fitness function T(R) and the damage effectiveness fitness function E(R), and is normalized using the minimum-maximum normalization method. Specifically, it is: f(R)=ω1T(R)+ω2E(R) Where ω1 and ω2 are the weight coefficients corresponding to the total mission time fitness function and the damage effectiveness fitness function respectively; The minimum-maximum normalization method performs normalization processing as follows: Where, d min is the minimum value in the data, d max is the maximum value in the data, d norm The data are normalized.

5. The airport target firepower distribution method based on the improved Hippo optimization algorithm according to claim 4 is characterized in that: The total mission time fitness function T(R) takes the straight-line distance from the starting point to each target point as a quantitative indicator of time. The position information of the fighter and the target are both known, then: Where T(R) is the distance fitness value, For fighter U i location, Target T j location, Target T j-1 Position, D i For fighter U i The fitness value within the execution task sequence.

6. The airport target firepower distribution method based on the improved Hippo optimization algorithm according to claim 4 is characterized in that: The damage effectiveness fitness function is: Where E(R) is the fitness value of the damage effect, represents the target number of group i, Indicates whether the jth target in the i-th group is selected to be attacked, ξ i represents the weight coefficient of group i.

7. According to claim 1, a method for allocating firepower to airport targets based on an improved Hippo optimization algorithm is characterized in that: The improved Hippo optimization algorithm implementation process described in step S3 is as follows: Step S3-1, determine the encoding form of the population individuals in the Hippo algorithm, use the number of targets as the dimension of the solution space, and the number of fighters as the range of the solution in the solution space. When the number of targets is n F When , the encoding form of the population individuals in the Hippo algorithm is: X i ={x ij |j=1,2…h} Where, X i The i-th individual in the population, x ij represents the code of the jth position of the i-th individual, x ij ∈{0,1,…,n F }; Step S3-2: Decode the code of the population individual in the Hippo algorithm, and fill in the corresponding code by judging the code number at any position in the solution. and described R is the matrix storing the tasks performed by fighters in task allocation. ij =1 means fighter i attacks target j, It is a grouping matrix, marking the attack situation of the fighter jets on the group. Indicates target group B i The lth target is hit, and the specific decoding method is: Where x kj is the code of the jth position of the kth individual. This formula indicates that by judging whether the value of the solution is equal to the number of the fighter, if it is equal, the position of the corresponding aircraft in the mission matrix is ​​set to 1, otherwise it is set to 0; Step S3-3: Generate a corresponding initial firepower allocation solution based on the typical targets and the number of fighters, use the SPM chaotic mapping method to generate chaotic values ​​in the solution space, discretize the chaotic values ​​into the solution space according to the encoding form, and randomly initialize the population of the Hippo algorithm under the constraints of step S2 to generate an initial Hippo population, i.e., the initial firepower allocation solution; Step S3-4, after generating the initial firepower allocation solution, the firepower allocation solution is searched through the adaptive weight position update mechanism and the reverse learning strategy as the exploration phase of the improved Hippo optimization algorithm; Specifically, according to the exploration phase 1 of the improved Hippo optimization algorithm, the position of the hippo population is updated to obtain the firepower allocation solution; through the exploration phase 2, the safe position of the hippo population is explored and the candidate solutions of the firepower allocation solution are calculated; By integrating the original search strategy in the development phase with the reverse learning strategy, the firepower allocation solution is updated to obtain a better solution and a better potential solution; Step S3-5: Compare the differences in different dimensions between the best individuals of two adjacent generations of the hippo population, i.e., the current generation and the previous generation, through the adjacent generation dimension crossover optimization strategy, and select the dimension with the largest difference for crossover operation. If the fitness value of the individual after crossover is better than that of the original individual, the crossover result is retained; otherwise, the original individual is kept unchanged; Step S3-6: The population is continuously updated and iterated through the algorithms of step S3-4 and step S3-5 until the iteration stop condition is met, and finally the final firepower allocation result is output.

8. The method for allocating firepower to airport targets based on the improved Hippo optimization algorithm according to claim 7, characterized in that: The SPM chaotic mapping method is specifically as follows: Where x i represents the i-th chaotic value that satisfies the SPM chaotic mapping, x i+1 represents the i+1th chaotic value, mod() represents the remainder function, rand() represents a random number between the interval [0,1], and η and μ are factors related to the chaotic state.

9. The method for allocating firepower to airport targets based on the improved Hippo optimization algorithm according to claim 7, characterized in that: The steps S3-4 are specifically as follows: Exploration Phase 1: In the improved Hippopotamus optimization algorithm, the hippopotamus updates its position in this phase. The following formula represents the position of the male hippopotamus: Where, represents the position of the male hippopotamus, that is, the firepower allocation solution represented by the individual, D represents the position of the dominant hippopotamus, that is, the solution corresponding to the firepower allocation scheme with the best fitness in the current iteration number, r1 represents a random number in the interval [0,1], I1 represents a random number in the interval [1,2], ω(t) represents the weight coefficient that changes with time, T represents the maximum number of iterations, and t represents the current iteration number; When the juvenile hippopotamus moves away from the female hippopotamus, the position update formula of the male hippopotamus, female hippopotamus and juvenile hippopotamus in the group is: Where, represents the position of female hippopotamus and juvenile hippopotamus in the group, i.e., the solution of firepower distribution, r2 represents the random vector; MG i represents the average value of randomly selected hippos, T represents the selection probability, and I2 represents a random number between the interval [1,2]; Exploration Phase 2: When attacked by predators or other creatures, the hippopotamus will react defensively. When predators or other creatures invade, the hippopotamus's position is: Where, Indicates the location of predators and other creatures invading the hippopotamus's territory, which is a candidate solution for the firepower allocation solution. represents a random vector with Levy distribution, which describes the position mutation of the predator when attacking the hippopotamus. j represents the position of the predator in the search space, represents the distance between the i-th hippopotamus and the predator. b, c, d, and g all represent uniformly distributed random numbers, but their value ranges are different. The value range of b is [2, 4], the value range of c is [1, 1.5], the value range of d is [2, 3], and the value range of g is [2, 4]. r3 represents a random number uniformly distributed in the interval [-1, 1]. Factors that cause hippos to adopt defensive behaviors to protect themselves from predators, F i represents the objective function value; Development stage: The original search strategy in the unimproved Hippo optimization algorithm is used to integrate reverse learning to update the location and find the nearest safe place. The updated location is: Where, represents the location of the hippopotamus that is being searched for the nearest safe place, i.e., the better solution or potential better solution in the current firepower allocation solution, X max (i) and X min (i) represents the upper and lower limits of the solution of the i-th hippopotamus in the solution space, r 41 Represents a random number uniformly distributed in the interval [0,1], r 45 Represents a random number that conforms to the normal distribution, t is the current number of iterations, and λ represents a random number uniformly distributed in the interval [0,1]. The above formula indicates that when λ>0.5, the first method is used to update the position, and when λ≤0.5, the reverse learning strategy is used to update the position.

10. The airport target firepower distribution method based on the improved Hippo optimization algorithm according to claim 1 is characterized in that: The specific mathematical expression of the adjacent generation dimension cross optimization strategy is as follows: Where, represents the position of the i-th hippopotamus when the number of iterations is t, Indicates the j-th dimension value of the optimal hippopotamus when the number of iterations is t-1, is the position after the cross dimension, f(·) is the fitness calculation function, for each hippopotamus i, according to the dimension difference Δ i,j Sort from large to small and select the dimension with the largest difference for crossover.

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