Multi-antiship missile collaborative route planning method based on particle swarm optimization algorithm

Abstract

The invention discloses a multi-anti-ship missile cooperative route planning method based on a particle swarm optimization algorithm, and the method comprises the steps: summarizing a multi-anti-ship missile cooperative route planning problem into a series of 1: 1 combat units, and carrying out the initialization definition of environment parameters; four-point constraints are provided for a series of 1: 1 combat units; aiming at the route planning of the multi-anti-ship missile, constructing a problem model of multi-anti-ship missile collaborative route planning by utilizing four-point constraint in combination with geometric knowledge and rules of the route planning of the anti-ship missile; based on the problem model and in combination with a particle swarm optimization algorithm, the multi-antiship missile collaborative route planning problem with a 1: 1 combat unit as a combat mode is solved; and outputting the collaborative route planning results of all the anti-ship missile 1: 1 combat units to a single standard coordinate system to obtain a complex multi-anti-ship missile collaborative route planning scheme. According to the technical scheme, the problem of complex multi-antiship missile collaborative route planning can be solved.

Description

Technical Field

[0001] This invention relates to the field of missile navigation control and route planning technology, and in particular to a collaborative route planning method for multiple anti-ship missiles based on particle swarm optimization algorithm. Background Technology

[0002] The flight path planning for anti-ship missiles involves determining their autonomous flight path before launch based on the battlefield situation, operational requirements, and missile flight performance, so that the missile can follow this path after launch. Since anti-ship missiles mostly employ a constant altitude and uniform speed sea-skimming flight during the autonomous phase, longitudinal factors can be ignored, and flight path planning can be completed in a two-dimensional plane.

[0003] Research in the field of cooperative route planning, both domestically and internationally, exhibits diversity and depth. Studies primarily focus on the cooperative planning of anti-ship missiles and unmanned aerial vehicles (UAVs). By combining intelligent optimization algorithms with geometric models, the route planning problem for anti-ship missiles has been effectively solved, but some shortcomings remain. For example, the combination of geometric principles and intelligent optimization algorithms has improved the efficiency of single-missile route planning and successfully extended to the cooperative planning of multiple missiles, but in-depth research on solving the cooperative route planning problem for multiple missiles is lacking. Furthermore, domestic scholars have extensively studied the application of intelligent optimization algorithms such as genetic algorithms and particle swarm optimization in anti-ship missile route planning. These algorithms can effectively handle multi-constraint, multi-objective optimization problems, improving the efficiency and quality of route planning. This research utilizes geometric principles in solving the cooperative route planning problem, but it does not reflect the geometric characteristics of the anti-ship missile's own trajectory. Overall, domestic and international research explores how to improve the efficiency, adaptability, and robustness of cooperative route planning through advanced algorithms and technologies. However, in terms of cooperation, the geometric characteristics of the anti-ship missile itself are neglected, and the problem of combining intelligent optimization algorithms to solve related issues is not addressed. Summary of the Invention

[0004] This invention solves the spatial coordination problem of multiple anti-ship missiles in cooperative route planning. It takes into account the geometric characteristics of the anti-ship missiles themselves, analyzes the mathematical and physical principles of anti-ship missile cooperative route planning in depth, and proposes an anti-ship missile cooperative route planning method suitable for the space environment based on these principles and combined with intelligent optimization algorithms.

[0005] This invention discloses a cooperative route planning method for multiple anti-ship missiles based on particle swarm optimization algorithm. The method includes the following steps: Step 1: Transform the complex right The problem of coordinated route planning for multiple anti-ship missiles in the operational environment can be summarized into a series of "1:1" operational units; Step 2: For the "1:1" combat unit of multiple anti-ship missiles, four constraints are proposed with the goal of solving the coordination problem; Step 3: For the cooperative route planning of multiple anti-ship missiles, a problem model for the cooperative route planning of multiple anti-ship missiles is constructed by combining the geometric knowledge and rules of anti-ship missile route planning with the four-point constraints, thus forming the spatial cooperative mechanism of multiple anti-ship missiles. Step 4: Solve the cooperative route planning problem of multiple anti-ship missiles with a combat unit ratio of "1:1" based on the problem model and particle swarm optimization algorithm; Step 5: Repeat steps 2 to 4 until the coordinated route planning of a series of "1:1" combat units corresponding to all anti-ship missiles has been resolved; Step 6: Output the collaborative route planning results of all anti-ship missile "1:1" combat units to a single standard coordinate system to obtain a complex multi-anti-ship missile collaborative route planning scheme.

[0006] Furthermore, step 2 also includes the following steps: Step 2.1: Establish a rectangular coordinate system; take the first waypoint of the route that first enters the monitoring area as the origin, and the major axis of the functional area to which the origin belongs as the coordinate system. Establish a rectangular coordinate system along the axes; Step 2.2: Initialize scan lines; set a vertical line. Axis, parallel to The scan line of the axis, and the initial scan line s coincides with the axis. axis; Step 2.3: Scan line s passes through all waypoints on all routes sequentially from left to right; Step 2.4: Define the total order relation and its changes based on the relationship between the route and scan line s; For the scanning algorithm to determine the intersection of flight paths, in the initial state of straight line s, it is related to the flight path. and routes The two routes intersect simultaneously, and the straight line s and Intersection of air routes The axis coordinates are ,and Intersection of air routes The axis coordinates are ,and Then it is called a straight line. exist The relationship between the two routes at this position of the axis is as follows: Conversely, it is called a straight line. exist The relationship between the two routes at this position of the axis is as follows: ; When the total order relationship between routes changes from Become This is the total order descent; When the total order relationship between routes changes from Become This is the total ascending order; The critical point is when the total order relation between routes is equal; Step 2.5: Construct four-point constraints based on total order relation changes; The four-point constraint is that there exist four waypoints such that the total order relation of the routes undergoes two transformations. Step 2.6: Based on the distribution of the four waypoints on the two intersecting routes, obtain the four conditions for determining the intersection; the four conditions for the four waypoints are: Case 1: Only two waypoints are on the same route, leading to the following intersection criteria:

[0007] Scenario 2: There are 3 waypoints on one waypoint, and the following intersection criteria are derived:

[0008] Scenario 3: All waypoints are on the same flight path, leading to the following intersection criteria:

[0009] Case 4: If two waypoints coincide, the following intersection criteria are derived:

[0010] express The j-th waypoint of the route, This represents the i-th waypoint of route a. This represents the (i+1)th waypoint of route a. This represents the (j+1)th waypoint of route b. , , , These represent the defined results of the cross product of the four-point constraint vectors for cases 1-4, respectively.

[0011] Furthermore, step 3 also includes the following steps: Step 3.1: All waypoints satisfying the missile route distance constraint must be within the functional area. Multiple routes must also satisfy four-point constraints. Based on the analysis of the four-point constraints, the four cases of the four-point constraints are set together, and the result set is defined as follows: for:

[0012] , , , These represent the defined results of the cross product of the four-point constraint vectors for cases 1-4, respectively. Step 3.2: Based on the geometric gradation patterns of functional areas and the analysis of four-point constraints, construct a set of functional constraints to form a spatial coordination mechanism: For any two routes and The set of vector cross product results related to the four-point constraints of the two waypoints The following necessary constraints must be met:

[0013] The waypoints in the multi-anti-ship missile cooperative route planning must meet the following necessary constraints:

[0014]

[0015] in, This represents the waypoints within the corresponding functional area i. This indicates the corresponding waypoint. The required set of vector cross product results. For the corresponding functional areas, To monitor the four-way cross product results formed by waypoints within the monitoring area; For the route and routes For example, when performing collaborative route planning, starting from the launch point... and launch point To the target point and target point Let the waypoints of the two routes be... The set of remaining waypoints is called the functional constraint set, denoted as . , is represented as:

[0016] Represented as n functional regions, Represented as the corresponding waypoint The set of vector cross product results that must be satisfied.

[0017] Furthermore, step 4 also includes the following steps: Step 4.1: Select a reasonable population size Number of single-dimensional components of particles And the algorithm parameters for the maximum number of iterations; Step 4.2: Determine if all particles have been initialized. If yes, proceed to step 4.6; otherwise, calculate... and The initial value is then used to proceed to step 4.3; Step 4.3: In the problem model Within the corresponding particle solution space, respectively for , , Perform random initialization under the constraints; let The value is 0, which corresponds to the component. The initial value is ; Step 4.4: Calculate the particle components after initialization. This corresponds to the total sequence difference between routes. And change the state variables corresponding to the particle components. ; Step 4.5: Determine the first Have all components in a particle been initialized? What are the state variables? Is it the particle component corresponding to 1? Is there a specific numerical value? If so, then... If the summation occurs, proceed to step 4.2; otherwise, calculate. , and Constraints Accumulate, then proceed to step 4.3; Step 4.6: Calculate the fitness value for each route. ; Step 4.7: Update the individual optimal solution and the global optimal solution ; Step 4.8: Let ; Step 4.9: Determine if all particles have been updated. If so, then... If yes, proceed to step 4.12; otherwise, proceed to step 4.10. Step 4.10: Let , ,right , and Perform an update and determine the updated version. , and Does it satisfy the condition of mapping to the particle's domain? The pseudo-problem model If the spatial conditions are not met, then let , Update again until the updated position satisfies the mapping to the particle's location. The pseudo-problem model Solve the conditions of the solution space; otherwise, go to step 4.11. Step 4.11: Determine the first... Have all components in each particle been updated? If so, then... Proceed to step 4.9; otherwise, calculate. , and Constraints Proceed to step 4.10; Step 4.12: Determine Check if the condition is met. If yes, proceed to step 4.6; otherwise, proceed to step 4.13. Step 4.13: Output the results.

[0018] Furthermore, in step 4.1, the population is represented as a matrix: ; in, For the size of the population, The first in the population individual; The functional constraint set consists of several ellipses and constraint sets. A route is composed of several ellipses sharing a common focus. The route is represented using polar coordinates. and routes The first waypoint of the route entering the monitoring area is designated as the pole, and a polar coordinate system is established with the long axis parallel to the functional area to which the pole belongs as the polar axis; assuming each route contains To record the position information and total order state of each waypoint, a fixed-length real-number encoded particle structure is used: ; in, and Recorded separately The waypoints are at the polar angles of the polar coordinates. Polar diameter and total order value , No. The first of the routes The polar coordinates and total sequence state of each waypoint can be represented as follows: Waypoints can exist in two states: within the detection area and outside the detection area. If a waypoint is outside the detection area, its total sequence value is... Using state variables The system identifies whether a waypoint exists within the detection area; a value of 1 indicates its presence, and a value of 0 indicates its absence. The determination is made using the polar radius of the detection area. The total order value in polar coordinates can be represented as... ; This represents the constraint value between different particles, that is, the difference between the total order value components of adjacent particles. If the route If a particle is composed of waypoints, then its dimension is pseudo-dimensional. .

[0019] Furthermore, in step 4.3, based on the established problem model... Based on the principle of non-detour routes, the polar angle value is determined as follows: The value of the polar radius varies with the polar angle, which limits all waypoints to the problem model. Functional areas Within the established polar coordinate system, The equation can be expressed as:

[0020] in, For the functional areas corresponding to the reverse collaborative route planning, For parameters, For the focal length, Eccentricity Indicates the polar radius corresponding to the functional region. Indicates functional area The equation of the ellipse, using Represented by variables; If a monitoring area exists within a functional area, the range of the polar radius within that monitoring area can be expressed as:

[0021] Furthermore, based on the principle of non-intersecting flight paths, the total sequence value components corresponding to different particles within the monitoring area are... The difference Must meet It limits all waypoints to the problem model. In Result set; Therefore, the parameters can be initially given. Initialization solution space range:

[0022] Indicates the safe distance between air routes; For state variables; For the route The eccentricity of the corresponding functional area; For the corresponding flight route The polar angle of the functional area; For the corresponding flight route The quasi-focal length of the functional area; a random initialization method is adopted, in which the particle components are randomly initialized in the solution space, that is, each particle is initialized to a random position in the solution space, and then a random velocity is initialized for each particle.

[0023] Furthermore, in step 4.4, within the established polar coordinates, The equation is expressed as:

[0024] in, for The polar angle is then substituted into the colfocal length. and eccentricity :

[0025] in, This is the actual path length. For the route Corresponding constant waypoint position index, It is a constant. The maximum effective range is defined as the long axis of the first functional area. The step size by which the scan line moves. The number of routes; For waypoints Then it must satisfy:

[0026] Then the problem model middle The total order value corresponding to the result set The resulting total order difference The equation can be expressed as:

[0027] in, For the route and routes The first in The coordinates of each waypoint are thus represented in polar coordinates. The equation can be expressed as:

[0028] For routes and routes Corresponding waypoints Then it must also satisfy:

[0029] Then the problem model Mapped to the pseudo solution space where the particle resides The middle should include:

[0030] For the route and The corresponding subscript is The particle components, For the route Subscript The corresponding polar particle component, For the route Subscript is a constant The polar angle of the waypoint, For the route Subscript The corresponding polar particle component, For the route Subscript is a constant The polar angle of the waypoint.

[0031] Furthermore, in step 4.6, a fuzzy satisfaction function is constructed as the objective function. Reasonable weights are determined based on actual needs, and a performance index is constructed using a multi-attribute fuzzy optimization method, which can be expressed as:

[0032] in, and These represent the actual distances of the flight routes. The root mean square deviation of the absolute value of the number of waypoints for each route The mean square error of the absolute value of the total sequence difference between all waypoints Satisfaction level; and The corresponding weight coefficients, and satisfying ; Determine the fitness function for individuals in the population. Sort in descending order using the following function:

[0033] in Represents the fitness function. For individuals The indicator of whether it intersects with an obstacle is... ,otherwise, ; For individuals The indicator of whether it intersects with other individuals is... ,otherwise, .

[0034] Furthermore, in step 4.7, the standard The basic principle of the algorithm is: A by A population of particles in pseudo Flying at a certain speed in the dimensional search space, the first The position of each particle is The corresponding speed is , can be represented as:

[0035] Its best position was , can be represented as:

[0036] The best position for all particles in the population to pass through is:

[0037] This indicates the update rate of the particle component corresponding to the subscript. This represents the local optimal solution for the particle component with the corresponding subscript. This represents the global optimal solution for the particle component with the corresponding subscript. After obtaining two optimal values, Zili updates its velocity and position using a formula, which can be expressed as:

[0038] in, It is called the inertia factor, and its value is non-negative; and For learning factors; and For the middle Random numbers between; This represents the particle's current position. This represents the current local optimum for the particle. The current update rate of the particles, This represents the current global optimal solution for the particle.

[0039] Furthermore, in step 4.10, when the corresponding component of the particle Next-generation unsatisfied problem model Mapped to the pseudo solution space where the particle resides In the middle, the next generation component is called the corresponding pseudo component. ; For particles that do not meet the requirements, their velocity and direction are dynamically adjusted. The updates gradually move in a reasonable direction, and the adjustment of the corresponding pseudo-components ensures that the particle components and the particles themselves also satisfy the constraint conditions. Particle pseudo-components and Gradually update until the problem model is satisfied Mapped to the pseudo solution space where the particle resides China-Singapore location, among which The new position of the pseudo-radius component is at a position conforming to the golden ratio; however, for the pseudo-total order difference component... The updated position must satisfy both the safe distance and the golden ratio, thus ensuring that the particles satisfy both the golden ratio and the safe distance. The expression can be represented as:

[0040] for The considerations can be explained from two aspects: First, the pseudo-radius component... The update is performed in a reasonable orientation, thereby driving the update of the pseudo-polar angle component; In conclusion, The algorithm's speed update formula can be expressed as:

[0041] in, For learning factors; For the middle Random numbers between; State variables; For processing items; When the particle does not meet the constraint conditions When the particles satisfy the constraints, , When a particle does not meet the constraints, a processing term for the particle is added to the original update rate; when the particle meets the constraints, the original update formula is followed.

[0042] The beneficial effects achieved by this invention are: This invention fundamentally solves the three core problems in the coordinated flight path planning of multiple anti-ship missiles: "course intersection, loss of control over safe distance, and poor adaptability to complex scenarios." It enables efficient coordinated attacks in multiple combat scenarios, ensuring that missile groups maintain a safe distance and avoid threat areas during sea-skimming flight, significantly improving the success rate and timeliness of saturation attacks, and providing key technical support for multi-missile coordinated operations in modern naval warfare.

[0043] 1. Construction of Functional Constraint Set: An innovative set-based modeling method combining four-point constraints and functional region constraints is proposed to efficiently identify and avoid critical states of route intersections. Simultaneously, functional region constraints such as missile range and threat avoidance are integrated to clarify the legal solution space boundary for multi-missile coordination, improving the constraint satisfaction accuracy of route planning by over 30% and fundamentally ensuring the safety of multi-missile coordination. 2. Improved Polar Coordinate Encoding: Overcoming the limitations of traditional encoding in expressing inter-particle cooperative constraints, route parameters are mapped to polar coordinate components of polar angle, polar radius, and total order value. This intuitively reflects the direction and distance of missile routes and their correlation with multiple missiles, improving the accuracy of particle cooperative constraint expression and providing a precise encoding carrier for multi-missile coordination algorithm optimization. 3. Particle Update Strategy Steps: A particle update mechanism combining distributed evolution with golden section correction is designed. Component-order updates ensure dynamic satisfaction of inter-particle constraints, while the golden section defines the update range to prevent particles from deviating from the legal solution space. This achieves a balance between algorithm search efficiency and solution optimality while ensuring constraint satisfaction. Attached Figure Description

[0044] Figure 1 A flowchart of a collaborative route planning method for multiple anti-ship missiles based on particle swarm optimization algorithm; Figure 2 This is a multiplayer mode, a classic multiplayer battle mode; Figure 3 To illustrate the scanning diagram, the origin of the four-point constraint is derived using a scanning algorithm; Figure 4 This describes the distribution of waypoints, specifically the distribution of the four waypoints within the four-point constraint. Figure 5 The spatial coordination mechanism of multiple anti-ship missiles is derived from the problem model of coordinated route planning. Figure 6 The overall framework of this invention is a framework for guiding the operation of intelligent optimization algorithms based on problem models; Figure 7 This refers to the algorithm's encoding structure, specifically the improved encoding structure required for this algorithm. Figure 8 An abstract diagram representing the constraints inherent to the particles themselves; Figure 9 To establish inter-particle constraint circles, a safety distance is used to construct constraint circles to represent the constraints between particles. Figure 10 To constrain the new positions of particles, the golden ratio is used to update or adjust the new positions of the particles. Figure 11 This is a flowchart illustrating the algorithm's specific process. Figure 12 Waypoint deviation is an indicator set in the simulation experiment. Figure 13 The effectiveness of the invention is verified by providing a route planning result diagram. Figure 14 A comparison chart of superior route planning results is provided to demonstrate the effectiveness of the algorithm compared to the original algorithm. Figure 15 This is a comparison chart of universal route planning results, demonstrating universality under different environments and combat modes. Detailed Implementation

[0045] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as a result. However, these embodiments are merely exemplary and do not constitute any limitation on the scope of the present invention. Those skilled in the art should understand that modifications or substitutions can be made to the details and form of the technical solutions of the present invention without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0046] like Figure 1 As shown, the purpose of this invention is to provide a cooperative route planning method for multiple anti-ship missiles based on particle swarm optimization algorithm, characterized by comprising the following steps: Step 1: Transform the complex right The problem of coordinated route planning for multiple anti-ship missiles in the operational environment can be summarized into a series of "1:1" operational units.

[0047] Step 2: For the "1:1" combat unit of multiple anti-ship missiles, four constraints are proposed with the goal of solving the coordination problem.

[0048] Step 3: For the cooperative route planning of multiple anti-ship missiles, a problem model for cooperative route planning of multiple anti-ship missiles is constructed by using four-point constraints combined with geometric knowledge and rules of anti-ship missile route planning, thus forming the spatial cooperative mechanism of multiple anti-ship missiles.

[0049] Step 4: Solve the problem of coordinated route planning for multiple anti-ship missiles with a combat unit ratio of "1:1" based on the problem model and particle swarm optimization algorithm.

[0050] Step 5: Repeat steps 2 to 4 until the coordinated route planning of a series of "1:1" combat units corresponding to all anti-ship missiles has been resolved.

[0051] Step 6: Output the collaborative route planning results of all anti-ship missile "1:1" combat units to a single standard coordinate system to obtain a complex multi-anti-ship missile collaborative route planning scheme.

[0052] set up This is the corresponding anti-ship missile assembly (i.e., the launch point). This is the set of target points corresponding to anti-ship missiles. Route The path can be represented as And since the first waypoint is the waypoint following the launch point, and the target point is the last waypoint (i.e., the target point), then each waypoint has... One waypoint and one launch point. Since anti-ship missiles typically fly at high speeds skimming the sea surface during their flight phase, the flight space can be simplified to a two-dimensional plane.

[0053] Definition 1: The distance between anti-ship missiles on different routes must satisfy the condition that the minimum distance is not less than the minimum safe distance, that is: (1) in, During flight Anti-ship missiles along the route and The actual distance between anti-ship missiles along the route; This refers to the safe distance between anti-ship missiles on different routes.

[0054] When multiple anti-ship missiles are used for coordinated anti-ship missile route planning against multiple targets, there may be overlapping functional areas. In these overlapping functional areas, routes may interfere with each other.

[0055] Using mathematical induction, step 1 can be described as proposition 1: Proposition 1: In right In the combat mode, it is summarized as a series of "1:1" combat units.

[0056] Regarding combat modes In the middle, consider One attack unit and One target unit. Assume... For all If the inductive hypothesis is true, then proof is required. It holds true. And for any One attack unit and One target unit, namely Then, the m-to-n combat mode can be decomposed into at most n "1:1" units.

[0057] Let the (m+1)th attack unit be denoted as .according to The combat behavior can be discussed as follows: Idle: due to Not involved in the attack, therefore removed. The remaining m attack units and n target units, according to the inductive hypothesis P(m,n), can be decomposed into at most n "1:1" units (denoted as set S). Afterwards, since it is idle, its decomposition remains unchanged, still being set S. Therefore, P(m+1,n) holds true.

[0058] Attacking a target j (1≤j≤n): Considering the remaining m attack units and n target units, according to the inductive hypothesis P(m,n), there exists a set S that can be decomposed into at most n "1:1" units. In S, target j may or may not be attacked; consider the following cases: (1) Target j is attacked in S: In S, there exists a "1:1" unit where attack group (containing one or more attack units) G attacks target j. When When attacking target j, Join attack group G to form a new attack group. Update this unit to The interaction with target j is "1:1". Other elements in S remain unchanged. Therefore, the decomposition still results in at most n "1:1" elements. Therefore, P(m+1,n) holds.

[0059] (2) Target j was not attacked in S: In S, target j was not attacked by any attack group. When When attacking target j, add a new "1:1" unit: attack group. With target j as an example, other units in S remain unchanged. Since target j was not previously attacked, new units are added, but the total number of units does not exceed n (because there are at most n targets). Therefore, it is decomposed into at most n "1:1" units. Therefore, P(m+1,n) holds true.

[0060] By mathematical induction, P(m,n) holds for all m ≥ 0 and for any fixed n. Since n is arbitrary, this conclusion holds for all m and n.

[0061] However, among the many "1:1" combat modes of multi-target cooperative route planning for multiple anti-ship missiles, "2v2" cooperative route planning is a typical and fundamental case. Therefore, this invention assumes a formation consisting of two platforms that will explore cooperative route planning for anti-ship missiles against two targets, such as... Figure 2 As shown.

[0062] Definition 2: Overlapping functional areas are the monitoring areas.

[0063] For m routes, each route contains n (m≥2, n≥2) waypoints. The minimum time complexity for brute-force enumeration of any two routes and intersection checks using the waypoints is O(n). The highest time complexity can reach However, by using a scanning algorithm, the time complexity can be reduced to O(n).

[0064] Proposition 2: Determine whether m routes with n waypoints intersect using brute force enumeration, with a time complexity of O(n). .

[0065] For m routes, each with n waypoints, using brute force to determine route intersections requires traversing all possible combinations of waypoints between two routes. The time complexity for determining intersections between two routes is: (2) So for m routes, the total cost is... For waypoint combinations, i.e. (3) The complexity of using brute force enumeration to determine whether m routes with n waypoints intersect is: (4) The scanning algorithm for four-point constraints can be described as follows: Figure 3 As shown.

[0066] Step 2.1: Establish a rectangular coordinate system. Taking route a and route b as examples, the launch point and target point are A and B, respectively. and A rectangular coordinate system is established with the first waypoint of the route that first enters the monitoring area as the origin and the long axis of the functional area parallel to the origin as the x-axis.

[0067] Step 2.2: Initialize the scan lines. Initialize the scan lines and set a straight line s perpendicular to the x-axis and parallel to the y-axis. The initial line s coincides with the y-axis.

[0068] Step 2.3: Scan line s sequentially from left to right, passing through all waypoints on the route.

[0069] The number of steps that line s moves from left to right each time is the average distance between waypoints on multiple routes. Let the actual distance of the route be L, the number of steps that line s moves be h, and the distance between waypoints on a single route be l, then the following formula can be derived:

[0070] Proposition 3: Use a scanning algorithm to determine whether m routes with n waypoints intersect, with a time complexity of O(n).

[0071] As described above, the time complexity of the scanning algorithm is: s moves a fixed step h each time until all waypoints are visited, therefore the time complexity is: (8) For the scanning algorithm to determine the intersection of flight routes, in the initial state of the straight line s, when it intersects with both flight routes a and flight routes b simultaneously, let the y-axis coordinate value of the intersection point of the straight line s and flight route a be , and the y-axis coordinate value of the intersection point O with flight route b or (the initial state is the origin) be , and , then the relationship between the two flight routes at this position of the x-axis of the straight line s is called a > b; conversely, if the y-axis coordinate of the intersection point is less than the y-axis coordinate of the intersection point , then the relationship between the two flight routes at this position of the x-axis of the straight line s is called a < b. For this reason, the following definitions can be made: Definition 3: There is a y-axis value D of the intersection points of different flight routes and the straight line s. The flight routes form a total order relationship composed of D values, and the D value is the total order value.

[0072] As the straight line s passes through the intersection point from left to right to the straight line , the total order relationship between a and b will change (from a > b to a = b). When the straight line s continues to move to , the total order relationship between a and b will change again (from a = b to a < b). For this reason, the following definitions can be made: Definition 4: When the total order relationship between the flight routes changes from ">" to "=", it is a total order descent.

[0073] Definition 5: When the total order relationship between the flight routes changes from "=" to "<", it is a total order ascent.

[0074] Definition 6: When the total order relationship between the flight routes is equal, it is the critical point.

[0075] Step 2.4: Total order value change. When the total order relationship of the flight routes shows a total order descent, it can be observed that flight route a and flight route b intersect at the critical point. After this critical point, the total order relationship may rise or continue to maintain the critical state (i.e., the critical point).

[0076] Step 2.5: Four-point constraint. The change of the total order relationship of the flight routes is determined by the intersection points of the straight line s and the flight routes. In the classic non-coincident intersection scenario, in the two boundary states before and after the change of the total order relationship, there are two intersection points of the straight line s and the flight routes respectively. Thus, four characteristic points are formed to mark the change of the total order relationship of the flight routes. These characteristic points are located in the interval of the adjacent flight route points on the left and right of the critical state of the two flight routes, and two need to be selected from each of flight routes a and b. Considering that there may be flight route points in the critical state, to avoid missing selection, the selection of flight route points needs to follow the principle of priority. For this reason, the following definitions can be made: Definition 7: When the total order relation of a route decreases, routes may intersect, that is, they intersect at the critical state. In the case of classical intersection, there are four waypoints that cause the total order relation of the routes to undergo two transformations, which are called four-point constraints.

[0077] By using the cross product of the four waypoints in Definition 7, we can determine whether two ways intersect.

[0078] Step 2.6: Four Intersection Cases. The origin of these four cases can be described as follows: Proposition 4: For these 4 waypoints on two intersecting routes, and the case where no two waypoints have a common point, there are 3 possible cases.

[0079] Because waypoints exist in a specific order, their sorting can be disregarded. Furthermore, since waypoints on a route are fixed, the route sorting can also be disregarded. For the distribution of n points on two intersecting lines, there are two possible scenarios: (1) All points are on one line: There is only one scenario, as the line sorting is not considered. (2) k points are on one line, and the remaining nk points are on another line: For each value of k from 1 to n-1, there is one scenario. Because the route sorting is not considered, each scenario corresponding to each value needs to be divided by 2 and rounded up. Therefore, the number of possible distribution scenarios for n points on two intersecting lines is... It can be expressed by the following formula:

[0080] Therefore, among these four waypoints on the two intersecting routes, they can be divided into... This is one of the situations.

[0081] Proposition 5: For four waypoints on two intersecting routes, there are two waypoints that share a common point, and there is only one such case where two waypoints share a common point.

[0082] From equation (11), we can see that a single route cannot have a single route point that is the same as another route point. Therefore, two routes can only have two points that are the same as another route point. We can disregard the ordering of route points, and we can also disregard the ordering of routes, for the same reason as propositions 1-4.

[0083] For n points on two intersecting lines, there is no distribution where all points are on the same flight path and no two points overlap. The analysis is as follows: If k points are on one line, and there are cases where two points share a point, then the remaining nk-1 points are on another line. For each value of k from 1 to n-2, there is one case. Since the order of the routes is not considered, each case corresponding to each value needs to be divided by 2 and rounded up.

[0084] Then, the distribution of n waypoints on two intersecting ways, where two points coincide, is as follows: .

[0085]

[0086] Therefore, among the four waypoints on two intersecting routes, there exist two waypoints that are divisible by a common point. This is one of the situations.

[0087] Conclusion: There are a total of four possible distributions of the four waypoints on two intersecting air routes. The four possible distributions of the four waypoints are as follows: Figure 4 As shown.

[0088] Case 1: Only two waypoints are on the same route, leading to the following intersection criteria:

[0089] Scenario 2: There are 3 waypoints on one waypoint, and the following intersection criteria are derived:

[0090] Scenario 3: All waypoints are on the same flight path, leading to the following intersection criteria:

[0091] Case 4: If two waypoints coincide, the following intersection criteria are derived:

[0092] Taking case 1 as an example, using the vector cross product, vectors sum vector Intersection yields vectors and , and exist Both sides, vectors exist The counterclockwise direction, that is ;vector exist The clockwise direction, that is The cross product has opposite signs. and In vector Both sides of , so vector sum vector They intersect. Similarly, this can also be proven. In vector Both sides.

[0093] The same applies to other situations.

[0094] Step 3 can be described as follows: The problem model and the cooperative mechanism of multiple anti-ship missiles can be described as follows: The search space is established by combining the geometric gradation rules of reverse route planning with a four-point constraint method. For example... Figure 5 As shown, the launch point for route a is a, and the target point is the waypoint. As the reverse route progresses, the indices of the waypoints gradually increase.

[0095] Step 3.1: Aggregation. Due to the limitation of the maximum range of anti-ship missiles, all waypoints satisfying the missile's flight path distance constraints must be within the functional area. Furthermore, due to the adverse effects of intersecting flight paths, multiple flight paths must also satisfy four-point constraints. Based on the analysis of these four-point constraints, aggregation is performed on the four cases of these constraints. Let the result set C be:

[0096] in, These correspond to the definitions of the cross product of four four-point constraint vectors, respectively.

[0097] Step 3.2: Construct the problem model, i.e., the functional constraint set. Based on the geometric gradation law of functional regions and the four-point constraint analysis, construct the functional constraint set to form a spatial coordination mechanism. This can be described as follows: For any two routes a and b, the set of vector cross products related to the four-point constraints of these two routes is... The following necessary constraints must be met:

[0098] The waypoints in the multi-anti-ship missile cooperative route planning must meet the following constraints:

[0099] in, For the corresponding functional areas, The result of the cross product of the four waypoints.

[0100] When planning the coordinated flight path of multiple anti-ship missiles, the following definition can be obtained from the geometric gradient law of functional areas and the four-point constraint analysis: Definition 8: When performing cooperative route planning using routes a and b as examples, the routes from launch point a and launch point b to the target point are respectively... and target point Let n be the waypoints of the two routes (n≥2). The set of the remaining waypoints is called the functional constraint set (FCS), denoted as . Then it can be expressed as:

[0101] The problem model, which combines particle swarm optimization to solve the cooperative route planning problem, can be described as follows: Figure 6 As shown: For step 4, as Figure 11 As shown, the process can be summarized into the following steps: Step 4.1: Algorithm Preparation. Choose a suitable population size m, the number of single-dimensional components n per particle, and the maximum number of iterations. Set the algorithm parameters and let i=1, j=1, k=1.

[0102] The population can be represented as a matrix. Where m is the population size, Let be the i-th individual (i=1,2,3,...,m) in the population. The functional constraint set accurately defines the scope of the search space. Since the functional constraint set consists of several ellipses and constraint sets, and the same route consists of several ellipses sharing a common focus, the route is suitable for representation using polar coordinates. Taking routes a and b as examples: the first route point of the route that enters the monitoring area first is taken as the pole, and the long axis parallel to the functional region to which the pole belongs is taken as the polar axis, establishing a polar coordinate system. Suppose each route contains n route points. In order to record the position information and total order state of each route point, the following fixed-length real-number encoded particle structure is adopted, which can be represented as:

[0103] in, and The polar angle θ, polar radius ρ, and total order value D of n waypoints in polar coordinates are recorded respectively. The polar coordinates and total order state of the j-th waypoint of the i-th waypoint can be expressed as: (Note: Waypoints can be either within or outside the detection area, in which case state variables are used.) The system identifies the waypoint; if the waypoint is not within the detection area, the corresponding total order value D is ∞, using state variables. The presence of a waypoint within the detection area is indicated by a value of 1 if it exists, and 0 otherwise (this can be determined using the polar radius range of the detection area below). In polar coordinates, the total order value can be expressed as D = ρ sinθ. Furthermore, This represents the constraint value between different particles, that is, the difference between the total order value components of adjacent particles. If the route consists of n waypoints, then the particle dimension is pseudo-4n, and its particle encoding structure is as follows: Figure 7 As shown.

[0104] Step 4.2: Preliminary initialization check. Check if all particles have been initialized. If so, proceed to step 4.6; otherwise, calculate the initial values ​​of κ and e, and proceed to step 4.3.

[0105] Step 4.3: Perform initialization. Within the particle solution space corresponding to the problem model FCS, respectively perform random initialization under the premise of satisfying the constraint conditions. Let be 0, and the initial value of the corresponding component be ∞.

[0106] According to the established problem model FCS and the principle of non -迂回 of the route, the polar angle takes values , and the value of the polar radius changes with the polar angle, which confines all route points within the functional region Ω(O) in the problem model FCS. In the established polar coordinate system, the equation of O can be expressed as:

[0107] where O is the functional region corresponding to the reverse collaborative route planning, κ is the quasi - focal length, and e(0 < e < 1) is the eccentricity.

[0108] If there is a monitoring region in the functional region, the range of the polar radius within the monitoring region can be expressed as:

[0109] Furthermore, according to the principle of non - intersection of the routes, the difference of the total order value component D corresponding to different particles within the monitoring region needs to satisfy , which confines all route points within the

[0110] result set in the problem model FCS. Thus, the initial solution space range of the parameter

[0111] In this paper, a random initialization method is adopted to randomly initialize the particle components in the solution space. That is, each particle is initialized to a random position in the solution space, and then a random velocity is initialized for each particle. The population size, the number of route points, and the minimum safety distance are parameters related to the algorithm that need to be determined by the user.

[0112] Step 4.4: Calculate the total order difference. Calculate the particle component after initializing the particles according to Equation (30), which corresponds to the total order difference between the routes, and change the state variable corresponding to the particle component.

[0113] Based on the traditional PSO algorithm, considering an algorithm that takes into account the correlation between particle components and between particles using the established problem model FCS, the correlation between particle components and between particles will be mapped into the evolutionary formula below.

[0114] Lemma 1: Formula (23) expresses the correlation between waypoints of path a, i.e., between particle components. In the established polar coordinates, The equation is expressed as:

[0115] in, for The polar angle is then substituted into the colfocal length. and eccentricity We can obtain:

[0116] Where L is the actual path length, j1 is a constant, and la is the maximum effective range, i.e., the major axis of the first functional region; according to Lemma 1, for waypoints Then it must satisfy:

[0117] Lemma 2: Formula (25) expresses the relationship between path a and path b, i.e., between particle a and particle b, and is reflected in the components. In the established rectangular coordinate system, the problem model FCS... The total order difference generated by the total order value D corresponding to the result set The equation can be expressed as:

[0118] in, Let be the coordinates of the i-th waypoint in routes a and b, and thus their corresponding polar coordinates. The equation can be expressed as:

[0119] Therefore, for the waypoints corresponding to route a and route b Then it must also satisfy:

[0120] The problem model FCS is then mapped to the pseudo solution space where the particle resides. The middle should include:

[0121] Definition 9: Due to the effect of the functional constraint set, there are correlations between the components of a particle and between particles. In order to reflect this correlation, the constraints between each component and the accompanying particle are updated sequentially and step by step. This strategy is called the distributional companion evolution strategy.

[0122] Definition 10: The position update of the subsequent component of a particle is constrained by the position update of the preceding component, and the distance between particles is constrained by a safety distance. Constraint circle restriction, such as Figure 9 As shown; the internal constraints of a particle can be abstracted as an atomic nucleus structure, such as Figure 8 As shown. Based on the constraints of itself and other particles, the position of the particle's subsequent component and the updated position are both within the corresponding limited range. The set of particles with this constraint capability is called the constraint term of FCS.

[0123] Step 4.5: Initialization Check. Determine whether all components in the i-th particle have been initialized, and the state variables... Is it the particle component corresponding to 1? If there is a specific numerical value, then increment i (accumulate) and go to step 4.2; otherwise, calculate... and The constraints are defined, j++, proceed to step 4.3.

[0124] Step 4.6: Calculate fitness values. Calculate the fitness value for each route. .

[0125] The fitness function of this invention mainly considers three aspects: the actual flight distance is relatively short, the absolute value of the root mean square error of the number of waypoints is relatively small, and the absolute value of the root mean square error of the total sequence difference of each waypoint is relatively small. The reasons are as follows: (1) Long flight distance will increase the dispersion error of the missile's self-control point endpoint and increase the probability of waypoint intersection within the monitoring area; (2) The number of waypoints determines the scan line step size. The shorter the step size, the stronger the constraint on waypoint intersection; (3) The smaller the total sequence difference within the monitoring area, the smaller the waypoint movement space and the higher the intersection probability. In order to avoid the difference in the magnitude of the single objective function leading to a huge difference in its influence on the overall objective, a fuzzy satisfaction function of the objective function can be constructed. The reasonable weight can be determined in combination with the actual needs. The performance index can be constructed by the multi-attribute fuzzy optimization method, which can be expressed as:

[0126] in, and These are respectively expressed as the satisfaction with the actual flight distance L of the route, the root mean square error n of the absolute value of the number of waypoints for each route, and the root mean square error σ of the absolute value of the total sequence difference for each waypoint; and The corresponding weight coefficients, and satisfying .

[0127] Determine the fitness function for individuals in the population. Sort in descending order using the following function:

[0128] Where a is an individual The indicator of whether it intersects with an obstacle is a=1, otherwise a=0; b represents the individual. The indicator of whether an object intersects with other individuals is b=1; otherwise, b=0.

[0129] Step 4.7: Update the optimal solution. Update the individual. and global The optimal solution.

[0130] The evolutionary formula is based on the PSO algorithm. The basic principle of the improved algorithm is: a population of m particles flies at a certain speed in a pseudo-4n-dimensional search space, and the position of the i-th particle is... The corresponding speed is , can be represented as:

[0131] Its best position was , can be represented as

[0132] The best position that all particles in the population pass through is

[0133] As shown in step 4.3, PSO is initialized with a swarm of random particles, resulting in a random solution. The optimal solution is then found iteratively. In each iteration, the particles update themselves by tracking two "optimal solutions." After finding these two optimal values, each particle updates its velocity and position using a formula, which can be expressed as:

[0134] Where ω is called the inertia factor, and its value is non-negative; and For learning factors; and A random number between (0, 1); This represents the particle's current position.

[0135] Step 4.8: Reset. Let i=1, j=1.

[0136] Step 4.9: Preparatory judgment for particle update. Determine whether all particles have been updated. If so, increment k and go to step 4.12; otherwise, go to step 4.10.

[0137] Step 4.10: Perform particle update. Let According to formula (40) and Perform an update and determine the updated version. and Does it satisfy equation (39)? If not, then let Update according to equation (40) until the updated position satisfies equation (32); otherwise, proceed to step 4.11.

[0138] according to Figure 9 It can be seen that, under the constraint of the constraint circle between particles, the smaller the radius of the constraint circle (i.e., the safe distance), the better. As the particle gets closer to the optimal solution, the constraint circle becomes more limited, and Definition 12 can be used for further processing.

[0139] Definition 11: When the corresponding component of the particle When the next generation does not satisfy equation (32), its next generation component is called the corresponding pseudo component. ; The role of the FCS constraint term is to control the update speed and direction of particle components, ensuring that the position after each update satisfies equation (32). For particles that do not satisfy this equation, their speed and direction are dynamically adjusted. The updates gradually move in a reasonable direction, and with the adjustment of the corresponding pseudo-components, the constraints between particle components and particles are also satisfied. The following definitions apply: Definition 12: Golden Ratio In the FCS constraint terms, the particle pseudo-components are... and The pseudo-radius component is gradually updated to a new position that satisfies equation (32), where j = n+1,...,2n. The new position of the pseudo-radius component is in a position that conforms to the golden ratio. However, for the pseudo-total order difference component... The updated position must satisfy both the golden ratio and the safe distance, thus ensuring that the particles satisfy both the golden ratio and the safe distance. Figure 10 As shown; The golden ratio The expression can be represented as:

[0140] for The considerations can be explained from two aspects: First, the pseudo-radius component... The update is performed towards a reasonable orientation, thereby driving the update of the pseudo-polar angle components; secondly, the total sequence difference is updated towards a reasonable value, thereby reducing the limitations of the constraint circle.

[0141] In summary, the speed update formula for the FCS-PSO algorithm can be expressed as:

[0142] in, For learning factors; A random number between (0, 1); For state variables; This is a processing term. When the particle does not satisfy constraint condition (32), , When the particle satisfies constraint condition (32), When a particle does not meet the constraints, a processing term for the particle is added to the original update rate; when the particle meets the constraints, the original update formula is followed.

[0143] Step 4.11: Check particle update. Determine if all components in the i-th particle have been updated. If so, increment i and go to step 4.9; otherwise, calculate... and The constraints are defined, j++, proceed to step 4.10.

[0144] Step 4.12: Iterative judgment. Judgment If the condition is true, proceed to step 4.6; otherwise, proceed to step 4.13.

[0145] Step 4.13: Output the results.

[0146] In step 6, the waypoint coordinates within the particle need to be converted from the corresponding polar coordinate system back to the standard coordinate system.

[0147] To fully verify the performance of the proposed algorithm, this invention designs a simulation experiment to conduct system verification from the following three dimensions: (1) effectiveness, i.e., verifying whether the algorithm can achieve its design goal under the preset scenario; (2) superiority, i.e., by comparing with the basic algorithm, proving the improvement of the algorithm in performance indicators; (3) universality, i.e. verifying the robustness and adaptability of the algorithm under different parameter configurations, environmental conditions or task requirements.

[0148] The simulation experiment was set as follows: (1) Simulation platform: The simulation environment was built based on Python 3.12.0. (2) Threat source setting: Threat sources were randomly distributed in different areas, with a threat radius of 50~150km. (3) Missile parameters: The maximum missile range was 5000km, and the minimum safe distance was 2km. (4) Algorithm parameters: Population size N=75, maximum number of iterations was 300, learning factor c1=c2=2, and inertia weight ω=0.7. (5) Comparison algorithm: The standard PSO algorithm was selected as the benchmark, and the experiment was conducted with the same parameters. The comparison indicators included execution time, route deviation, average actual route distance, mean square deviation of waypoints, and fitness value improvement rate.

[0149] The reasons for selecting the following four evaluation indicators in this paper are as follows: The straight-line distance between the starting and ending points is used. This is the optimal route length, also known as the theoretical optimal route.

[0150] (1) Execution time This can reflect the complexity of different algorithms.

[0151] (2) Route deviation Route deviation reflects the geometric deviation between the planned route length and the theoretically optimal route length. The formula for route deviation is shown in equation (42).

[0152] (3) Average actual distance of the flight route It is used to measure the average actual length of multiple routes in different comparative experiments to assess the sustainability of collaborative route planning.

[0153] (4) Mean square deviation of waypoints Used to measure the geometric deviation of a waypoint from the optimal route, such as Figure 12 The formula for the mean square deviation of the waypoints is shown in equation (43).

[0154]

[0155] (5) Fitness value improvement rate : Used to measure the improvement rate of the overall evaluation of a route in different experiments, indicating the degree of optimization of the overall performance of the route.

[0156] Example 1: Validity Test The effectiveness verification mainly verifies whether the cooperative route planning can effectively solve the coordination problem of multiple anti-ship missiles and whether there are any improvements in adaptability. Relevant environmental parameters are shown in Table 1, and experimental results are shown in Table 2. Figure 13 As shown.

[0157]

[0158]

[0159] In validity verification, such as Figure 13 As shown, the two routes planned by the algorithm successfully avoided threat areas and route intersections under the action of the functional constraint set, completing the collaborative route planning, and the fitness improvement rate was 3.38%. By introducing the functional constraint set and the golden section correction mechanism, the comprehensive performance of route planning was increased. While ensuring the safety and stability of the route, it approached the theoretical optimal solution, verifying the effectiveness of the algorithm improvement.

[0160] Example 2: Superiority Test The superiority verification mainly verifies whether it has advantages over the standard PSO in solving the coordination problem of multiple missiles in cooperative route planning, and whether there are improvements in relevant data. Relevant environmental parameters are shown in Table 1, and experimental comparison results are shown in Table 3. Figure 14 As shown.

[0161]

[0162] In the superiority verification, the two routes successfully avoided intersection and completed cooperative route planning under the influence of the functional constraint set, while the PSO algorithm failed to achieve this avoidance. As shown in Table 3, compared with the standard PSO, the improved algorithm has increased execution time, average actual route distance lengthened by 0.3%, and route deviation increased by 24%. This indicates that although the execution time and route length have increased, it is to avoid routes and obstacles, and the increase in actual route distance compared with the theoretical route is acceptable. The mean square deviation of waypoints is 300.8, which is better than the 516.8 of the standard PSO, indicating that the waypoints in the monitoring area are closer to the theoretical optimal route planning than PSO, and effectively maintain the stable relationship between routes. In terms of fitness improvement rate, compared with the standard PSO algorithm, the fitness value improvement rate increased from 0.21% to 3.38%, and the optimization effect improved by 15.1%. This indicates that, compared to the PSO algorithm, this algorithm significantly enhances the overall performance of route planning by introducing a functional constraint set and a golden section correction mechanism. While ensuring route safety and stability, it more efficiently approximates the theoretical optimal solution, verifying the superiority of the algorithm.

[0163] Example 3: Universality Test The universality verification mainly verifies the robustness and adaptability of the collaborative route planning system compared to the standard PSO under different parameter configurations, environmental conditions, or mission requirements, and whether it also possesses superiority and effectiveness compared to the standard PSO. Relevant environmental parameters are shown in Table 4, and experimental comparison results are shown in Table 5. Figure 15 As shown.

[0164]

[0165]

[0166]

[0167] In generalization testing, the improved algorithm demonstrated superior performance compared to the standard PSO algorithm across various operational modes. For example... Figure 15As shown in Table 5, under different operational modes, the algorithm can effectively generate cooperative routes that do not intersect and meet safe distance constraints, while the standard PSO algorithm fails in route intersection avoidance. Table 5 shows that in the 5v5 mode, the mean squared deviation of waypoints (89.7) is significantly lower than that of PSO (130.3), indicating that it can still maintain route geometric stability in large-scale missions. In the (2v2, 3v3, 5v5) modes, the route deviations (0.053, 0.083, 0.086) are all lower than those of PSO (0.097, 0.123, 0.129), indicating that its planned paths are closer to the theoretically optimal routes. The average actual route distance is shorter, verifying its ability to reduce cooperative errors. The improvement rates in all modes (6.37%, 0.69%, 3.32%) are better than those of PSO (3.61%, 0.06%, 0.24%), proving that its overall performance improvement is consistent across scenarios. As shown in Table 5, even with increased obstacles and randomly distributed threat sources, the mean square deviation and fitness values ​​of waypoints remain superior, indicating that the functional constraint set mechanism can effectively cope with environmental uncertainties. Execution time increases with mission scale, which is the cost of introducing the functional constraint set and golden ratio correction. However, this cost results in a significant improvement in route safety and planning quality, making it reasonable for military applications.

[0168] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformations or equivalent substitutions fall within the scope of protection of the present invention; the parts of the present invention not described in detail are well-known technologies to those skilled in the art.

Claims

1. A multi-anti-ship missile cooperative path planning method based on a particle swarm optimization algorithm, characterized in that, The multi-anti-ship missile cooperative path planning method based on the particle swarm optimization algorithm comprises the following steps. Step 1: The complex The problem of multi-anti-ship missile cooperative path planning in the combat environment of is reduced to a series of "1:1" combat units. Step 2: For the "1:1" combat unit of the multi-anti-ship missile, four constraints are proposed to solve the cooperation problem; Step 3: For the cooperative path planning of the multi-anti-ship missile, the problem model of the multi-anti-ship missile cooperative path planning is constructed by combining the four constraints, the geometric knowledge and rules of anti-ship missile path planning, and the spatial cooperation mechanism of the multi-anti-ship missile is formed; Step 4: Based on the problem model and the particle swarm optimization algorithm, the cooperative path planning problem of the multi-anti-ship missile with the "1:1" combat unit as the combat mode is solved; Step 5: Repeat steps 2 to 4 until the cooperative path planning of all anti-ship missiles corresponding to a series of "1:1" combat units is solved; Step 6: The cooperative path planning results of all anti-ship missiles "1:1" combat units are output to a single standard coordinate system to obtain a complex multi-anti-ship missile cooperative path planning scheme.

2. The method according to claim 1, wherein, In step 2, the following steps are further included: Step 2.1: Establish a rectangular coordinate system; take the first waypoint of the air route entering the monitoring area secondly as the origin, and take the long axis parallel to the functional area to which the origin belongs as the x-axis to establish a rectangular coordinate system axis to establish a rectangular coordinate system; Step 2.2: Initialize scan line; set a vertical axis, parallel to the axis of the scan line, and the initial scan line s coincides with the axis. Step 2.3: Set the initial scan line s to the first pixel of the scan line. Step 2.4: Set the initial scan line s to the last pixel of the scan line. Step 2.5: Set the initial scan line s to the first pixel of the scan line. Step 2.3: The scan line s passes through all the waypoints on the route from left to right in turn; Step 2.4: Based on the relationship between the route and the scan line s, the total order relationship and the total order relationship change are defined; For scanning algorithms to determine intersecting flight paths, in straight lines... In the initial state, with the route and routes The two routes intersect at the same time, in a straight line and Intersection of air routes The axis coordinates are ,and Intersection of air routes The axis coordinates are ,and Then it is called a straight line. exist The relationship between the two routes at this position of the axis is as follows: Conversely, it is called a straight line. exist The relationship between the two routes at this position of the axis is as follows: ; When the total order relation between the routes changes from to , that is, total order falls; When the total order relation between the routes changes from to , that is, total order rises; When the total order relationship between the routes is equal, it is a critical point; Step 2.5: Four-point constraints are constructed based on the total order relationship change; The four-point constraint is that there are four waypoints such that the total order relationship of the route changes twice; Step 2.6: Based on the distribution of the four waypoints on the two intersecting routes, four intersection condition judgment conditions are obtained; for the four situations of the four waypoints: Case 1: Only two waypoints are on one route, and the following intersection judgment condition is obtained: ； Case 2: There are three waypoints on one route, and the following intersection judgment condition is obtained: ； Case 3: All waypoints are on one route, and the following intersection judgment condition is obtained: ； Case 4: There are two co-point situations, and the following intersection judgment condition is obtained: ； represents the jth waypoint of the b-route, represents the ith waypoint of the a-route, represents the i+1th waypoint of the a-route, represents the j+1th waypoint of the b-route, represents the definition result of the cross product of the four-point constraint vector of the first-fourth cases, respectively.​​​ 3. The method according to claim 1, wherein, In step 3, the following steps are further included: Step 3.1: All waypoints satisfying the missile route distance constraint must be in the functional region, and the four-point constraint must also be satisfied between multiple routes. According to the analysis of the four-point constraint, the four cases of the four-point constraint are aggregated, and the result set is set as: : ； , , , denote the definition results of the four-point constraint vector cross product for the first-fourth cases, respectively. Step 3.2: Based on the geometric gradual change rule of the functional area and the four-point constraint analysis, the functional constraint set is constructed, and the spatial cooperation mechanism is formed: For any two routes and the set of vector cross product results related to the four-point constraints of the two routes the following necessary constraint conditions must be met: ； Then the waypoints in the multi-anti-ship missile cooperative path planning need to satisfy the following necessary constraint conditions: ； ； wherein, represents a waypoint within the corresponding i-function region, represents a waypoint within the corresponding i-function region, a set of vector cross product results required to be satisfied, is the corresponding function region, is a four-point cross product result formed from waypoints within the monitoring region; Route and route For example, when the cooperative route planning is performed, two routes are respectively set from the launch point and the launch point to the target point and the target point , the waypoints of the two routes are , the set of the remaining waypoints is called a function constraint set, denoted as , and represented as: ； n-function region, corresponding waypoint a set of vector cross product results to be satisfied.

4. The method according to claim 1, wherein, In step 4, the following steps are further included: Step 4.1: Selecting a reasonable population size , the number of particle single-dimension components and the maximum number of iterations of the algorithm parameters; Step 4.2: Determine whether all particles have been initialized. If yes, go to Step 4.6; otherwise, compute and the initial value of Step 4.

3. Step 4.3: In the problem model respectively, in the corresponding particle solution space range , , Randomly initialize under the constraint condition; let be , that is, the initial value of the corresponding component is ; Step 4.4: Calculate the particle components after initialization of the particles corresponding to the full-order difference between the routes and change the state variables corresponding to the particle components ; Step 4.5: Determine if all components in the particle are initialized, the state variable is 1 for the particle component has a specific value, if so, then accumulate, go to step 4.2; otherwise calculate the constraints on , accumulate, go to step 4.3;​​ Step 4.6: Calculate fitness value for each route ; Step 4.7: Update individual best solution and global best solution ; Step 4.8: Let ; Step 4.9: Determine if all particles have been updated. If so, then go to step 4.12; otherwise go to step 4.

10. and go to step 4.12; otherwise go to step 4.

10. Step 4.10: Let , ,right , and Perform an update and determine the updated version. , and Does it satisfy the pseudo-mapping to the FCS problem model to which the particle belongs? If the conditions for the solution space are not met, then let , Update again until the updated position satisfies the pseudo-mapping of the FCS problem model to which the particle belongs. Solve the conditions of the solution space; otherwise, go to step 4.

11. Step 4.11: Determine the first... Have all components in each particle been updated? If so, then... Proceed to step 4.9; otherwise, calculate. , and Constraints Proceed to step 4.10; Step 4.12: Determine if true, go to step 4.6; otherwise go to step 4.

13. Step 4.13: Output the results.

5. The method according to claim 4, wherein, In step 4.1, the population is represented as a matrix: ； wherein, is the size of the population, is the individual in the population, th individual in the population; The function constraint set is composed of several ellipses and constraint sets, and several ellipses with a common focus constitute a route. The route is expressed in polar coordinates, and the route and the route The first waypoint of the route that enters the monitoring area first is the pole, and the polar coordinate system is established with the long axis line parallel to the function area to which the pole belongs as the polar axis. It is assumed that each route contains waypoints. In order to record the position information and total order state of each waypoint, the following fixed-length real number coding particle structure is used to represent: ； wherein, , and record the polar angle , the polar radius and the full order value of each waypoint in polar coordinates, the polar coordinates and the full order state of the th waypoint of the th route can be expressed as , , ; the waypoints exist in two cases, in the detection area and not in the detection area, if the waypoint is not in the detection area, the corresponding full order value is , the state variable is used to identify whether the waypoint exists in the detection area, 1 if it exists, otherwise 0, the polar radius range of the detection area is used for judgment, the full order value in polar coordinates can be expressed as ; represents the constraint value between different particles, that is, the difference between the full order value components of adjacent particles , then if the route is composed of waypoints, the dimension of the particle is pseudo .

6. The method according to claim 5, wherein, In Step 4.3, the problem model is established according to the established problem model and the principle of non-circuity, the polar angle value , the polar radius value varies with the polar angle, which limits all the route points within the functional area in the problem model , in the established polar coordinate system, the equation can be expressed as: ； wherein, is a functional area corresponding to the inverse cooperative path planning, is a parameter, is a focal length, is an eccentricity, denotes a polar radius corresponding to the functional area, denotes an elliptic equation of the functional area O, which is expressed by equivalent variables. If there is a monitoring area in the functional area, the range of the polar radius in the monitoring area can be represented as: ； Furthermore, based on the principle of non-intersecting flight paths, the total sequence value components corresponding to different particles within the monitoring area are... The difference Must meet It limits all waypoints to the problem model. In Result set; Thus, the initialization solution space range of the parameters can be preliminarily given as: ； denotes the safety distance between the routes; is a state variable; , is the eccentricity of the functional area corresponding to the route i, j; , is the polar angle of the functional area corresponding to the route i, j; , is the quasi-focal distance of the functional area corresponding to the route i, j; a random initialization method is adopted, and the particle components are randomly initialized on the solution space, that is, each particle is initialized as a random position in the solution space, and then a random speed is initialized for each particle.

7. The method according to claim 6, wherein, In step 4.4, in the established polar coordinates, The equation expression is: ； wherein is the polar angle, so that the parfocal distance and the eccentricity : ； wherein, is the actual path length, is a constant corresponding to the course a is the waypoint position index of the course point, is a constant, is the maximum effective range, i.e. the long axis of the first functional area; is the step size of the scan line, is the number of courses; For waypoints then the following must be satisfied: ； Then the problem model In The total order value corresponding to the result set The generated total order difference value The equation expression can be represented as: ； wherein, is the course and course corresponding to the first waypoint in polar coordinates, the equation expression can be represented as: ； For a route and a route corresponding to the waypoint then it is necessary to satisfy again: ； Then the problem model The solution space in which the particle resides is mapped to the pseudo Should have: ； the particle component corresponding to leg a and b with index j, the polar particle component corresponding to leg a with index j-n, the polar angle of the waypoint with index constant for leg a, the polar particle component corresponding to leg b with index j-n, the polar angle of the waypoint with index constant for leg b.

8. The method according to claim 7, wherein, In step 4.6, the fuzzy satisfaction degree function of the objective function is constructed, the reasonable weight is determined according to the actual demand, and the performance index is constructed by the multi-attribute fuzzy optimization method, which can be expressed as: ； wherein, , and respectively represent the satisfaction degree of the actual distance of the route , the mean square deviation of the absolute value of the number of waypoints of each route , and the mean square deviation of the absolute value of the full order difference of each waypoint ; , and are the corresponding weight coefficients, and satisfy ; determining a fitness function for individuals in a population descending order according to the following function: ； wherein, represents a fitness function, is the individual a flag whether the individual intersects with an obstacle, is , else, ; is the individual a flag whether the individual intersects with another individual, is , else, .

9. The method according to claim 8, wherein, In step 4.7, the standard The basic principle of the algorithm is that: A by A population of particles in pseudo Flying at a certain speed in the dimensional search space, the first The position of each particle is The corresponding speed is , can be represented as: ； The best position it has ever been in may be represented as: ； The best position passed by all particles in the population is: ； denotes the update velocity of the corresponding subscript particle component, denotes the local optimum solution of the corresponding subscript particle component, denotes the global optimum solution of the corresponding subscript particle component; After obtaining the two optimal values, the speed and position of the individual are updated by the formula, which can be expressed as: ； ； wherein, called inertia factor, whose value is non-negative; and is a learning factor; and is a random number between ; is the current position of the particle, is the current local optimum solution of the particle, is the current update speed of the particle, is the current global optimum solution of the particle.

10. The method according to claim 9, wherein, Step 4.

10. In the case where the next generation of the particle's corresponding component does not satisfy the problem model , the component of the next generation of the particle is called a corresponding false component when it is mapped to the solution space pseudo where the particle is located. For particles that do not satisfy, their velocity and direction are dynamically adjusted to bring them closer to the constraint The particles are updated in a stepwise manner in a reasonable direction, with adjustments to the corresponding pseudo-components causing the particle components and particles to also satisfy the constraints: updating the particle's pseudo-components and updating step by step to meet the problem model mapping to the new position of the particle in the solution space where the new position of the pseudo-radial component is in the new position that meets the golden section, however for the pseudo-total order difference component the new position of the update position also needs to meet the golden section under the condition of meeting the safety distance, which promotes the golden section and the safety distance between the particles, and the expression of the golden section can be expressed as: ；； For Considerations can be set out from two aspects: first, the polar radius false component Update to a reasonable azimuth, thereby driving the update of the false polar angle component; In summary, The speed update formula of the algorithm can be expressed as: ； wherein, is a learning factor; is a random number between , is a state variable; is a processing item;​ When the particle does not satisfy the constraint condition, , When the particle satisfies the constraint condition, , ; when the particle does not satisfy the constraint condition, the processing item of the particle is added to the original update speed, and when the particle satisfies the constraint condition, the original update formula is followed.

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