A method for deploying underwater detection nodes in a designated area based on genetic algorithms

Abstract

This invention discloses an adaptive and rapid deployment method for underwater detection nodes based on a genetic algorithm, belonging to the field of sensor network node deployment technology. The method includes collecting and preparing relevant data on the detection area and underwater nodes; preprocessing the water depth data of the detection area, performing coordinate transformation and convolution operations; designing a fitness function and constraints, and constructing a resource allocation model; and using an improved genetic algorithm to determine a node deployment method based on maximizing the fitness function. This invention employs the aforementioned adaptive and rapid deployment method for underwater detection nodes based on a genetic algorithm, which features fast decision-making speed, short optimization iteration time, and strong search capability, and can adapt to situations where the detection area has complex shapes and numerous, oddly shaped obstacles.

Description

Technical Field

[0001] This invention relates to the field of sensor node deployment technology, and in particular to a method for deploying underwater detection nodes in a designated area based on a genetic algorithm. Background Technology

[0002] Underwater detection node networks have broad application prospects in fields such as marine exploration, disaster early warning, and submarine detection. During the deployment of underwater detection nodes, it is necessary to transform the underwater sensor network into a two-dimensional network topology to improve the effective coverage of underwater nodes on the bottom or in shallow waters and near the shore of oceans, rivers, and lakes, thereby ensuring good detection performance of the network nodes. However, due to the complex shape of the detection area and the presence of numerous and oddly shaped obstacles, these constraints make it difficult to find the optimal solution using traditional underwater deployment methods. Furthermore, the complex underwater topography and sudden changes in water depth pose a severe challenge to the deployment of underwater nodes. Therefore, researching underwater detection node deployment methods with adaptability to complex terrain is crucial for improving the detection and coverage effects of detection networks.

[0003] On the other hand, due to the large number of detection nodes that need to be deployed during regional detection, traditional geometrically based optimization deployment methods suffer from computational complexity and long solution times. However, in scenarios with high real-time requirements and urgent tasks, such as submarine detection, rapid decision-making on the deployment method of underwater detection nodes is often necessary, making traditional underwater detection node deployment methods unsuitable. Currently, methods for rapid adaptive deployment of underwater detection nodes are still relatively rare. Therefore, researching an optimization deployment method with fast decision-making speed, short optimization iteration time, and strong search capabilities is of significant research importance for solving the coverage deployment problem of underwater detection node networks. Summary of the Invention

[0004] The purpose of this invention is to provide a method for deploying underwater detection nodes in a designated area based on a genetic algorithm, which improves the coverage of the node network in complex terrain and marine environments.

[0005] To achieve the above objectives, this invention provides a method for deploying underwater detection nodes in a designated area based on a genetic algorithm, comprising the following steps:

[0006] S1. Collect and prepare relevant data on the detection area and underwater nodes, including the water depth threshold D for node placement. p The number of underwater detection nodes to be assigned, n; the detection radius of each node, r; and the set of boundary coordinates of obstacles within the sea area, C. o The set of latitude and longitude coordinates of the specified detection area boundary, C;

[0007] S2. Preprocess the water depth data of the detection area, and perform coordinate transformation and convolution operations;

[0008] S3. Design the fitness function and constraints, and construct the resource allocation model;

[0009] S4. Using an improved genetic algorithm, determine a node deployment method based on maximizing the fitness function.

[0010] Preferably, in step S1, the set of boundary coordinates of obstacles within the sea area This indicates that there are a total of k obstacles.

[0011] Among them, obstacles This indicates that each obstacle is surrounded by its own distinct vertices;

[0012] The specified set of latitude and longitude coordinates of the detection area boundary

[0013] in, This represents the i-th boundary point of the detection area. Represents longitude coordinates. This represents the latitude coordinates, and l represents the total number of boundary points in the detection area.

[0014] Preferably, the specific steps of S2 are as follows:

[0015] S21. Find the following in set C: λ min , λ max This forms a rectangular region Q, where, Let represent the minimum latitude of all coordinate points in set C. λ represents the maximum latitude of all coordinate points in set C. min Let λ represent the minimum longitude of all coordinate points in set C. max Let q represent the maximum longitude of all coordinate points in set C, and let q represent the maximum longitude of all coordinate points in set Q. (qlon，qlat) The following formulas all hold true:

[0016]

[0017] S22. Use the semi-versus formula to determine the length w and width h of the rectangular region Q;

[0018] S23. Establish a rectangular coordinate system and map the boundary points;

[0019] S24. Rasterize the rectangular region Q, dividing it into h rows and w columns of grid with a step size of one kilometer. Simultaneously, map the rasterized region into a matrix A' with h rows and w columns, where the elements A' in A' are... (i,j) The value is the average depth of the area covered by the grid cell in the i-th row and j-th column;

[0020] S25. Process matrix A' by inverting all elements of matrix A' to obtain matrix A, which is A'. (i,j) =-A' (i,j) Given that 1 ≤ i ≤ h, 1 ≤ j ≤ w, design the convolution kernel matrix K based on the node detection radius r. (2r+1)×(2r+1) The matrix A to be convolved is convolved with the convolution kernel K by performing an equal-size convolution operation to obtain the target matrix B with the same dimension as matrix A.

[0021] Preferably, the formula for the length w of the rectangular region Q in step S22 is as follows:

[0022]

[0023] The formula for the width h of the rectangular region Q is as follows:

[0024]

[0025] Where R is the average radius of the Earth, and [·] represents the rounding operation.

[0026] Preferably, the specific steps of S23 are as follows:

[0027] S231. Establish a rectangular coordinate system, with the lower left corner of the rectangular region Q as the origin, and establish a rectangular coordinate system O with a step size of one kilometer. xy The horizontal axis represents longitude, and the vertical axis represents latitude. The horizontal axis ranges from [0, w], and the vertical axis ranges from [0, h].

[0028] S232. Map boundary points, mapping the latitude and longitude coordinates of all boundary points to O. xy In the coordinate system, the centroid of the detection area is calculated. The boundary points of the detection area are sorted according to the angle from each boundary point to the centroid. All coordinates within the detection area are extracted using the scanline method. The coordinates of each obstacle are calculated, and overlapping parts are removed, forming a set of deployable coordinates E, defined as... Where m is the total number of coordinates that can be arranged. Let i be the latitude of the i-th available coordinate. Let be the longitude of the i-th available coordinate.

[0029] Preferably, the convolution kernel matrix K (i,j) The value is:

[0030]

[0031] Preferably, the specific steps of S3 are as follows:

[0032] S31. Define the set of coordinates to be deployed. The set of coordinates to be deployed for underwater nodes within the region is as follows: in, Represents the coordinates of the i-th node;

[0033] S32. Design the fitness function. The designed fitness function is shown below:

[0034] f(n) = max(f1(n) - f2(n));

[0035] Where f1(n) is the sum of water depths within the detection range of all nodes; f2(n) is the penalty function for overlapping detection ranges of nodes;

[0036] S33. Set constraints, set the constraints as water depth constraints, ensure that all nodes are placed below the required water depth, and use the penalty function method for constraint;

[0037] S34. Establish an underwater node resource allocation model based on the designed fitness function and constraints.

[0038] Preferably, the specific formula for f1(n) in S32 is as follows:

[0039]

[0040] The specific formula for f2(n) is shown below:

[0041]

[0042] Where r is the node detection radius, D i Let i represent the i-th element in set D, where set D = {d} ij |d ij <2r},1≤i <n,i<j≤b,d ij Let be the Euclidean distance between any two nodes i and j, denoted as

[0043] Preferably, the specific steps of S4 are as follows:

[0044] S41. Initialize the population using integer encoding. The chromosome length is n, where the i-th gene position represents the i-th node, and its gene value x ranges from [1, m]. This represents E. x The coordinates in the set are given, and m is the number of elements in set E; initialize a population with N chromosomes according to the encoding rules;

[0045] S42. Perform population iteration, set the termination condition for the iteration, and when the stopping condition is met, the algorithm ends and returns the best individual found.

[0046] S43. Conduct fitness assessment, calculate the fitness value of each individual according to the designed fitness function, perform statistical analysis on the current population, and record its best individual and average fitness.

[0047] S44. Perform crossover operation. Using the crossover operator, randomly generate two random numbers smaller than the chromosome length, independently select two mothers from the population, and swap the genes between the gene loci corresponding to the random numbers.

[0048] S45. Perform mutation operation. Use mutation operator to randomly select an individual from a chromosome population and copy it as Cr. Perform high-probability mutation on Cr to obtain the mutated individual Cr1. Perform two-point crossover on Cr and Cr1 to obtain new individuals Cr2 and Cr3. Finally, compare Cr, Cr1, Cr2 and Cr3 and select the individual with the highest applicability to replace the original individual.

[0049] S46. Perform selection operation. Using the selection operator, merge the parent population with the population that has completed crossover and mutation operations to obtain a population of size 2N. Select N chromosomes from this population as the new population according to the tournament selection method. If the new population contains the globally optimal chromosome, return to S42. Otherwise, replace the chromosome with the worst fitness in the new population with the globally optimal chromosome, and return to S42.

[0050] Preferably, the iteration conditions set in S42 are as follows:

[0051] The population iteration count reaches a set value: G = N G Where G is the number of iterations, N G This represents the maximum number of iterations.

[0052] Evolutionary stagnation occurs when, starting from generation i, the range of variation of the globally optimal individual in the population over h consecutive iterations is less than a set threshold, specifically expressed as:

[0053] |f * (i+h)-f * (i)|≤V,i∈[1,N G -h],h∈[1,N G ];

[0054] Among them, f * (n) is the global optimal individual fitness function value in the nth iteration, V is the threshold for judging whether the evolution has stalled, and h is the upper limit of the evolution stall counter.

[0055] Therefore, the present invention employs the above-mentioned method for deploying underwater detection nodes in a designated area based on a genetic algorithm, which has the following beneficial effects:

[0056] (1) The present invention has a fast deployment decision speed and a significant improvement in the time to determine the deployment location of nodes. Simulation verification shows that the deployment time can be completed within 2 seconds.

[0057] (2) The genetic algorithm used in this invention has high robustness, high adaptability to detection space, obstacles and various constraints, and can be implemented in parallel. It can search for excellent solutions faster in a multi-processor or distributed environment.

[0058] (3) The present invention uses an optimized fitness function design, with the average depth within the detection range as part of the fitness function, which eliminates the influence of poor detection effect caused by excessive changes in terrain depth. Furthermore, it uses convolution operation for preprocessing, which can save the preprocessed map data locally, reducing the program optimization iteration time.

[0059] (4) This invention innovatively uses breeding mutation operators to replace traditional mutation operators, which enhances local search capabilities without changing global search capabilities.

[0060] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0061] Figure 1 This is a flowchart of a method for deploying underwater detection nodes in a designated area based on a genetic algorithm, according to the present invention.

[0062] Figure 2 This is a population iteration curve diagram of a method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to the present invention.

[0063] Figure 3 This is a coordinate diagram of the underwater node layout for a method of deploying underwater detection nodes in a designated area based on a genetic algorithm, according to the present invention. Detailed Implementation

[0064] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0065] Example

[0066] like Figure 1 As shown, this invention provides a method for deploying underwater detection nodes in a designated area based on a genetic algorithm, comprising the following steps:

[0067] S1. Collect and prepare relevant data on the detection area and underwater nodes, including the water depth threshold D for node placement. p The number of underwater detection nodes to be assigned, n; the detection radius of each node, r; and the set of boundary coordinates of obstacles within the sea area, C. o , the set of latitude and longitude coordinates of the specified detection area boundary C.

[0068] Set of boundary coordinates of obstacles within the sea area

[0069] Among the obstacles This indicates that each obstacle is surrounded by its own distinct vertices, and k represents the number of obstacles;

[0070] The specified set of latitude and longitude coordinates of the detection area boundary

[0071] in This represents the i-th boundary point of the detection area. Represents longitude coordinates. This represents the latitude coordinates, and l represents the total number of boundary points in the detection area.

[0072] In this embodiment, the depth threshold D of node arrangement p =2000, the number of underwater detection nodes to be assigned is n=20, and the node detection radius is r=15.

[0073] Set of latitude and longitude coordinates of obstacle boundary in

[0074] The set of boundary coordinates of the detection area is C = {(120.03°, 21.6°), (120.87°, 21.2°), (121.65°, 21.2°), (121.65°, 19.94°), (121.36°, 20.3°), (120.37°, 19.49°), (119.66°, 19.89°), (119.66°, 20.31°)}.

[0075] S2. Preprocess the water depth data of the detection area, and perform coordinate transformation and convolution operations.

[0076] S21. Find the following in set C: λ min , λ max This forms a rectangular region Q, where, Let represent the minimum latitude of all coordinate points in set C. λ represents the maximum latitude of all coordinate points in set C. min Let λ represent the minimum longitude of all coordinate points in set C. max Let q represent the maximum longitude of all coordinate points in set C, and let q represent the maximum longitude of all coordinate points in set Q. (qlon，qlat) The following formulas all hold true:

[0077]

[0078] In this embodiment, the detection area with a minimum longitude of 119.66°, a minimum latitude of 19.49°, a maximum longitude of 121.65°, and a maximum latitude of 21.6° is found in set C, forming a rectangular area Q with a longitude from 119.66° to 121.65° and a latitude from 19.49° to 21.6°.

[0079] S22. Use the semi-versus formula to determine the length w and width h of the rectangular region Q;

[0080] The formula for the length w of the rectangular region Q is as follows:

[0081]

[0082] The formula for the width h of the rectangular region Q is as follows:

[0083]

[0084] Where R is the average radius of the Earth, R = 6371.4 km, and [·] represents the rounding operation.

[0085] In this embodiment,

[0086]

[0087] S23. Establish a rectangular coordinate system and map the boundary points.

[0088] S231. Establish a rectangular coordinate system, with the lower left corner of the rectangular region Q as the origin, and establish a rectangular coordinate system O with a step size of one kilometer. xy The horizontal axis represents longitude and the vertical axis represents latitude. The horizontal axis ranges from [0, w] and the vertical axis ranges from [0, h]. In this embodiment, the longitude coordinate range is [0, 209] and the latitude coordinate range is [0, 235].

[0089] S232. Map boundary points: Map the latitude and longitude of all boundary points of the probe area to O. xy In this embodiment, the coordinates are {(39,235), (126,191), (207,191), (209,51), (178,91), (75,0), (0,45), (0,92)}. All obstacle vertex coordinates are mapped to O. xy Below, their coordinates are {(41,38), (49,24), (65,24), (73,38), (65,53), (49,53)}.

[0090] At the same time in O xy In the coordinate system, the centroid of the detection area is calculated as follows: Next, the boundary points of the detection area are sorted according to the angle from each boundary point to the centroid. Then, a scan line algorithm is used to scan horizontally line by line, calculating the intersection points of the scan line and the polygon. Then, all coordinates within the detection area are extracted based on the parity of the intersection points. Similarly, all coordinates within each obstacle are calculated. The parts where all coordinates within the detection area coincide with all coordinates within each obstacle are removed, thus forming the set of all deployable coordinates within the detection area E = {(75,0), (76,0), ..., (41,234)}, totaling 33018 deployable points.

[0091] S24. Rasterize the rectangular region Q, dividing it into h rows and w columns of grid with a step size of one kilometer. Simultaneously, map the rasterized region into a matrix A' with h rows and w columns, where the elements A' in A' are... (i,j) The value is the average depth of the area covered by the grid in the i-th row and j-th column. In this embodiment, the grid is 235 rows and 209 columns.

[0092] S25. Process matrix A' by inverting all elements in matrix A' to obtain matrix A, which means turning the underwater depth data into positive numbers and the surface values ​​into negative numbers.

[0093] A (i,j) =-A' (i,j) , 1≤i≤235, 1≤j≤209;

[0094] Design the convolution kernel matrix K based on the node detection radius r. (2r+1)×(2r+1) In this embodiment, the node detection radius r is 15 kilometers, then the convolution kernel matrix K 31×31 , where K (i,j) The value is:

[0095]

[0096] Perform an equal-size convolution operation between the matrix A to be convolved and the convolution kernel K to obtain the target matrix B with the same dimension as matrix A.

[0097] S3. Design the fitness function and constraints to construct a resource allocation model.

[0098] S31. Define the set of coordinates to be deployed. The set of coordinates to be deployed for underwater nodes within the region is as follows: in, This represents the coordinates of the i-th node.

[0099] S32. Design the fitness function. The designed fitness function is shown below:

[0100] f(n) = max(f1(n) - f2(n));

[0101] Where f1(n) is the sum of water depths within the detection range of all nodes; f2(n) is the penalty function for overlapping detection ranges of nodes.

[0102] The specific formula for f1(n) is as follows:

[0103]

[0104] The specific formula for f2(n) is shown below:

[0105] f2(n)=∑ i＝1 r 4.5 / (D i +1), D i ∈D;

[0106] Where r is the node detection radius, D i Let i represent the i-th element in set D, where set D = {d} ij |d ij <2r},1≤i <n,i<j≤n,d ij Let be the Euclidean distance between any two nodes i and j, denoted as

[0107] S33. Set constraints, set the constraints to water depth constraints, ensure that all nodes are placed below the required water depth, and use the penalty function method for constraint.

[0108] S34. Establish an underwater node resource allocation model based on the designed fitness function and constraints.

[0109] S4. Using an improved genetic algorithm, determine a node deployment method based on maximizing the fitness function.

[0110] S41. Initialize the population using integer encoding. The chromosome length is n, where the i-th gene position represents the i-th node, and its gene value x ranges from [1, m]. This represents E. x The coordinates in the set are m, and m is the number of elements in the set E. The population with N chromosomes is initialized according to the encoding rules. In this embodiment, the gene value x ranges from [1, 33018] and the number of chromosomes is 50.

[0111] S42. Perform population iteration, set the termination condition for the iteration, and when the stopping condition is met, the algorithm ends and returns the best individual found.

[0112] The specific iteration conditions are set as follows:

[0113] (1) The number of population iterations reaches a set value: G = N G Where G is the number of iterations, N GThe maximum number of iterations is set to 200 in this embodiment, i.e., G = 200.

[0114] (2) Evolution stagnates, meaning that starting from generation i, the range of variation of the globally optimal individual in the population after h consecutive iterations is less than a set threshold, specifically expressed as:

[0115] |f * (i+h)-f * (i)|≤V,i∈[1,N G -h],h∈[1,N G ];

[0116] Among them, f * (n) is the global optimal individual fitness function value in the nth iteration, V is the threshold for judging whether the evolution has stalled, and h is the upper limit of the evolution stall counter.

[0117] In this embodiment, |f * (i+2)-f * (i)|≤10 -6 , i∈[1,198].

[0118] S43. Conduct fitness assessment, calculate the fitness value of each individual according to the designed fitness function, perform statistical analysis on the current population, and record its best individual and average fitness.

[0119] S44. Perform crossover operation. Use the crossover operator to randomly generate two random numbers smaller than the chromosome length. In this embodiment, the chromosome length is 20. Select two mothers independently from the population and swap the genes between the gene positions corresponding to the random numbers. Set the probability of each individual being selected for crossover operation to 0.7.

[0120] S45. Perform mutation operation. Use mutation operator to randomly select an individual from a chromosome population and copy it as Cr. Perform mutation with a probability of 0.1 on each gene locus on Cr to obtain the mutated individual Cr1. Perform two-point crossover on Cr and Cr1 to obtain new individuals Cr2 and Cr3. Finally, compare Cr, Cr1, Cr2 and Cr3 and select the individual with the highest applicability to replace the original individual.

[0121] S46. Perform a selection operation. Using the selection operator, merge the parent population with the population that has completed crossover and mutation operations to obtain a population of size 2N. Select N chromosomes from this population as the new population according to the tournament selection method. If the new population contains the globally optimal chromosome, return to S42; otherwise, replace the chromosome with the worst fitness in the new population with the globally optimal chromosome, and return to S42.

[0122] In this embodiment, the population size is 100 and the number of chromosomes is 50.

[0123] The simulation environment was PyCharm 2024.2.1, Python 3.10, R5 5600H 3.30GHz processor, 16.0GB of memory, and the runtime was 1.81s.

[0124] The simulation layout results are shown in Table 1:

[0125] Table 1 Allocation Results

[0126] (13,82) (15,52) (162,64) (68,84) (148,29) (70,18) (40,96) (44,65) (66,115) (96,114) (71,49) (158,171) (111,192) (103,11) (16,116) (116,52) (81,191) (134,79) (41,32) (104,83)

[0127] Table 2 Population Iteration Log

[0128]

[0129] Population iteration curve as shown Figure 2 As shown, the horizontal axis represents the number of iterations, the vertical axis represents the fitness function value, the yellow line is the iteration curve of the globally optimal individual, and the blue line is the iteration curve of the population average fitness value.

[0130] The simulation layout coordinates are obtained as follows: Figure 3 As shown, the red part represents the coordinates that satisfy the constraints, and the white part represents the coordinates that do not satisfy the constraints. The white hexagonal area represents the obstacle.

[0131] Therefore, the present invention employs the above-mentioned method for deploying underwater detection nodes in a designated area based on a genetic algorithm, which can solve the problem of rapid deployment of multi-constrained underwater nodes in a two-dimensional topology.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for deploying underwater detection nodes in a designated area based on a genetic algorithm, characterized in that, Includes the following steps: S1. Collect and prepare relevant data on the detection area and underwater nodes, including the water depth thresholds for node placement. Number of underwater detection nodes to be allocated Node detection radius Set of boundary coordinates of obstacles within the sea area The set of latitude and longitude coordinates of the specified detection area boundary ; S2. Preprocess the water depth data of the detection area, and perform coordinate transformation and convolution operations; S3. Design the fitness function and constraints, and construct the resource allocation model, specifically including: S31. Define the set of coordinates to be deployed. The set of coordinates to be deployed for underwater nodes within the region is as follows: ， Represents the coordinates of the i-th node; S32. Design the fitness function. The designed fitness function is as follows: ； in, The sum of water depths within the detection range of all nodes; The penalty function for overlapping detection ranges of nodes; S33. Set constraints, set the constraints as water depth constraints, ensure that all nodes are placed below the required water depth, and use the penalty function method for constraint; S34. Establish an underwater node resource allocation model based on the designed fitness function and constraints; S4. Using an improved genetic algorithm, determine a node deployment method based on maximizing the fitness function.

2. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 1, characterized in that: In step S1, the set of boundary coordinates of obstacles within the sea area , indicating shared ownership An obstacle, Among them, obstacles This indicates that each obstacle is surrounded by its own distinct vertices; The specified set of latitude and longitude coordinates of the detection area boundary , in, This represents the i-th boundary point of the detection area. Represents longitude coordinates. Represents latitude coordinates, This represents the total number of boundary points in the detection area.

3. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 1, characterized in that, The specific steps of S2 are as follows: S21. Find the following in set C: , , , Forming a rectangular area ,in, Let represent the minimum latitude of all coordinate points in set C. This represents the maximum latitude of all coordinate points in set C. Let represent the minimum longitude of all coordinate points in set C. Represents the maximum longitude of all coordinate points in set C, for All coordinate points in The following formulas all hold true: ； S22. Use the semi-versus formula to determine a rectangular region. The length w and width h; S23. Establish a rectangular coordinate system and map the boundary points; S24, Rasterized rectangular area Divide the area into steps of one kilometer. Divide into equal parts OK The raster of columns, while mapping the rasterized areas to behaviors. Listed as matrix ,in elements in The value is the average depth of the area covered by the grid cell in the i-th row and j-th column; S25, Processing Matrix , matrix Inverting all elements in the matrix yields the matrix. ,for , Based on the node detection radius Design convolution kernel matrix The matrix to be convolved With convolution kernel Perform equal-size convolution to obtain a target matrix with the same dimensions as matrix A. .

4. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 3, characterized in that, The formula for the length w of the rectangular region Q in step S22 is as follows: ； rectangular area The formula for the width h is as follows: ； in, The average radius of the Earth This indicates the integer division operation.

5. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 3, characterized in that, The specific steps of S23 are as follows: S231. Establish a rectangular coordinate system, with a rectangular region as the reference. The origin is set at the lower left corner, and a rectangular coordinate system is established with each kilometer as the step size. The horizontal axis represents longitude, and the vertical axis represents latitude. The range of values ​​for the horizontal axis is... The range of values ​​for the vertical axis is: ; S232. Map boundary points, mapping the latitude and longitude coordinates of all boundary points to... In the coordinate system, the centroid of the detection area is calculated. The boundary points of the detection area are sorted according to the angle from each boundary point to the centroid. All coordinates within the detection area are extracted using the scan line method. The coordinates of each obstacle are calculated, and overlapping parts are removed to form a set of deployable coordinates. Defined as Where m is the total number of coordinates that can be arranged. For the first A latitude that can be used to arrange coordinates. For the first A longitude that can be used to arrange coordinates.

6. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 3, characterized in that, convolution kernel matrix The value is: 。 7. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 1, characterized in that, S32 The specific formula is as follows: ； The specific formula is as follows: ； in, The detection radius of the node. Represents a set The i-th element in the set , For any two nodes and The Euclidean distance between them is expressed as .

8. The method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 1, characterized in that, The specific steps for S4 are as follows: S41. Initialize the population using integer encoding. The chromosome length is n, where the i-th gene position represents the i-th node and its gene value. The value range of is [1, m], indicating that represents The coordinates in the set E are m, where m is the number of elements in set E. Initialize a population with N chromosomes according to the encoding rules; S42. Perform population iteration, set the termination condition for the iteration, and when the stopping condition is met, the algorithm ends and returns the best individual found. S43. Conduct fitness assessment, calculate the fitness value of each individual according to the designed fitness function, perform statistical analysis on the current population, and record its best individual and average fitness. S44. Perform crossover operation. Using the crossover operator, randomly generate two random numbers smaller than the chromosome length, independently select two mothers from the population, and swap the genes between the gene loci corresponding to the random numbers. S45. Perform mutation operations using the mutation operator. Randomly select an individual from a chromosome population and replicate it. ,right Perform high-probability mutations to obtain mutated individuals. In the and By performing a two-point intersection, a new individual is obtained. and Finally, for , , and Compare the individuals and select the one with the highest applicability to replace the original one; S46. Perform selection operation. Using the selection operator, merge the parent population with the population that has completed crossover and mutation operations to obtain a population of size 2N. Select N chromosomes from this population as the new population according to the tournament selection method. If the new population contains the globally optimal chromosome, return to S42. Otherwise, replace the chromosome with the worst fitness in the new population with the globally optimal chromosome, and return to S42.

9. A method for deploying underwater detection nodes in a designated area based on a genetic algorithm according to claim 8, characterized in that, The specific iteration conditions set by S42 are as follows: The population iteration count has reached the set value: Where G is the number of iterations, This represents the maximum number of iterations. Evolutionary stagnation occurs when, starting from generation i, the range of variation of the globally optimal individual in the population over h consecutive iterations is less than a set threshold, specifically expressed as: ； in, For the first The globally optimal individual fitness function value in the next iteration. The threshold for determining whether evolution has stagnated. This is the upper limit of the evolution stagnation counter.

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