Heterogeneous directional sensor network deployment method and system, computer storage medium and program

Abstract

The invention discloses a heterogeneous directional sensor network deployment method which comprises the following steps: an initialization stage: firstly, randomly initializing each element of each individual in a population, enabling the length of an individual code to be the number of target points, enabling each element to be in one-to-one correspondence with each target point, and enabling each element to be in one-to-one correspondence with each target point; each element represents which deployment position the corresponding target point is covered by the directional sensor, calculating the fitness of each individual, the corresponding network deployment and the population evolution stage, calculating variation and cross individuals for the current individual and calculating the fitness and the network deployment of the cross individuals in each iteration, replacing the target point if the target point is smaller than the current individual, and calculating the population evolution stage if the target point is smaller than the current individual. The variation individual is obtained by weighted summation of other three individuals, and the crossing individual is obtained by replacing the current individual element with the variation individual element. And an output stage: after iteration is finished, selecting the network deployment of the individual with the minimum fitness as the final deployment. The invention further discloses a system, a computer storage medium and a program for implementing the method. The probability of searching the feasible solution can be improved, and the network deployment cost can be reduced.

Description

Technical Field

[0001] The present invention relates to a heterogeneous directional sensor network deployment method, system, computer storage medium and program, belonging to the technical field of network planning. Background Art

[0002] The deployment of a heterogeneous directional sensor network for target coverage not only requires selecting the deployment locations and working directions of directional sensors, but also requires selecting the types of directional sensors, which is a relatively complex NP-hard problem and it is impossible to obtain an optimal solution within polynomial time. Therefore, heuristic algorithms need to be designed to obtain high-quality approximate solutions.

[0003] The prior art uses a microbial genetic algorithm to solve the minimum-cost deployment problem of a heterogeneous directional sensor network, and uses a 0-1 vector to represent chromosomes. Since there are a large number of candidate deployment tuples, the chromosome encoding is very long, making the scalability of this method relatively low. Moreover, this encoding is prone to improper use of deployment tuples, redundancy of deployment tuples, and missing of deployment tuples, resulting in low solution quality.

[0004] There is also a method that uses a variable-length genetic algorithm for solving, and uses a subset of candidate deployment tuple identification numbers to encode the deployment of directional sensors. However, the results of the crossover operation and the mutation operation cannot guarantee that there can be at most one deployment tuple at the same deployment location. That is to say, there will be multiple deployment tuples at the same deployment location, which violates the constraint condition that at most one directional sensor can be deployed at each deployment location. Both the initialization result and the results of its crossover operation and mutation operation will have problems such as redundancy of deployment tuples and improper use of deployment tuples, thus resulting in a relatively high network deployment cost and also low solution quality. Summary of the Invention

[0005] Aiming at the defects of the above prior art, the present invention provides a heterogeneous directional sensor network deployment method to solve the problems of redundancy and improper use of deployment tuples and reduce the network deployment cost. The present invention also provides a heterogeneous directional sensor network deployment system, computer storage medium and program for implementing this method.

[0006] The technical solution of the present invention is a heterogeneous directional sensor network deployment method, including the following steps: In the initialization phase, first randomly initialize each element of each individual in the population. The length of the individual encoding is the number of target points, and each element corresponds to each target point one by one. Each element represents which directional sensor at which deployment location covers the corresponding target point, and calculate the fitness of each individual and the corresponding network deployment. The fitness is where ndc represents the network deployment cost, w represents the weighting coefficient, tpc represents the total number of target points,nct represents the number of target points that can be covered. The network deployment includes the positions, types, and working directions of all deployed directional sensors, and the network deployment cost is the total price of all deployed directional sensors; Population evolution stage. In each iteration, for each individual, calculate the mutant individual and the crossover individual, calculate the fitness of the crossover individual and the corresponding network deployment, and replace the current individual with the crossover individual when the fitness of the crossover individual is less than that of the current individual. The mutant individual is obtained by weighted summation of three other individuals except the current individual, and the crossover individual is obtained by selectively replacing the elements of the current individual with the elements of the mutant individual; Output stage. After the population evolution iteration ends, use the network deployment corresponding to the individual with the minimum fitness as the final network deployment.

[0007] Further, the calculation of the mutant individual is specifically as follows: randomly select three different individuals in the population, all of which are different from the current individual, weight the difference between two of them with an amplification factor and sum it with the third individual to obtain a mutant individual. The mutant individual constructs a new individual using the linear representation of the individual, so as to make full use of the association between each solution and help search for a better feasible solution.

[0008] Further, the calculation of the crossover individual is specifically as follows: the crossover individual is initialized according to the current individual, and a dimension of the crossover individual is randomly selected j and its value is modified to the value of the dimension of the mutant individual j . For each other dimension of the crossover individual k , its value is modified to the value of the dimension of the mutant individual with a set crossover probability k . The crossover individual not only retains some excellent characteristics of the current individual but also introduces new characteristics of the mutant individual, which helps to balance global search and local search.

[0009] Further, calculating the fitness of the individual and the corresponding network deployment is to iteratively calculate the network deployment until the network deployment cannot be optimized. Each iteration of calculating the network deployment includes: Calculate the set of target points covered by each deployment position according to the individual values i ; T i ; Calculate the type and working direction of each deployment position i so that the maximum number of target points in T i can be covered and the price is minimized. If T i is empty, no sensor is deployed at the position i ; For each target point, each deployed sensor is traversed in sequence to find the sensor that can cover the target point and has the minimum price. If found, the value of the dimension corresponding to the target point in the individual is modified to the index of the deployment position of the sensor in the set of deployment positions that can cover the target point.

[0010] Another technical solution of the present invention is: a heterogeneous directional sensor network deployment system, including: An initialization module, used to randomly initialize each element of each individual in the population. The length of the individual encoding is the number of target points, and each element corresponds to each target point one by one. Each element represents which directional sensor at which deployment position covers the corresponding target point, and calculates the fitness of each individual and the corresponding network deployment. , where ndc represents the network deployment cost, w represents the weighting coefficient, tpc represents the total number of target points, nct represents the number of target points that can be covered. The network deployment includes the positions, types, and working directions of all deployed directional sensors. The network deployment cost is the total price of all deployed directional sensors; A population evolution module, used in each iteration, for each individual, calculates the mutated individual and the crossed individual, calculates the fitness of the crossed individual and the corresponding network deployment, and replaces the current individual with the crossed individual when the fitness of the crossed individual is less than that of the current individual. The mutated individual is obtained by weighted summation of three other individuals except the current individual, and the crossed individual is obtained by randomly selecting and replacing the elements of the current individual with the elements of the mutated individual; An output module, used after the population evolution iteration ends, to use the network deployment corresponding to the individual with the minimum fitness as the final network deployment.

[0011] Further, the population evolution module includes a mutated individual calculation module, and the mutated individual calculation module is used to randomly select three different individuals in the population, all of which are different from the current individual, and sum the difference between two of them weighted by the amplification factor and the third individual to obtain a mutated individual.

[0012] Further, the population evolution module includes a crossed individual calculation module, and the crossed individual calculation module is used to initialize the crossed individual according to the current individual, randomly select a dimension of the crossed individual j , and modify its value to the value of the dimension of the mutated individual j . For each other dimension of the crossed individual k , modify its value to the value of the dimension of the mutated individual k with a set crossover probability.

[0013] Further, it includes a fitness and network deployment calculation module, which is used to iteratively calculate the network deployment until the network deployment cannot be optimized. Each iterative calculation of the network deployment includes: Calculating each deployment location according to the individual values i The set of target points covered T i ; Calculating the type and working direction of each deployment location i so as to be able to cover T i the most target points in and with the minimum price. If T i is empty, no sensor is deployed at the location i ; For each target point, sequentially traverse each deployed sensor to find the sensor that can cover the target point and has the minimum price. If found, modify the value of the dimension corresponding to the target point in the individual to the index of the deployment location of the sensor in the set of deployment locations that can cover the target point.

[0014] Another technical solution of the present invention is: a computer storage medium, on which a computer program is stored. When the computer program is executed by a processor, the foregoing heterogeneous directional sensor network deployment method is implemented.

[0015] Another technical solution of the present invention is: a computer program, which when executed by a processor, implements the foregoing heterogeneous directional sensor network deployment method.

[0016] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows: The present invention adopts a more efficient and concise individual coding, improves scalability, and designs a network deployment calculation method based on this individual coding. It can not only reasonably use deployment tuples to ensure that there is at most one deployment tuple at the same deployment location, solve the problem of violating deployment constraints in VLGA, but also can perform local optimization on individuals. Mutated individuals help explore a broader solution space and increase the possibility of finding a better solution. Crossed individuals retain some excellent characteristics of the current individual and introduce new characteristics of the mutated individual, which helps to balance global search and local search. Generally, the present invention increases the probability of finding a feasible solution, and compared with the variable-length genetic algorithm, the network deployment cost obtained is lower. Description of the Drawings

[0017] Figure 1 It is a flow schematic diagram of the heterogeneous directional sensor network deployment method for the embodiment.

[0018] Figure 2Schematic flowchart of calculating the fitness of an individual and the corresponding network deployment in the heterogeneous directional sensor network deployment method of the embodiment.

[0019] Figure 3 Experimental result graph of the heterogeneous directional sensor network deployment method and the variable-length genetic algorithm of the embodiment. Specific implementation manners

[0020] The present invention will be further described below in conjunction with embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading this description, various equivalent modifications of this description by those skilled in the art all fall within the scope defined by the appended claims of this application.

[0021] A heterogeneous directional sensor network deployment system involved in this embodiment includes: An initialization module, which is used to randomly initialize each element of each individual in the population. The length of the individual encoding is the number of target points, and each element corresponds to each target point one by one. Each element represents which directional sensor at which deployment position covers the corresponding target point, calculates the fitness of each individual and the corresponding network deployment, and the fitness is , where ndc represents the network deployment cost, w represents the weighting coefficient, tpc represents the total number of target points, nct represents the number of target points that can be covered, and the network deployment includes the positions, types, and working directions of all deployed directional sensors. The network deployment cost is the total price of all deployed directional sensors.

[0022] A population evolution module, which is used to calculate the mutant individual and the crossover individual for each individual in each iteration. Among them, calculate the fitness of the crossover individual and the corresponding network deployment, and replace the current individual with the crossover individual when the fitness of the crossover individual is less than that of the current individual. The calculation of the mutant individual is carried out by the mutant individual calculation module, and the mutant individual is obtained by weighted summation of three other individuals except the current individual. The calculation of the crossover individual is carried out by the crossover individual calculation module, and the crossover individual is obtained by selecting and replacing the elements of the current individual with the elements of the mutant individual.

[0023] An output module, which is used to use the network deployment corresponding to the individual with the minimum fitness as the final network deployment after the population evolution iteration ends.

[0024] This system iteratively calculates the network deployment by the fitness and network deployment calculation module until the network deployment cannot be optimized. Each iteration of calculating the network deployment includes: Calculate the set of target points covered by each deployment position according to the individual values i T ​i ; Calculate the type and working direction of each deployment location so that the maximum number of target points in i can be covered and the price is minimized. If T i is empty, no sensor is deployed at the location T i ; i For each target point, sequentially traverse each deployed sensor to find the sensor that can cover the target point and has the minimum price. If found, modify the value of the dimension corresponding to the target point in the individual to the index of the deployment location of the sensor in the set of deployment locations that can cover the target point.

[0025] Suppose the number of target points is tpc , the number of candidate deployment locations of the directional sensor is dsc , the number of types of directional sensors is tyc , the price of the i th type of directional sensor is p i , the number of candidate working directions of the directional sensor is wdc . In the method of the present invention, the population size is set to ps , use to represent the i th individual, and use j to represent the T th generation of population evolution. The termination condition of the method of the present invention is to complete w . Use C i to represent the weighted coefficient of the number of uncovered target points. Let i represent the set of deployment locations that can cover the target point

[0026] Model the sensing range of the directional sensor using a sector area. The target coverage matrix M has a size of dsc × tyc × wdc × tpc , and its element represents whether the directional sensor deployed at the location i of type j can cover the target point k using the working direction l , = 1 indicates yes, = 0 indicates no. Based on M each C l can be established, and .

[0027] A heterogeneous directional sensor network deployment method implemented by a heterogeneous directional sensor network deployment system. Specifically, please refer to Figure 1 as shown below, including: Step 101: For each individual , encode it into an indication of the deployment positions covering each target point. Thus, the length of the individual is tpc , and its j -th element represents the index of the deployment position covering the target point j in C j . Randomly initialize each element to a value in , and then use the CF algorithm to recalculate and its fitness and the corresponding network deployment.

[0028] Step 102: t = 1.

[0029] Step 103: i = 1.

[0030] Step 104: Perform a mutation operation to generate a mutant individual . The mutation operation is specifically as follows: Assume the current individual is i . First, randomly select three different individuals j , k , l , none of which can be the individual i . Let af represent the amplification factor, then the mutant individual is . Then, round and limit the value of each of its elements within its domain. Step 105: Perform a crossover operation on and to generate a crossover individual . The crossover operation is specifically as follows: Assume the current individual is i . First, randomly select a target point j . Let cp represent the crossover probability, and let rand represent a random function in the interval [0, 1], then the crossover individual is calculated according to the following formula: .

[0031] Step 106: Call the CF algorithm to calculate the new and its fitness and the corresponding network deployment.

[0032] Step 107: If the fitness of is less than the fitness of , then Update to , and update the fitness and the corresponding network deployment.

[0033] Step 108: i = i + 1.

[0034] Step 109: If i ≤ ps , then go to Step 104.

[0035] Step 110: t = t + 1.

[0036] Step 111: If t ≤ T , then go to Step 103.

[0037] Step 112: Find the individual with the minimum fitness, and output its fitness and the corresponding network deployment.

[0038] Please refer to Figure 2 as shown. The method for calculating the fitness and the network deployment using the CF algorithm in the above method includes the following steps: Step 201: ndc = ∞.

[0039] Step 202: Calculate the set of target points Z covered by each deployment location i . T i .

[0040] Step 203: i = 1, c = 0.

[0041] Step 204: SD { i} = [ ].

[0042] Step 205: If T i is empty, then go to Step 218.

[0043] Step 206: mp = ∞, mn = 0.

[0044] Step 207: j = 1.

[0045] Step 208: k = 1.

[0046] Step 209: Calculate the number of target points that can be covered by the directional sensor (priced at i ), of type j , deployed at location p j ), using the working direction k to cover T i . n .

[0047] Step 210: If ( n > mn ) or ( n > 0 and n == mn and p j < mp ), then go to Step 211; otherwise, go to Step 213.

[0048] Step 211: mn = n , mp = p j .

[0049] Step 212: SD { i} = j , k ].

[0050] Step 213: k = k + 1.

[0051] Step 214: If k ≤ wdc , then go to Step 209.

[0052] Step 215: j = j + 1.

[0053] Step 216: If j ≤ tyc , then go to Step 208.

[0054] Step 217: c = c + mp .

[0055] Step 218: i = i + 1.

[0056] Step 219: If i ≤ dsc , then go to Step 204.

[0057] Step 220: If c < ndc , then go to Step 221; otherwise, go to Step 234.

[0058] Step 221: ndc = c .

[0059] Step 222: nct = 0.

[0060] Step 223: i = 1.

[0061] Step 224: j = 1, mp = ∞, ms = 0.

[0062] Step 225: If SD { j} ≠ [ ] and the type deployed at location j is SD { j}(1) and the sensor uses the working direction SD { j}(2) and can cover the target point i and p SD{j}(1) < mp , then go to Step 226; otherwise, go to Step 227.

[0063] Step 226: ms = j , mp = p SD{j}(1) .

[0064] Step 227: j = j +1.

[0065] Step 228: If j ≤ dsc , then go to Step 225.

[0066] Step 229: If ms >0, then go to Step 230; otherwise, go to Step 232.

[0067] Step 230: Set Z ( i ) to be ms the index in C i .

[0068] Step 231: nct = nct + 1.

[0069] Step 232: i = i + 1.

[0070] Step 233: If i ≤ tpc , then go to Step 224; otherwise, go to Step 202.

[0071] Step 234: fv = ndc + w ( tpc - nct ).

[0072] Step 235: Return the new Z , network deployment SD (the positions, types, and working directions of all deployed directional sensors), and the fitness fv .

[0073] To verify the advantages of the method of the present invention, experiments were conducted to compare the network deployment costs obtained by the method of the present invention and the variable-length genetic algorithm (VLGA). In the experiment, two types of directional sensors could be deployed. The sensing angle of the first type of directional sensor was p / 2, the sensing radius was 30 meters, and the price was 1080 yuan. The sensing angle of the second type of directional sensor was p / 3, the sensing radius was 40 meters, and the price was 720 yuan. Each directional sensor had four available working directions, namely 0, p / 2, p, and 3p / 2. The number of candidate deployment positions of the directional sensors was fixed at 60, while the number of target points took different values. For each value of the number of target points, 20 problem instances were randomly generated, and the average results of each algorithm were calculated. For each problem instance, the positions of each target point and each candidate deployment position were randomly generated. The population sizes of both algorithms were 100, and the number of evolution generations was 1000. In the method of the present invention, the crossover probability cp was set to 0.9, the amplification factor af was set to 0.5, and the weighting coefficient w in the individual fitness calculation formula was set to 10 8 . The experimental program was developed using MATLAB.

[0074] The following are the experimental process data of representative instances for different numbers of target points: For the instance with 10 target points, the target point positions are as follows: The position of the 1st target point is (50.581846, 74.344241).

[0075] The position of the second target point is (105.543168, 105.834707).

[0076] The position of the third target point is (7.064129, 38.995338).

[0077] The position of the fourth target point is (108.722730, 66.574874).

[0078] The position of the fifth target point is (10.328413, 116.448377).

[0079] The position of the sixth target point is (33.072540, 119.880754).

[0080] The position of the seventh target point is (0.724075, 54.068432).

[0081] The position of the eighth target point is (50.836780, 75.989666).

[0082] The position of the ninth target point is (79.128476, 106.817832).

[0083] The position of the tenth target point is (4.993869, 74.149592).

[0084] The candidate deployment positions are as follows: The first candidate deployment position is (23.324648, 118.766377).

[0085] The second candidate deployment position is (109.604100, 76.165085).

[0086] The third candidate deployment position is (40.575893, 10.209897).

[0087] The fourth candidate deployment position is (8.042051, 39.503661).

[0088] The fifth candidate deployment position is (17.193248, 86.941745).

[0089] The sixth candidate deployment position is (16.312999, 83.198571).

[0090] The seventh candidate deployment position is (114.167329, 37.451106).

[0091] The 8th candidate deployment location is (51.240810, 59.783708).

[0092] The 9th candidate deployment location is (36.613943, 73.994783).

[0093] The 10th candidate deployment location is (85.109931, 22.569896).

[0094] The 11th candidate deployment location is (80.329451, 102.691739).

[0095] The 12th candidate deployment location is (75.167333, 97.549134).

[0096] The 13th candidate deployment location is (24.945805, 118.058282).

[0097] The 14th candidate deployment location is (118.110714, 74.089031).

[0098] The 15th candidate deployment location is (49.722185, 115.053429).

[0099] The 16th candidate deployment location is (13.181789, 2.689100).

[0100] The 17th candidate deployment location is (43.716762, 62.592640).

[0101] The 18th candidate deployment location is (1.672372, 97.627034).

[0102] The 19th candidate deployment location is (74.453432, 92.173396).

[0103] The 20th candidate deployment location is (24.103424, 7.239394).

[0104] The 21st candidate deployment location is (105.246904, 64.365943).

[0105] The 22nd candidate deployment location is (79.153736, 80.286222).

[0106] The 23rd candidate deployment location is (37.213971, 87.671560).

[0107] The 24th candidate deployment location is (53.251658, 95.533810).

[0108] The 25th candidate deployment location is (3.009749, 59.794381).

[0109] The 26th candidate deployment location is (88.973330, 84.334644).

[0110] The 27th candidate deployment location is (86.144761, 8.317543).

[0111] The 28th candidate deployment location is (0.265587, 87.264743).

[0112] The 29th candidate deployment location is (44.138022, 117.723266).

[0113] The 30th candidate deployment location is (114.032505, 41.120070).

[0114] The 31st candidate deployment location is (39.252430, 63.217146).

[0115] The 32nd candidate deployment location is (11.012343, 75.792877).

[0116] The 33rd candidate deployment location is (73.255241, 11.550385).

[0117] The 34th candidate deployment location is (24.808864, 18.789460).

[0118] The 35th candidate deployment location is (22.668656, 96.621312).

[0119] The 36th candidate deployment location is (90.339925, 63.667566).

[0120] The 37th candidate deployment location is (63.654248, 45.783823).

[0121] The 38th candidate deployment location is (45.474047, 14.063596).

[0122] The 39th candidate deployment location is (18.924416, 14.683620).

[0123] The 40th candidate deployment location is (46.212660, 75.259120).

[0124] The 41st candidate deployment location is (48.955771, 62.465051).

[0125] The 42nd candidate deployment location is (110.233996, 16.276690).

[0126] The 43rd candidate deployment location is (79.852519, 38.897763).

[0127] The 44th candidate deployment location is (72.109974, 1.568237).

[0128] The 45th candidate deployment location is (56.047192, 21.287279).

[0129] The 46th candidate deployment location is (23.694285, 14.290053).

[0130] The 47th candidate deployment location is (58.686425, 9.919034).

[0131] The 48th candidate deployment location is (70.011494, 12.364170).

[0132] The 49th candidate deployment location is (4.103471, 70.474345).

[0133] The 50th candidate deployment location is (11.534674, 97.713143).

[0134] The 51st candidate deployment location is (14.136355, 86.717014).

[0135] The 52nd candidate deployment location is (58.822644, 34.234035).

[0136] The 53rd candidate deployment location is (63.314740, 34.544936).

[0137] The 54th candidate deployment location is (49.671150, 27.383143).

[0138] The 55th candidate deployment location is (65.512514, 10.746609).

[0139] The 56th candidate deployment location is (11.680861, 12.493790).

[0140] The 57th candidate deployment location is (38.201655, 13.210714).

[0141] The 58th candidate deployment location is (53.754569, 1.640301).

[0142] The 59th candidate deployment location is (8.440371, 96.123660).

[0143] The 60th candidate deployment location is (8.912243, 10.140045).

[0144] The network deployment is as follows: Deploy the second type of directional sensor at the 2nd position, with its working direction being 3π / 2.

[0145] Deploy the second type of directional sensor at the 4th position, with its working direction being π / 2.

[0146] Deploy the second type of directional sensor at the 5th position, with its working direction being 0.

[0147] Deploy the first type of directional sensor at the 26th position, with its working direction being π / 2.

[0148] Deploy the second type of directional sensor at the 29th position, with its working direction being π.

[0149] Deploy the second type of directional sensor at the 49th position, with its working direction being 3π / 2.

[0150] For the instance with the number of target points being 15, the target point locations are as follows: The location of the 1st target point is (97.968168, 55.044879).

[0151] The location of the 2nd target point is (85.227696, 100.203585).

[0152] The location of the 3rd target point is (39.286844, 21.894996).

[0153] The location of the 4th target point is (48.532867, 13.294674).

[0154] The location of the 5th target point is (117.437609, 15.093966).

[0155] The location of the 6th target point is (98.627161, 83.322270).

[0156] The location of the 7th target point is (76.102688, 38.629756).

[0157] The position of the 8th target point is (109.637785, 88.352112).

[0158] The position of the 9th target point is (73.638396, 96.315816).

[0159] The position of the 10th target point is (114.313906, 64.588061).

[0160] The position of the 11th target point is (48.360532, 21.378173).

[0161] The position of the 12th target point is (47.884292, 19.462133).

[0162] The position of the 13th target point is (27.818373, 1.929062).

[0163] The position of the 14th target point is (17.953334, 57.625356).

[0164] The position of the 15th target point is (11.487411, 22.604526).

[0165] The candidate deployment locations are as follows: The 1st candidate deployment location is (30.843607, 90.386706).

[0166] The 2nd candidate deployment location is (78.386634, 24.898029).

[0167] The 3rd candidate deployment location is (45.799114, 111.673376).

[0168] The 4th candidate deployment location is (88.302257, 27.114802).

[0169] The 5th candidate deployment location is (96.679145, 47.905056).

[0170] The 6th candidate deployment location is (2.400180, 14.111981).

[0171] The 7th candidate deployment location is (19.426644, 75.547228).

[0172] The 8th candidate deployment location is (13.481375, 79.137094).

[0173] The 9th candidate deployment location is (50.612737, 11.379330).

[0174] The 10th candidate deployment location is (104.911549, 93.002211).

[0175] The 11th candidate deployment location is (89.966659, 71.624236).

[0176] The 12th candidate deployment location is (60.651636, 70.545910).

[0177] The 13th candidate deployment location is (20.846136, 114.318727).

[0178] The 14th candidate deployment location is (46.559114, 28.409979).

[0179] The 15th candidate deployment location is (101.649653, 23.651955).

[0180] The 16th candidate deployment location is (10.389225, 50.916705).

[0181] The 17th candidate deployment location is (68.722833, 27.028301).

[0182] The 18th candidate deployment location is (106.523098, 29.108886).

[0183] The 19th candidate deployment location is (76.051382, 59.341843).

[0184] The 20th candidate deployment location is (19.440560, 96.408116).

[0185] The 21st candidate deployment location is (69.036598, 69.112840).

[0186] The 22nd candidate deployment location is (113.381009, 19.631306).

[0187] The 23rd candidate deployment location is (55.849288, 49.210851).

[0188] The 24th candidate deployment location is (73.056337, 39.674555).

[0189] The 25th candidate deployment location is (105.235875, 19.289220).

[0190] The 26th candidate deployment location is (95.917545, 3.822508).

[0191] The 27th candidate deployment location is (11.209622, 91.614509).

[0192] The 28th candidate deployment location is (32.968897, 58.279744).

[0193] The 29th candidate deployment location is (42.674952, 82.137684).

[0194] The 30th candidate deployment location is (29.914669, 39.475926).

[0195] The 31st candidate deployment location is (73.598356, 84.467850).

[0196] The 32nd candidate deployment location is (9.245632, 64.685291).

[0197] The 33rd candidate deployment location is (27.303332, 52.497929).

[0198] The 34th candidate deployment location is (102.348125, 77.161242).

[0199] The 35th candidate deployment location is (62.753560, 85.866212).

[0200] The 36th candidate deployment location is (97.945789, 55.620935).

[0201] The 37th candidate deployment location is (90.349101, 35.710494).

[0202] The 38th candidate deployment location is (110.528999, 94.658329).

[0203] The 39th candidate deployment location is (10.954907, 17.270593).

[0204] The 40th candidate deployment location is (7.508458, 28.895913).

[0205] The 41st candidate deployment location is (26.242383, 82.604276).

[0206] The 42nd candidate deployment location is (93.016642, 16.395241).

[0207] The 43rd candidate deployment location is (31.025374, 54.679552).

[0208] The 44th candidate deployment location is (22.415488, 12.669212).

[0209] The 45th candidate deployment location is (118.190551, 68.171296).

[0210] The 46th candidate deployment location is (44.007849, 40.290396).

[0211] The 47th candidate deployment location is (42.187398, 82.979651).

[0212] The 48th candidate deployment location is (54.451938, 97.665446).

[0213] The 49th candidate deployment location is (28.622897, 24.681679).

[0214] The 50th candidate deployment location is (7.612127, 65.823660).

[0215] The 51st candidate deployment location is (45.214707, 23.629977).

[0216] The 52nd candidate deployment location is (26.043268, 14.045114).

[0217] The 53rd candidate deployment location is (8.792032, 91.534679).

[0218] The 54th candidate deployment location is (94.499262, 27.913365).

[0219] The 55th candidate deployment location is (108.083862, 64.452475).

[0220] The 56th candidate deployment location is (98.456069, 73.127097).

[0221] The 57th candidate deployment location is (104.817612, 9.235835).

[0222] The 58th candidate deployment location is (7.255372, 62.798761).

[0223] The 59th candidate deployment location is (99.455735, 113.823327).

[0224] The 60th candidate deployment location is (40.764989, 43.473166).

[0225] The network deployment is as follows: Deploy a directional sensor of the second type at the 1st location, with its working direction being 3π / 2.

[0226] Deploy a directional sensor of the second type at the 2nd location, with its working direction being π.

[0227] Deploy a directional sensor of the first type at the 6th location, with its working direction being 0.

[0228] Deploy a directional sensor of the second type at the 10th location, with its working direction being 3π / 2.

[0229] Deploy a directional sensor of the second type at the 11th location, with its working direction being 3π / 2.

[0230] Deploy a directional sensor of the second type at the 48th location, with its working direction being 0.

[0231] Deploy a directional sensor of the second type at the 55th location, with its working direction being π / 2.

[0232] Deploy a directional sensor of the second type at the 57th location, with its working direction being 0.

[0233] For the instance with 20 target points, the target point locations are as follows: The location of the 1st target point is (38.018515, 71.434940).

[0234] The location of the 2nd target point is (95.835485, 86.354471).

[0235] The location of the 3rd target point is (7.452923, 109.424365).

[0236] The location of the 4th target point is (118.332870, 43.738895).

[0237] The location of the 5th target point is (75.848457, 62.001871).

[0238] The location of the 6th target point is (12.265926, 40.377809).

[0239] The position of the 7th target point is (77.111208, 40.713268).

[0240] The position of the 8th target point is (32.389847, 39.957915).

[0241] The position of the 9th target point is (111.287812, 51.277612).

[0242] The position of the 10th target point is (59.320742, 13.014407).

[0243] The position of the 11th target point is (117.773754, 41.574063).

[0244] The position of the 12th target point is (31.548208, 38.328124).

[0245] The position of the 13th target point is (89.403885, 46.558096).

[0246] The position of the 14th target point is (81.677401, 49.101681).

[0247] The position of the 15th target point is (118.443527, 96.260930).

[0248] The position of the 16th target point is (119.295470, 93.947698).

[0249] The position of the 17th target point is (33.736969, 89.612784).

[0250] The position of the 18th target point is (106.891955, 21.341350).

[0251] The position of the 19th target point is (30.066939, 91.670411).

[0252] The position of the 20th target point is (9.739861, 82.082157).

[0253] The candidate deployment positions are as follows: The 1st candidate deployment position is (91.738938, 103.771732).

[0254] The 2nd candidate deployment position is (116.686243, 84.386764).

[0255] The 3rd candidate deployment location is (42.588461, 85.025208).

[0256] The 4th candidate deployment location is (45.313961, 34.881407).

[0257] The 5th candidate deployment location is (29.098184, 98.385848).

[0258] The 6th candidate deployment location is (94.687418, 66.335983).

[0259] The 7th candidate deployment location is (18.603387, 59.225838).

[0260] The 8th candidate deployment location is (108.307766, 112.868132).

[0261] The 9th candidate deployment location is (67.022484, 114.989984).

[0262] The 10th candidate deployment location is (57.495778, 104.380268).

[0263] The 11th candidate deployment location is (116.594817, 62.111132).

[0264] The 12th candidate deployment location is (5.064034, 33.787691).

[0265] The 13th candidate deployment location is (76.909907, 11.434865).

[0266] The 14th candidate deployment location is (114.821396, 91.975851).

[0267] The 15th candidate deployment location is (0.747952, 5.326482).

[0268] The 16th candidate deployment location is (30.109079, 76.764217).

[0269] The 17th candidate deployment location is (114.484780, 116.891341).

[0270] The 18th candidate deployment location is (98.198749, 11.217960).

[0271] The 19th candidate deployment location is (1.132873, 107.711715).

[0272] The 20th candidate deployment location is (85.266801, 94.994301).

[0273] The 21st candidate deployment location is (89.037381, 75.394841).

[0274] The 22nd candidate deployment location is (119.830079, 54.972486).

[0275] The 23rd candidate deployment location is (79.884625, 100.772013).

[0276] The 24th candidate deployment location is (103.951486, 68.036708).

[0277] The 25th candidate deployment location is (30.564374, 117.657143).

[0278] The 26th candidate deployment location is (69.944242, 42.679096).

[0279] The 27th candidate deployment location is (115.854344, 88.406991).

[0280] The 28th candidate deployment location is (15.394539, 108.474190).

[0281] The 29th candidate deployment location is (22.177679, 109.467340).

[0282] The 30th candidate deployment location is (13.390725, 51.067213).

[0283] The 31st candidate deployment location is (17.555921, 28.815426).

[0284] The 32nd candidate deployment location is (27.916895, 70.574954).

[0285] The 33rd candidate deployment location is (31.178386, 53.049001).

[0286] The 34th candidate deployment location is (14.191929, 59.833605).

[0287] The 35th candidate deployment location is (30.845756, 60.918740).

[0288] The 36th candidate deployment location is (86.399931, 101.000778).

[0289] The 37th candidate deployment location is (83.486863, 51.209821).

[0290] The 38th candidate deployment location is (110.470164, 66.871365).

[0291] The 39th candidate deployment location is (52.723459, 67.527688).

[0292] The 40th candidate deployment location is (46.710248, 84.455552).

[0293] The 41st candidate deployment location is (57.937307, 78.773411).

[0294] The 42nd candidate deployment location is (25.479887, 74.827126).

[0295] The 43rd candidate deployment location is (67.418908, 83.185399).

[0296] The 44th candidate deployment location is (41.285375, 114.372856).

[0297] The 45th candidate deployment location is (77.359817, 98.599892).

[0298] The 46th candidate deployment location is (105.261421, 74.662168).

[0299] The 47th candidate deployment location is (98.599338, 96.867405).

[0300] The 48th candidate deployment location is (109.878153, 78.031891).

[0301] The 49th candidate deployment location is (10.234853, 101.384399).

[0302] The 50th candidate deployment location is (89.132848, 26.133454).

[0303] The 51st candidate deployment location is (100.386805, 65.876420).

[0304] The 52nd candidate deployment location is (61.168460, 85.576424).

[0305] The 53rd candidate deployment location is (18.921783, 15.586351).

[0306] The 54th candidate deployment location is (53.995482, 74.996764).

[0307] The 55th candidate deployment location is (45.302306, 32.547384).

[0308] The 56th candidate deployment location is (88.475383, 44.314013).

[0309] The 57th candidate deployment location is (103.753018, 36.429727).

[0310] The 58th candidate deployment location is (70.539563, 11.264833).

[0311] The 59th candidate deployment location is (1.414142, 98.625359).

[0312] The 60th candidate deployment location is (59.726902, 19.527124).

[0313] The network deployment is as follows: Deploy the second type of directional sensor at the 4th position, with its working direction being π.

[0314] Deploy the first type of directional sensor at the 8th position, with its working direction being 3π / 2.

[0315] Deploy the second type of directional sensor at the 11th position, with its working direction being 3π / 2.

[0316] Deploy the second type of directional sensor at the 13th position, with its working direction being π / 2.

[0317] Deploy the second type of directional sensor at the 19th position, with its working direction being 0.

[0318] Deploy the second type of directional sensor at the 20th position, with its working direction being 3π / 2.

[0319] Deploy the second type of directional sensor at the 22nd position, with its working direction being 3π / 2.

[0320] Deploy the second type of directional sensor at the 26th position, with its working direction being 3π / 2.

[0321] Deploy a directional sensor of the first type at the 35th position, with its working direction being π / 2.

[0322] For an instance with 25 target points, the target point positions are as follows: The position of the first target point is (24.555753, 109.236806).

[0323] The position of the second target point is (6.721928, 45.071694).

[0324] The position of the third target point is (30.582066, 34.743086).

[0325] The position of the fourth target point is (54.650636, 65.039691).

[0326] The position of the fifth target point is (48.751370, 81.121117).

[0327] The position of the sixth target point is (44.621515, 85.917580).

[0328] The position of the seventh target point is (108.078895, 85.236903).

[0329] The position of the eighth target point is (23.032409, 22.394597).

[0330] The position of the ninth target point is (7.767156, 1.498388).

[0331] The position of the tenth target point is (44.076860, 65.349959).

[0332] The position of the eleventh target point is (60.371358, 23.346881).

[0333] The position of the twelfth target point is (42.603922, 85.441338).

[0334] The position of the thirteenth target point is (107.457321, 48.177991).

[0335] The position of the fourteenth target point is (14.135747, 61.817402).

[0336] The position of the fifteenth target point is (28.365969, 16.719451).

[0337] The position of the 16th target point is (63.986080, 69.554503).

[0338] The position of the 17th target point is (101.493626, 6.752688).

[0339] The position of the 18th target point is (17.463970, 28.382287).

[0340] The position of the 19th target point is (75.624416, 54.081736).

[0341] The position of the 20th target point is (19.414538, 68.888334).

[0342] The position of the 21st target point is (92.378727, 5.868526).

[0343] The position of the 22nd target point is (110.597263, 108.418789).

[0344] The position of the 23rd target point is (18.369588, 76.189806).

[0345] The position of the 24th target point is (109.652598, 55.303237).

[0346] The position of the 25th target point is (38.659687, 85.658407).

[0347] The candidate deployment positions are as follows: The 1st candidate deployment position is (107.306973, 104.179812).

[0348] The 2nd candidate deployment position is (60.385830, 4.995683).

[0349] The 3rd candidate deployment position is (98.661588, 19.901545).

[0350] The 4th candidate deployment position is (39.759353, 11.221304).

[0351] The 5th candidate deployment position is (111.445250, 56.139870).

[0352] The 6th candidate deployment position is (76.942439, 51.597550).

[0353] The 7th candidate deployment location is (53.425977, 43.535645).

[0354] The 8th candidate deployment location is (87.373628, 44.488650).

[0355] The 9th candidate deployment location is (45.234871, 94.318372).

[0356] The 10th candidate deployment location is (54.750105, 11.792320).

[0357] The 11th candidate deployment location is (106.897667, 102.791671).

[0358] The 12th candidate deployment location is (58.451599, 93.845789).

[0359] The 13th candidate deployment location is (21.828066, 73.329306).

[0360] The 14th candidate deployment location is (77.702207, 14.440683).

[0361] The 15th candidate deployment location is (92.791125, 76.330033).

[0362] The 16th candidate deployment location is (35.886425, 38.485143).

[0363] The 17th candidate deployment location is (27.480891, 38.212753).

[0364] The 18th candidate deployment location is (74.178635, 56.080412).

[0365] The 19th candidate deployment location is (88.501159, 91.509908).

[0366] The 20th candidate deployment location is (29.455749, 107.951200).

[0367] The 21st candidate deployment location is (114.622135, 78.498314).

[0368] The 22nd candidate deployment location is (3.303761, 42.423754).

[0369] The 23rd candidate deployment location is (32.099249, 92.565956).

[0370] The 24th candidate deployment location is (88.444906, 48.117384).

[0371] The 25th candidate deployment location is (92.754713, 50.583692).

[0372] The 26th candidate deployment location is (81.077214, 75.166192).

[0373] The 27th candidate deployment location is (80.971909, 28.484991).

[0374] The 28th candidate deployment location is (64.136621, 12.712055).

[0375] The 29th candidate deployment location is (66.088704, 99.688263).

[0376] The 30th candidate deployment location is (76.342647, 82.099984).

[0377] The 31st candidate deployment location is (14.189050, 90.287443).

[0378] The 32nd candidate deployment location is (62.272842, 47.176305).

[0379] The 33rd candidate deployment location is (39.319671, 46.026980).

[0380] The 34th candidate deployment location is (88.885316, 91.378550).

[0381] The 35th candidate deployment location is (90.335154, 66.116194).

[0382] The 36th candidate deployment location is (102.751010, 3.220750).

[0383] The 37th candidate deployment location is (24.650226, 85.453284).

[0384] The 38th candidate deployment location is (90.625802, 53.901633).

[0385] The 39th candidate deployment location is (81.101033, 82.098773).

[0386] The 40th candidate deployment location is (68.574024, 116.236811).

[0387] The 41st candidate deployment location is (70.542540, 31.442216).

[0388] The 42nd candidate deployment location is (4.263467, 101.537223).

[0389] The 43rd candidate deployment location is (56.034601, 31.626711).

[0390] The 44th candidate deployment location is (45.154605, 29.428665).

[0391] The 45th candidate deployment location is (86.294786, 48.818189).

[0392] The 46th candidate deployment location is (71.425053, 119.476686).

[0393] The 47th candidate deployment location is (7.530062, 108.095146).

[0394] The 48th candidate deployment location is (98.688892, 71.410464).

[0395] The 49th candidate deployment location is (72.494319, 76.395086).

[0396] The 50th candidate deployment location is (115.365723, 16.452592).

[0397] The 51st candidate deployment location is (85.638470, 20.392008).

[0398] The 52nd candidate deployment location is (12.021631, 104.048260).

[0399] The 53rd candidate deployment location is (31.443028, 108.656767).

[0400] The 54th candidate deployment location is (50.460239, 30.385352).

[0401] The 55th candidate deployment location is (63.661976, 63.663444).

[0402] The 56th candidate deployment location is (100.556992, 51.697391).

[0403] The 57th candidate deployment location is (22.779933, 21.208815).

[0404] The 58th candidate deployment location is (66.687593, 114.897513).

[0405] The 59th candidate deployment location is (105.739067, 34.541533).

[0406] The 60th candidate deployment location is (92.071902, 37.904409).

[0407] The network deployment is as follows: Deploy a directional sensor of the second type at the 3rd position, with its working direction being π / 2.

[0408] Deploy a directional sensor of the second type at the 4th position, with its working direction being π.

[0409] Deploy a directional sensor of the second type at the 5th position, with its working direction being π.

[0410] Deploy a directional sensor of the second type at the 7th position, with its working direction being π / 2.

[0411] Deploy a directional sensor of the second type at the 12th position, with its working direction being π.

[0412] Deploy a directional sensor of the second type at the 17th position, with its working direction being π / 2.

[0413] Deploy a directional sensor of the second type at the 18th position, with its working direction being 3π / 2.

[0414] Deploy a directional sensor of the first type at the 34th position, with its working direction being 0.

[0415] Deploy a directional sensor of the first type at the 57th position, with its working direction being π / 2.

[0416] Deploy a directional sensor of the second type at the 60th position, with its working direction being 3π / 2.

[0417] For the instance with 30 target points, the target point positions are as follows: The position of the 1st target point is (18.376904, 9.897743).

[0418] The position of the 2nd target point is (103.190079, 75.954703).

[0419] The position of the 3rd target point is (64.588081, 60.198634).

[0420] The position of the 4th target point is (116.855904, 45.049117).

[0421] The position of the 5th target point is (117.196528, 24.756293).

[0422] The position of the 6th target point is (62.151285, 42.804387).

[0423] The position of the 7th target point is (110.964033, 101.846702).

[0424] The position of the 8th target point is (96.577165, 22.497259).

[0425] The position of the 9th target point is (1.281868, 74.076790).

[0426] The position of the 10th target point is (27.193903, 83.647649).

[0427] The position of the 11th target point is (108.403576, 7.141976).

[0428] The position of the 12th target point is (37.158307, 13.837463).

[0429] The position of the 13th target point is (15.314776, 109.702648).

[0430] The position of the 14th target point is (49.397980, 103.692912).

[0431] The position of the 15th target point is (80.836456, 62.716096).

[0432] The position of the 16th target point is (112.950152, 93.056813).

[0433] The position of the 17th target point is (98.432433, 84.512712).

[0434] The position of the 18th target point is (112.759649, 35.138137).

[0435] The position of the 19th target point is (52.938903, 85.083846).

[0436] The position of the 20th target point is (27.721716, 11.314251).

[0437] The position of the 21st target point is (105.387162, 46.546644).

[0438] The position of the 22nd target point is (76.896503, 118.163297).

[0439] The position of the 23rd target point is (10.823036, 107.571521).

[0440] The position of the 24th target point is (93.153922, 14.693352).

[0441] The position of the 25th target point is (58.673518, 51.521925).

[0442] The position of the 26th target point is (78.808162, 36.088429).

[0443] The position of the 27th target point is (108.458938, 98.666228).

[0444] The position of the 28th target point is (36.562475, 73.746020).

[0445] The position of the 29th target point is (6.564621, 103.509134).

[0446] The position of the 30th target point is (101.258178, 82.824231).

[0447] The candidate deployment locations are as follows: The 1st candidate deployment location is (51.006889, 4.411468).

[0448] The 2nd candidate deployment location is (23.267179, 54.841236).

[0449] The 3rd candidate deployment location is (21.266499, 94.121057).

[0450] The 4th candidate deployment location is (92.851978, 91.230751).

[0451] The 5th candidate deployment location is (2.863929, 58.177009).

[0452] The 6th candidate deployment location is (97.739885, 82.932582).

[0453] The 7th candidate deployment location is (49.257396, 26.632497).

[0454] The 8th candidate deployment location is (110.891872, 62.289832).

[0455] The 9th candidate deployment location is (92.336959, 101.046056).

[0456] The 10th candidate deployment location is (40.218060, 92.601407).

[0457] The 11th candidate deployment location is (104.577835, 106.379230).

[0458] The 12th candidate deployment location is (112.089388, 28.019836).

[0459] The 13th candidate deployment location is (15.021103, 103.410563).

[0460] The 14th candidate deployment location is (63.759445, 94.372801).

[0461] The 15th candidate deployment location is (67.794746, 54.134252).

[0462] The 16th candidate deployment location is (49.847015, 20.463564).

[0463] The 17th candidate deployment location is (81.065743, 4.944697).

[0464] The 18th candidate deployment location is (99.463962, 0.374649).

[0465] The 19th candidate deployment location is (113.329455, 63.671211).

[0466] The 20th candidate deployment location is (33.307313, 110.224532).

[0467] The 21st candidate deployment location is (115.991071, 37.491989).

[0468] The 22nd candidate deployment location is (20.718538, 54.436445).

[0469] The 23rd candidate deployment location is (107.378978, 28.489737).

[0470] The 24th candidate deployment location is (69.296796, 7.509632).

[0471] The 25th candidate deployment location is (19.431040, 69.228842).

[0472] The 26th candidate deployment location is (110.092367, 44.568265).

[0473] The 27th candidate deployment location is (77.662744, 62.441732).

[0474] The 28th candidate deployment location is (23.231664, 72.497521).

[0475] The 29th candidate deployment location is (91.025077, 43.442299).

[0476] The 30th candidate deployment location is (50.912977, 35.469791).

[0477] The 31st candidate deployment location is (103.152309, 42.893655).

[0478] The 32nd candidate deployment location is (27.083829, 56.519134).

[0479] The 33rd candidate deployment location is (85.360626, 14.878572).

[0480] The 34th candidate deployment location is (11.509461, 107.530922).

[0481] The 35th candidate deployment location is (34.307122, 4.772440).

[0482] The 36th candidate deployment location is (68.576192, 45.799625).

[0483] The 37th candidate deployment location is (70.420322, 25.408026).

[0484] The 38th candidate deployment location is (118.669378, 88.972395).

[0485] The 39th candidate deployment location is (29.599275, 18.583301).

[0486] The 40th candidate deployment location is (79.797088, 25.968383).

[0487] The 41st candidate deployment location is (86.204375, 18.392949).

[0488] The 42nd candidate deployment location is (65.384522, 11.374814).

[0489] The 43rd candidate deployment location is (28.903931, 96.377989).

[0490] The 44th candidate deployment location is (90.663975, 0.043897).

[0491] The 45th candidate deployment location is (64.255549, 85.916684).

[0492] The 46th candidate deployment location is (102.504542, 62.873298).

[0493] The 47th candidate deployment location is (36.050057, 0.573363).

[0494] The 48th candidate deployment location is (27.140317, 113.352606).

[0495] The 49th candidate deployment location is (15.014780, 23.579820).

[0496] The 50th candidate deployment location is (17.925154, 48.675534).

[0497] The 51st candidate deployment location is (11.507777, 95.498319).

[0498] The 52nd candidate deployment location is (46.571002, 2.470885).

[0499] The 53rd candidate deployment location is (85.902546, 48.756826).

[0500] The 54th candidate deployment location is (100.328734, 25.003719).

[0501] The 55th candidate deployment location is (58.157293, 3.392582).

[0502] The 56th candidate deployment location is (102.104513, 55.749718).

[0503] The 57th candidate deployment location is (36.103157, 5.937940).

[0504] The 58th candidate deployment location is (119.421532, 49.388349).

[0505] The 59th candidate deployment location is (97.041678, 76.017876).

[0506] The 60th candidate deployment location is (119.367721, 11.352891).

[0507] The network deployment is as follows: Deploy a directional sensor of the second type at the 3rd position, with its working direction being 0.

[0508] Deploy a directional sensor of the second type at the 8th position, with its working direction being π / 2.

[0509] Deploy a directional sensor of the second type at the 16th position, with its working direction being π.

[0510] Deploy a directional sensor of the second type at the 19th position, with its working direction being 3π / 2.

[0511] Deploy a directional sensor of the second type at the 20th position, with its working direction being π.

[0512] Deploy a directional sensor of the first type at the 22nd position, with its working direction being π / 2.

[0513] Deploy a directional sensor of the second type at the 24th position, with its working direction being 0.

[0514] Deploy a directional sensor of the second type at the 26th position, with its working direction being π.

[0515] Deploy a directional sensor of the second type at the 37th position, with its working direction being π / 2.

[0516] Deploy a directional sensor of the second type at the 45th position, with its working direction being π / 2.

[0517] The experimental results are as Figure 3 shown. It can be seen from the experimental results that the network deployment cost obtained by the method of the present invention is lower than that obtained by the VLGA algorithm.

[0518] Finally, it should be noted that the specific methods of the above embodiments can form a computer program product. Therefore, the computer program product implemented by this application can be stored on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.).

Claims

1. A heterogeneous directional sensor network deployment method, characterized in that It includes the following steps: In the initialization stage, each element of each individual in the population is randomly initialized first. The length of the individual encoding is the number of target points, and each element corresponds to a target point one by one. Each element represents which directional sensor at which deployment location covers the corresponding target point. Calculate the fitness of each individual and the corresponding network deployment. The fitness is , where ndc represents the network deployment cost, w represents the weighting coefficient, tpc represents the total number of target points, nct represents the number of target points that can be covered. The network deployment includes the positions, types, and working directions of all deployed directional sensors. The network deployment cost is the total price of all deployed directional sensors; Population evolution stage: In each iteration, for each individual, calculate the mutated individual and the crossover individual, calculate the fitness of the crossover individual and the corresponding network deployment, and replace the current individual with the crossover individual when the fitness of the crossover individual is less than that of the current individual. The mutated individual is obtained by weighted summation of three other individuals except the current individual, and the crossover individual is obtained by selectively replacing the elements of the current individual with the elements of the mutated individual; Output stage: After the population evolution iteration ends, use the network deployment corresponding to the individual with the minimum fitness as the final network deployment.

2. The heterogeneous directional sensor network deployment method according to claim 1, characterized in that Specifically, for calculating the mutated individual, randomly select three different individuals in the population, all of which are different from the current individual, weight the difference between two of them with an amplification factor and sum it with the third individual to obtain a mutated individual.

3. The heterogeneous directional sensor network deployment method according to claim 1, wherein Specifically, the calculation of the crossover individual is as follows: The crossover individual is initialized according to the current individual, and a dimension of the crossover individual is randomly selected j , and its value is modified to the dimension of the mutant individual j . For each of the other dimensions of the crossover individual k , its value is modified to the dimension of the mutant individual k with a set crossover probability.

4. A heterogeneous directional sensor network deployment method according to claim 1, characterized in that Calculating the fitness of an individual and the corresponding network deployment means iteratively calculating the network deployment until the network deployment cannot be optimized. Each iteration of calculating the network deployment includes: Calculate each deployment location according to the individual values i The set of target points covered T i ; Calculate each deployment location i of the type and working direction so as to be able to cover T i the maximum number of target points in and with the minimum price. If T i is empty, no sensor is deployed at the location i ; For each target point, sequentially traverse each deployed sensor, find the sensor that can cover the target point and has the minimum price. If found, modify the value of the dimension corresponding to the target point in the individual to the index of the deployment position of the sensor in the set of deployment positions that can cover the target point.

5. A heterogeneous directional sensor network deployment system, characterized in that, It includes: An initialization module, which is used to randomly initialize each element of each individual in the population. The length of the individual encoding is the number of target points, and each element corresponds to each target point one by one. Each element represents which directional sensor at which deployment location covers the corresponding target point, calculates the fitness of each individual and the corresponding network deployment, and the fitness is , where ndc represents the network deployment cost, w represents the weighting coefficient, tpc represents the total number of target points, nct represents the number of target points that can be covered. The network deployment includes the positions, types, and working directions of all deployed directional sensors. The network deployment cost is the total price of all deployed directional sensors; Population evolution module, which is used to calculate the mutated individual and the crossover individual for each individual in each iteration, calculate the fitness of the crossover individual and the corresponding network deployment, and replace the current individual with the crossover individual when the fitness of the crossover individual is less than that of the current individual. The mutated individual is obtained by weighted summation of three other individuals except the current individual, and the crossover individual is obtained by selectively replacing the elements of the current individual with the elements of the mutated individual; Output module, which is used to use the network deployment corresponding to the individual with the minimum fitness as the final network deployment after the population evolution iteration ends.

6. The heterogeneous directional sensor network deployment system according to claim 5, wherein The population evolution module includes a mutated individual calculation module, which is used to randomly select three different individuals in the population, all of which are different from the current individual, weight the difference between two of them with an amplification factor and sum it with the third individual to obtain a mutated individual.

7. The heterogeneous directional sensor network deployment system according to claim 5, characterized in that, The population evolution module includes a cross individual calculation module, which is used to initialize the cross individual according to the current individual and randomly select a dimension of the cross individual j , and modify its value to the dimension value of the mutant individual j . For each of the other dimensions of the cross individual k , modify its value to the dimension value of the mutant individual with a set cross probability k .

8. The heterogeneous directional sensor network deployment system according to claim 5, wherein It includes a fitness and network deployment calculation module, which is used to iteratively calculate the network deployment until the network deployment cannot be optimized. Each iteration of calculating the network deployment includes: Calculate each deployment location according to the individual value i Target point set covered T i ; Calculate each deployment location i of the type and working direction so as to be able to cover T i the most target points in and with the minimum price. If T i is empty, no sensor is deployed at the location i ; For each target point, sequentially traverse each deployed sensor, find the sensor that can cover the target point and has the minimum price. If found, modify the value of the dimension corresponding to the target point in the individual to the index of the deployment position of the sensor in the set of deployment positions that can cover the target point.

9. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the heterogeneous directional sensor network deployment method described in any one of claims 1 to 4.

10. A computer program, characterized in that, When the computer program is executed by a processor, it implements the heterogeneous directional sensor network deployment method described in any one of claims 1 to 4.

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