A subset selection method based on distribution estimation algorithm

Abstract

The application discloses a subset selection method based on a distribution estimation algorithm, and relates to the technical field of sensor network deployment. The specific scheme is as follows: initializing a probability model; generating a sample pool with a size of P according to the probability model; evaluating the target function value of all samples in the sample pool; for a maximum optimization problem, arranging the samples in the sample pool in descending order according to the target function value, and extracting samples from the sample pool at a sample rate for learning and updating the probability model; applying the learning samples to update the probability model; repeating the above process until a preset upper limit of iteration times is reached, and outputting a final subset by using the final probability model M, and determining the deployment point of the sensor in a two-dimensional region by inquiring the elements in the subset. The application improves the distribution estimation algorithm, so that the subset selection problem under a complex target function can be effectively solved, and the application is beneficial to many practical application problems such as machine learning feature selection, sensor network deployment and the like.

Description

Technical Field

[0001] This invention relates to the field of sensor network deployment technology, and specifically to a subset selection method based on a distribution estimation algorithm. Background Technology

[0002] Subset selection is a widespread problem in many technological fields, aiming to find a subset of a set that optimizes a certain performance metric. For example, in machine learning, feature selection is often required to determine a subset of features in the feature space for more efficient and effective training of machine learning models. Furthermore, in sensor network deployment, it is often necessary to select several deployment points from a pre-defined set of deployment points and deploy a certain number of sensors to maximize coverage of a specific area.

[0003] Sensor network deployment is a hot research area with wide applications in military reconnaissance and civilian security camera surveillance. In sensor network deployment, a common problem involves selecting several deployment points from a pre-defined set of deployment points and deploying a certain number of sensors to better detect a specific area. This can be considered a subset selection problem, where a subset of a fixed size is chosen from a set of all points. For sensor network deployment, the pre-defined set of deployment points is the entire set, and the selected fixed-size subset represents the points used to deploy the sensors. Therefore, the subset selection problem for sensor network deployment is: selecting a fixed-size subset from the pre-defined set of deployment points, which corresponds to a certain number of sensors, and then deploying the sensors using this subset.

[0004] The subset selection problem is generally NP-hard (Non-deterministic polynomial-time hardness), and its solution is not easy. The subset selection problem has attracted much attention from researchers. One of the most classic research results is the conclusion given in 1978 by George Nemhauser, a Nobel laureate in theory and a member of the National Academy of Engineering, and others: when the objective function f satisfies "monotonicity" and "submodularity", a greedy algorithm can obtain an approximation ratio of (1-1 / e), and this approximation ratio is the optimal polynomial-time approximation ratio. However, in practical applications, the objective function f is often nonlinear and non-convex, and may even be impossible to express explicitly, lacking good mathematical properties.

[0005] Regarding sensor network deployment, some academic research primarily relies on deployment schemes based on genetic algorithms and particle swarm optimization (PSO). However, subset selection problems often require choosing a fixed-size subset from a set. The crossover and mutation operators of genetic algorithms, and the speed update strategies of PSO, can easily violate this fixed-size characteristic. Greedy algorithms are also unsuitable for solving this problem because the objective function of sensor network deployment is often non-convex and non-linear, lacking favorable mathematical properties.

[0006] Currently, there is no technical solution that can achieve effective subset selection when facing the complex objective functions involved in sensor network deployment problems. Summary of the Invention

[0007] In view of this, the present invention provides a subset selection method based on a distribution estimation algorithm, which can effectively select subsets from a set to optimize the complex objective function in the sensor network deployment problem.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: Addressing the two-dimensional sensor network deployment problem, where the preset number of deployment points is D, and the number of sensors is Q, where Q is less than D, the ultimate goal of the two-dimensional sensor network deployment problem is to select Q dimensions from D dimensions, i.e., to perform subset selection; the subset selection method includes the following steps:

[0009] Step 1: Initialize the probability model M with dimension D; where the preset deployment point set corresponds to a probability model M with dimension D, where D is the number of preset deployment points; the probability value corresponding to each dimension is in the interval (0,1), which is used to represent the probability that a sensor will be deployed at the corresponding deployment point.

[0010] Step 2: Generate a sample pool of size P according to the probability model M, where each sample corresponds to a solution and the dimension is D.

[0011] Step 3: Evaluate the objective function values ​​of all samples in the sample pool.

[0012] Step 4: For the maximization optimization problem, sort the samples in the sample pool in descending order according to the objective function value, and extract the proportion of samples r from the sample pool to learn and update the probability model.

[0013] Step 5: Update the probability model M using the learning samples extracted in Step 4.

[0014] Step 6: Determine whether the number of algorithm iterations has reached the preset upper limit T. If it has, terminate the method and store the probability model M; otherwise, proceed to step 2.

[0015] Step 7: Use the final probability model M to output the final subset, and determine the deployment points of the sensors in the two-dimensional region by querying the elements in the subset.

[0016] Further, step two: Generate a sample pool of size P according to the probability model M, where each sample corresponds to a solution, and the dimension is D; specifically:

[0017] For each sample, generate a random distribution of dimension D between 0 and 1. Compare the value of each bit of this random distribution with the value of the probability model M. If the former value is less than the latter, set the corresponding dimension of the current sample to 1; otherwise, set it to 0.

[0018] Further, step three: evaluate the objective function values ​​of all samples in the sample pool, specifically:

[0019] For each sample, an auxiliary vector temp is generated with dimension D and all dimensions are 0. The k dimensions with the largest value in the sample are selected and the corresponding dimension of temp is set to 1. Specifically, all dimensions with a value of 1 in the sample are selected. If the dimension with a value of 1 is less than k, the dimension with the largest index of 0 in the sample is selected, until the number of selected dimensions reaches k.

[0020] The objective function calculation module takes temp as its input, and temp serves as the input to the objective function. The objective function value is calculated according to the needs of different practical problems.

[0021] Furthermore, in step three, the specific implementation of the objective function calculation module is as follows:

[0022] Construct a variant of the one-max problem, with the objective function being:

[0023]

[0024] in Let emp be a 0-1 binary decision vector of dimension D=100, and let emp be the input to the objective function. This analysis leads to the conclusion that when The objective function reaches its maximum value, which is also the optimal value, when the values ​​of the 6th-10th, 20th-24th, 54th-58th, and 96th-100th dimensions of the vector are all 1. Meanwhile, if the values ​​of other dimensions are all 0, the subset selection is more straightforward.

[0025] Furthermore, in step four, for a minimization optimization problem, the objective function value can be negativeed to transform it into a maximization optimization problem. The objective function value with the largest value is then extracted. n samples are used as learning samples, among which This indicates the floor function.

[0026] Further, in step five, the learning samples extracted in step four are used to update the probability model M, where the update process specifically includes correction and mutation;

[0027] The correction and mutation process is iterative, updating the probability model M sequentially using all training samples; the mathematical form of each correction process is:

[0028] P i ←P i ×(1.0-LR)+p i ×LR (1)

[0029] Among them, P i Let P represent the probability value of the i-th dimension of the probability model M, i∈1,...,D; in equation (1), the left-hand side of the ← symbol represents the updated P. i The right side represents the update formula; LR represents the set learning rate; p i Let p represent the value of the i-th dimension of the p-th sample, where p∈1,...,P, i∈1,...,D;

[0030] Furthermore, a floating-point number is randomly generated between 0 and 1; if this number is less than the set mutation probability MUT PROB Then, mutation occurs, and the mathematical form of each mutation process is:

[0031] P i ←P i ×(1.0-MUT SHIFT )+random(0.0 or 1.0)×(MUT) SHIFT (2)

[0032] Among them, P i Let P represent the probability value of the i-th dimension of the probability model M, i∈1,...,D; in equation (2), the left-hand side of the ← symbol represents the mutated P. i The right side represents the mutation formula; random(0.0 or 1.0) generates a random number with a value of 0 or 1; MUT SHIFT This indicates the set amount of variation.

[0033] Beneficial effects:

[0034] This invention improves the distribution estimation algorithm, enabling it to effectively solve the subset selection problem under complex objective functions in sensor network deployment. This is beneficial for many practical applications such as machine learning feature selection and sensor network deployment. The method provided by this invention can perform search and optimization more efficiently, learning the required solution space information. Simultaneously, this method can automatically learn a sparse probabilistic model, which is beneficial for decision-makers to directly perform subset selection. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating subset selection for the improved distribution estimation algorithm provided in this invention. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] This invention provides a subset selection method based on a distribution estimation algorithm; the process of the subset selection method is as follows: Figure 1 As shown. This method mainly addresses the deployment problem of two-dimensional sensor networks, focusing on subset selection for its complex objective function. Some mathematical symbols are defined as follows: a probability model M with dimension D; a sample pool of size P, where each sample corresponds to a solution and has dimension D; the dimension of the subset to be selected is k; the ratio of samples extracted from the sample pool to learn and update the probability model is r; and the upper limit of the number of algorithm iterations is T. The improved distribution estimation algorithm provided by this invention has a learning phase and an inference phase. Specifically, it includes the following steps:

[0038] Consider a two-dimensional sensor network deployment problem as an example. The total number of sensors is Q. The number of pre-defined deployment points in the two-dimensional space is D, and each pre-defined deployment point has a two-dimensional coordinate. First, the two-dimensional detection area is divided into uniformly divided grids, resulting in G grid points. The two-dimensional coordinates of each grid point g∈G are (x...). g y g ), calculate the q∈Q sensor pair point (x g y g The coverage rate is c qg Specifically, the following detection model can be adopted.

[0039]

[0040] Where d represents the distance between the q-th sensor and point (x). g y g The two-dimensional Euclidean distance between ) and r; q The maximum detection range of the q-th sensor depends on the type and characteristics of the sensor. Furthermore, considering the cooperative detection capability for Q sensors, the detection capability of Q sensors for G grid points is calculated, i.e., the objective function is...

[0041]

[0042] A smaller value for obj indicates better performance, suggesting that grid points are more effectively detected collaboratively by the sensor network. This objective function is non-convex and non-linear, making it a complex objective function.

[0043] To solve the aforementioned sensor network deployment problem using the improved distribution estimation algorithm provided in this invention, the preset deployment point set is first mapped to a probability model M of dimension D, where the value of each dimension is in the interval (0, 1). The closer the value is to 1, the greater the probability that a sensor will be deployed at that preset deployment point. Since the number of sensors is fixed, the ultimate goal is to select Q dimensions from the D dimensions, i.e., to perform subset selection.

[0044] Step 1: Initialize the probability model M. The probability model has dimension D, where the preset deployment point set corresponds to a probability model M of dimension D, where D is the number of preset deployment points. The probability value corresponding to each dimension is in the interval (0, 1), representing the probability that a sensor will be deployed at the corresponding deployment point. In this embodiment of the invention, the value of each dimension is 0.5.

[0045] Step 2: Generate a sample pool of size P based on probability model M (generating the sample pool based on probability model M). Specifically, for each sample, generate a random distribution of dimension D between 0 and 1, and compare each bit of this random distribution with the value of probability model M. If the former value is less than the latter, set the corresponding dimension of the sample to 1; otherwise, set it to 0.

[0046] Step 3: Evaluate the objective function values ​​of all samples in the sample pool. Specifically, for each sample, generate an auxiliary vector `temp` with dimension D, where all dimensions are 0. Select the k dimensions with the largest values ​​in the sample and set the corresponding dimension of `temp` to 1. Specifically, all dimensions with a value of 1 in the sample are selected; if the number of dimensions with a value of 1 is less than k, then select the dimension with the largest index of a zero in the sample, until the selected dimension reaches k. This step can guide the distribution estimation algorithm to learn a sparse probability model, which is beneficial for decision-makers to directly select subsets. The objective function calculation module takes `temp` as input, and `temp` serves as the input to the objective function. The objective function value needs to be calculated according to different practical problems.

[0047] Step 4: For maximization optimization problems, sort the samples in the sample pool in descending order based on the objective function value. For minimization optimization problems, the objective function value can be negatively taken to transform it into a maximization optimization problem. Extract the sample with the largest objective function value. n samples are used as learning samples, among which This represents the floor operation; r takes values ​​between (0, 1], and the ratio of samples extracted from the sample pool to learn and update the probability model is r.

[0048] Step 5: Update the probability model M using the learning samples extracted in Step 4. The update process specifically includes correction and mutation. These correction and mutation processes enable the distribution estimation algorithm to learn the necessary solution space information. The correction and mutation processes are iterative, updating the probability model M sequentially using all the learning samples. The mathematical form of each correction process is as follows:

[0049] P i ←P i ×(1.0-LR)+p i ×LR

[0050] Among them, P i Let P represent the probability value of the i-th dimension of the probability model M, i∈1,...,D; in equation (1), the left-hand side of the ← symbol represents the updated P. i The right side represents the update formula; LR represents the set learning rate (0, 1); p i Let represent the value of the i-th dimension of the p-th sample, where p∈1,...,P, i∈1,...,D. ← Assignment;

[0051] Furthermore, a floating-point number is randomly generated between 0 and 1. If this number is less than the set mutation probability MUT... PROB Then perform the mutation MUT. PROB (0, 1). The mathematical form of each mutation process is:

[0052] P i ←P i ×(1.0-MUT SHIFT )+random(0.0 or 1.0)×(MUT) SHIFT )

[0053] Among them, P i Let represent the probability value of the i-th dimension of the probability model M, i∈1,...,D; random(0.0 or 1.0) represents generating a random number with a value of 0 or 1; in equation (2), the symbol ← on the left represents the mutated P. i The right side represents the mutation formula; MUT SHIFT This indicates the set amount of variation.

[0054] Step 6: Determine if the algorithm has reached the upper limit T for the number of iterations. If it has, terminate the algorithm and store the probability model M; otherwise, proceed to step 2.

[0055] The improved distribution estimation algorithm provided by this invention has completed the learning phase, obtaining the iteratively updated probability model M. Step seven below is the inference phase, which involves determining how to use the probability model M to output the final solution.

[0056] Step 7: Define a vector R with dimension D and all dimensions having a value of 0. Load the stored probability model M, calculate the k dimensions with the largest values, and assign the corresponding dimension of vector R a value of 1. At this point, the dimensions of vector R with a value of 1 correspond to the elements of the selected set. These elements constitute the selected subset. By querying the locations of these elements in the subset within the preset deployment point set, it is possible to determine which points in the two-dimensional region to deploy sensors.

[0057] Example 1:

[0058] To further illustrate the effectiveness of the provided method, simulations are performed on the improved distribution estimation algorithm provided by this invention and the traditional distribution estimation algorithm under the sensor network deployment problem. Consider 20 homogeneous sensors deployed in an area of ​​20×20km. 2 Within the designated area, the sensor's maximum detection range is 5 km. The area is divided into uniformly sized grids of 1 × 1 km. 2 That is, 400 grid points are used to calculate the detection capability. Other experimental parameters are set as follows: D=100, P=500, k=20. T=50, LR=0.3, MUT PROB =0.1, MUT SHIFT =0.05. Considering 30 random experiments, the performance of the algorithm is shown in Table 1. The results show that the improved distribution estimation algorithm has better optimization performance, with an average detection capability of 54.76, while the average detection capability of the traditional algorithm is 60.83. Moreover, compared with the traditional algorithm, the improved distribution estimation algorithm provided by this invention is more stable.

[0059] Table 1 Comparison of the improved distribution estimation algorithm provided by this invention with traditional algorithms

[0060] algorithm Improved distribution estimation algorithm Traditional Algorithm Average detection capability 54.76 60.83 Standard deviation 2.43 3.69

[0061] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A subset selection method based on a distribution estimation algorithm, characterized in that, For the deployment problem of two-dimensional sensor networks, where the preset number of deployment points is D and the number of sensors is Q, where Q is less than D, the ultimate goal of the two-dimensional sensor network deployment problem is to select Q dimensions from D dimensions, i.e., to perform subset selection; the subset selection method includes the following steps: Step 1: Initialize the probability model Its dimension is The preset deployment point set corresponds to a probability model M with dimension D, where D is the number of preset deployment points; the probability value corresponding to each dimension is in the interval (0, 1), which is used to represent the probability that a sensor will be deployed at the corresponding deployment point; Step 2: According to the aforementioned probability model The generation scale is A sample pool, where each sample corresponds to a solution, with dimension O(n). ; Step 3: Evaluate the objective function values ​​of all samples in the sample pool, specifically: For each sample, generate an auxiliary vector. Its dimension is All dimensions are 0; the sample with the largest value is selected. Wei, and will The corresponding dimension is set to 1; specifically, all dimensions with a value of 1 in the sample are selected; if the dimension with a value of 1 is less than 1... Then select the dimension with the largest index of 0 in the sample, until the selected dimension reaches the maximum value. ; The input to the objective function calculation module is set as follows: , As input to the objective function, the objective function value is calculated according to the needs of different practical problems; Step 4: For the maximization optimization problem, based on the objective function value, sort the samples in the sample pool in descending order, and extract the proportion of samples from the sample pool used to learn and update the probability model. ; Step 5: Update the probability model using the learning samples extracted in Step 4. ; Step Six: Determine if the algorithm has reached the preset maximum number of iterations. If reached, the method terminates and the probability model is stored. Otherwise, proceed to step two. Step 7: Utilize the final probability model The final subset is output, and the deployment points of the sensors are determined in a two-dimensional region by querying the elements in the subset.

2. The subset selection method based on distribution estimation algorithm as described in claim 1, characterized in that, Step two: Based on the probability model The generation scale is A sample pool, where each sample corresponds to a solution, with dimension O(n). Specifically: For each sample, generate a dimension of... A random distribution between 0 and 1 is used to compare this random distribution with the probability model. For each value, if the former value is less than the latter value, the corresponding dimension of the current sample is set to 1; otherwise, it is set to 0.

3. The subset selection method based on distribution estimation algorithm as described in claim 1, characterized in that, In step three, the objective function calculation module is specifically implemented as follows: Construct a variant of the one-max problem, with the objective function being: （3） in for A 0-1 binary decision vector of dimension. As input to the objective function ;when The objective function reaches its maximum value, which is also the optimal value, when the values ​​of the 6th-10th, 20th-24th, 54th-58th, and 96th-100th dimensions of the vector are 1.

4. The subset selection method based on distribution estimation algorithm as described in claim 1, characterized in that, In step four, for a minimization optimization problem, the objective function value can be negative to transform it into a maximization optimization problem, and the objective function value with the largest value can be extracted. 1 sample is used as a training sample, where This indicates the floor function.

5. The subset selection method based on distribution estimation algorithm as described in claim 1, characterized in that, In step five, the learning samples extracted in step four are used to update the probability model M, and the update process specifically includes correction and mutation. The correction and mutation process is carried out cyclically, using all training samples to adjust the probabilistic model in turn. Update; the mathematical form of each correction process is: （1） in, Representing a probabilistic model No. The probability value of dimension, ; Symbols in equation (1) The left side represents the updated version. The right side represents the update formula; This indicates the set learning rate; Indicates the first The first sample Dimension value, , ; Furthermore, a floating-point number is randomly generated between 0 and 1; if this number is less than the set mutation probability... Then, mutation occurs, and the mathematical form of each mutation process is: （2） in, Representing a probabilistic model No. The probability value of dimension, ; Symbols in equation (2) The left side represents the mutated version. The right side represents the mutation formula; This indicates that a random number is generated, with a value of 0 or 1; This indicates the set amount of variation.

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