CN115099385B - Spectrum map construction method based on sensor layout optimization and adaptive Kriging model - Google Patents

Abstract

The present invention discloses a spectrum map construction method based on sensor layout optimization and adaptive Kriging model, belonging to the field of communication technology. The method comprises optimizing and selecting the sensor layout by using an improved artificial bee colony algorithm; finding a sensor estimation group from the selected sensors; calculating the semivariogram function value and fitting the semivariogram function; constructing an adaptive Kriging model, and constructing a spectrum map according to the adaptive Kriging model. The method for constructing a spectrum map proposed by the present invention has high accuracy.

Description

Spectrum map construction based on sensor layout optimization and adaptive Kriging model Method

Technical Field

The present invention belongs to the field of communication technology, and in particular relates to a spectrum map construction method based on sensor layout optimization and an adaptive Kriging model.

Background Art

In order to cope with the rapidly growing demand for frequency and the increasingly severe "spectrum deficit", cognitive radio technology has been proposed and developed rapidly. Its core idea is to adapt to the external wireless environment by sensing and understanding the electromagnetic environment and adaptively adjusting the working parameters of the radio system (such as frequency, power, modulation and coding method, etc.). The electromagnetic spectrum map aggregates the use of electromagnetic spectrum in a certain area, including spectrum data such as the frequency, strength, location, and historical change of each signal, and visualizes the regional electromagnetic environment. It can provide support for cognitive radio systems to grasp the occupancy of the surrounding electromagnetic spectrum, scientifically select available frequencies, and avoid potential frequency conflicts.

The spectrum data required for electromagnetic spectrum maps usually come from spectrum sensing networks composed of sensors with radio signal monitoring, receiving and processing capabilities, such as cognitive communication networks composed of cognitive radio nodes, spectrum monitoring networks composed of networked and collaborative spectrum monitoring nodes, etc. Studies have shown that the location layout of each node in these networks has a great impact on the generation performance of electromagnetic spectrum maps. In recent years, the construction of electromagnetic spectrum maps has faced two major challenges. First, the relationship between the accuracy of spectrum map generation and sensor layout is not clear enough. Most existing works randomly sample sensor locations to return sample data for building spectrum maps. For traditional random sampling layouts, increasing the number of sensors is the most effective solution for complex and adversarial application environments, but at the same time it brings problems such as increased data return and computing overhead, and unreliable links. Therefore, if the inherent characteristics of the spatial spectrum situation can be fully utilized, it is possible to generate spectrum maps with less data requirements. Second, the impact of signal propagation models is rarely considered during the construction of spectrum maps. Due to the above challenges, existing methods are difficult to construct spectrum maps with high accuracy.

Summary of the invention

Technical problem: The present invention provides a spectrum map construction method based on sensor layout optimization and adaptive Kriging model, which can improve construction accuracy.

Technical solution: The present invention provides a spectrum map construction method based on sensor layout optimization and adaptive Kriging model, comprising:

The improved artificial bee colony algorithm is used to optimize the sensor layout;

Finding a sensor estimation group from among the preferred sensors;

Calculate semivariogram values and fit semivariograms;

An adaptive Kriging model is constructed, and a frequency spectrum map is constructed according to the adaptive Kriging model.

Furthermore, the improved artificial bee colony algorithm includes improvements to the disturbance mechanism and fitness function, as well as improvements to the artificial bee colony.

Furthermore, the disturbance mechanism is improved as follows: the next state is explored by exchanging selected sensors with unselected sensors, wherein the selected sensors represent sensors used for interpolation and the unselected sensors represent sensors to be interpolated.

Furthermore, the perturbation mechanism and fitness function are used to generate new solutions, including:

When selecting the sensor to be replaced, consider replacing the sensor that has the least impact on the interpolation accuracy of the current sensor layout;

The sensor with the smallest impact on the interpolation accuracy in the current layout is determined by m-times interpolation error calculation. This point will be regarded as the sensor with the upper limit of exploration by the scout bee and will be discarded first in the next state transfer.

When selecting the sensors to be inserted, the respective weights η _i are considered according to the RMSE of each sensor.

Furthermore, the fitness function is shown in formula (5):

In the formula, is the estimated value for the unselected sensor, is the real data, and m ^* is the number of sensors.

Furthermore, the improvement of the artificial bee colony includes:

The employed bees search for new sensors according to formula (6), that is, generate a new sensor layout and share the sensor layout information with the observing bees, and select the sensor layout with the smallest fitness function value f according to the greedy strategy to maintain the optimal solution:

v _ij =η _kj ×x _kj (6)

Where, k＝1,2,...,NP j＝1,2,...,D and k≠i, η _kj is the weight matrix; _vij represents the new solution found by the employed bees.

The observation bee calculates the selection probability of each sensor according to formula (7), and gives priority to sensors with higher weights based on the information shared by the employed bees, thereby improving the convergence speed:

The scout bee discards the sensors that have reached the exploration limit and have low weights and searches for a new valuable sensor according to formula (8), thereby enhancing the ability to escape from the local optimum:

Where, r _ij is a random number between [0,1]; x _ij represents the new solution found by the scout bee; and Represents the upper and lower bounds of the j-th dimension of the problem.

Furthermore, the optimizing selection of sensor layout by using the improved artificial bee colony algorithm includes:

Initialize sensor position;

Hired bees generate new solutions based on the improved perturbation mechanism;

The observer bee generates new solutions from p _i according to probability;

The solution that the scout bee decided to abandon;

After multiple iterations, the optimal sensor position is output.

Furthermore, the method for finding a sensor estimation group from the selected sensors is: establishing a sensor estimation group Ω ₀ of the unknown point s ₀ according to the decorrelation distance d _cor , and the decorrelation distance of the unknown point is defined by the Moran index.

Furthermore, the semivariance value is calculated using the following formula:

Where _si is the point ( _xi , _yi ), _dij is the distance between the point ( _xi , _yi ) and the point ( _xj , _yj ), and N( _dij ) is the number of points with a distance h between them;

The semivariogram is fitted using an exponential model and by least squares fitting.

Furthermore, the method for constructing the adaptive Kriging model is: solving a set of linear equations called the Kriging model by the Lagrange multiplier method to obtain the weight coefficient ω _i , and the linear system is given by formula (12):

Where γ _ij is the semivariogram value between point (x _i , y _i ) and point (x _j , y _j ), φ is the Lagrange multiplier, and the weight coefficient ω _i is the estimated value that satisfies the point (x ₀ , y ₀ ) The optimal set of coefficients with the smallest difference from the true value P ₀ is At the same time, it satisfies the conditions for unbiased estimation γ _io is expressed as the semivariogram value between location i and the estimation point.

According to formula (13), the estimated point value is calculated

In the formula, is the estimated value of an attribute at the point (x ₀ ,y ₀ ), and _Pi is the sample value.

Compared with the prior art, the present invention firstly uses an improved artificial bee colony algorithm to generate the optimal sensor layout, which greatly improves the spectrum map recovery performance compared with the random layout. On this basis, an adaptive Kriging model based on shadow fading autocorrelation is proposed to construct the spectrum map. Considering the significant autocorrelation between sensor attributes caused by shadow fading with exponential decay of signal propagation, the spatial autocorrelation theory is introduced to establish the sensor estimation group, and the estimation result is obtained through the Kriging model. The simulation results show that the method of the invention has a huge performance advantage over other methods, can improve the construction accuracy of the spectrum map, and greatly reduce the overhead of sensor resources.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a spectrum map construction method based on sensor layout optimization and adaptive Kriging model in an embodiment of the present invention;

FIG2 is a flow chart of a spectrum map construction process according to an embodiment of the present invention;

3 is a schematic diagram of a sensor estimation group for establishing points according to decorrelation distances in an embodiment of the present invention;

FIG4 is a performance comparison curve of constructing a spectrum map when the standard deviation of shadow fading is 1 dB in a simulation experiment;

FIG5 is a curve diagram showing the performance comparison of spectrum map construction when the standard deviation of shadow fading is 3 dB in the simulation experiment;

FIG6 is a curve diagram showing the performance comparison of spectrum map construction when the standard deviation of shadow fading is 6 dB in the simulation experiment;

FIG7 is a graph showing the performance comparison of four methods for constructing spectrum maps;

Figure 8(a) is a schematic diagram of the original spectrum map simulation;

Figure 8(b) is a schematic diagram of spectrum map simulation constructed using ABC-SA;

Figure 8(c) is a schematic diagram of spectrum map simulation constructed using Random-IDW;

Figure 8(d) is a schematic diagram of spectrum map simulation constructed using Random-Splines;

Figure 8(e) is a schematic diagram of spectrum map simulation constructed using Random-NN;

FIG9 is a graph showing the RMSE performance based on actual measurement data.

DETAILED DESCRIPTION

The present invention is further described below in conjunction with the embodiments and drawings of the specification. First, the network architecture of the present application is as follows:

Multiple radiation sources and a set of sensors are arranged in the target area, where the location and transmission power of the radiation sources are unknown. The sensor measures the received signal strength (RSS) and is represented by P( _mi ), where _mi is the sensor location. The received signal power of sensor _mi can be modeled as:

P(m _i )＝K+10εlog ₁₀ (||m _p -m _i ||)+W _p(m) (1)

Where K is the free space path loss factor, ε is the path loss exponent, point m _p represents the location of a radiation source, and ||·|| represents the Euclidean distance between two vectors. is the shadow loss at point _mi that follows a log-normal distribution with standard deviation σ[17]. Therefore, the shadow fading at point _mi and point m _j shadow fading The correlation coefficient between

where d _cor is the correlation distance when ρ _i,j = 1/e. In this case, the shadow correlation coefficient ρ _i,j decreases exponentially as the distance between the receivers increases.

The process of modeling the spectrum map construction problem is divided into three operations: collecting sensor measurements, selecting sensors, and evaluating the field strength or power value at any location.

Assume that the set of given area grids is N, the set of all sensors is M, and select a subset from them As sensors used to construct spectrum maps, the present invention aims to determine the area M and the position of each sensor, given the number of available sensors m ^* =|M ^* |, and select the optimal set m ^* so that the RMSE error between the field strength estimation value and the actual value of the constructed spectrum map is minimized.

In the formula, represents the estimated values of all points in the grid, represents the true value, and N is the total number of grids.

The problem is modeled as:

Problem (3) is a combinatorial optimization problem, and it is difficult to obtain the global optimal solution in linear time.

Based on this, Figure 1 shows a flow chart of a spectrum map construction method based on sensor layout optimization and adaptive Kriging model in this application. In conjunction with Figure 1, the method of this application includes the following steps:

Step S100: Optimize the sensor layout using the improved artificial bee colony algorithm. In this application, the improved artificial bee colony algorithm mainly improves its disturbance mechanism and fitness function, as well as the artificial bee colony. The following is an explanation of the process of optimizing the sensor layout using the improved artificial bee colony algorithm, as shown in FIG2 , and in the explanation process, each improvement point is described in detail.

First, an initial solution _xi (i=1, 2, ... NP) is randomly generated in the search space, where NP represents the number of employed bees and each solution _xi is a D-dimensional vector, where D is the dimension of the problem.

Second, a new perturbation mechanism and fitness function are proposed. The next state is explored by exchanging the selected sensors with the unselected sensors. The selected sensors represent the sensors used for interpolation, and the unselected sensors represent the sensors to be interpolated. When selecting the sensors to be replaced, the sensors with the least impact on the interpolation accuracy of the current sensor layout are considered. The number of sensors in the current state is M ^* , and their numbers are Then, the sensor with the least impact on the interpolation accuracy in the current layout is determined by M ^* interpolation error calculations. This point will be regarded as the sensor of the exploration upper limit by the scout bee and will be discarded first in the next state transfer. At the same time, when selecting the sensor to be inserted, the respective weight η _i will be considered according to the RMSE of each sensor. The sensor with a larger weight (i.e., a larger RMSE) will be more likely to be selected, which will speed up the optimization selection of the sensor layout. Assuming that the number of sensors of the target is m, m ^* sensors are randomly selected as the starting state. Through these m ^* sensors, the attribute values of the other mm ^* sensors are estimated and compared with the known values to calculate the root mean square error RMSE for artificial bee colony decision-making. The formula is as follows:

In the formula, is the estimated value for the unselected sensor, It is real data.

Third, improve the artificial bee colony. The employed bees search for new sensors according to equation (6), that is, generate a new sensor layout and share the sensor layout information with the observer bees, and select the sensor layout with the smallest fitness function value f according to the greedy strategy to maintain the optimal solution.

v _ij =η _kj ×x _kj (6)

Where, k＝1,2,...,NP j＝1,2,...,D and k≠i, η _kj is the weight matrix; _vij represents the new solution found by the employed bees.

The observer bee calculates the selection probability of each sensor according to formula (7), and preferentially selects sensors with higher weights according to formula (6) based on the information shared by the employed bees to improve the convergence speed.

Where f is the fitness of each solution.

The scout bee discards the sensors that have reached the exploration limit and have low weights and searches for a new valuable sensor according to formula (8), thereby enhancing the ability to escape from the local optimum.

In the formula, _rij is a random number between [0,1], and Represents the upper and lower bounds of the j-th dimension of the problem.

Step S200: searching for a sensor estimation group from the preferred sensors.

In the propagation model of equation (1), the signal usually exists in the form of clusters, and the hole area is much larger than the spectrum occupied area, so theoretically the spatial autocorrelation of the spectrum map is significant. The most commonly used statistic is Global Moran’I, which is mainly used to describe the average correlation degree of all spatial units with the surrounding areas in the entire area. The calculation formula is as follows:

Where, I is Moran'I, and its value range is generally between -1 and 1. When I>0, it means that the attribute values in the target area have positive correlation in space. I＝0 means random distribution in the target area without spatial correlation. When I<0, it means that the attribute values in the target area have negative correlation in space. n is the total number of spatial units; z _i and z _j represent the attribute values of the i-th spatial unit and the j-th spatial unit respectively; is the mean of all spatial unit attribute values; w _ij is the spatial weight value. The unknown point s ₀ is defined by the Moran index to define the decorrelation distance, d _cor . As shown in FIG3 , the sensor estimation group of point s ₀ is established according to the decorrelation distance d _cor , Ω ₀ .

Step S300: Calculate the semivariogram value and fit the semivariogram.

The semivariogram is the core part of the Kriging model, which quantitatively describes the variable characteristics of the entire region. The semivariogram value is calculated according to formula (10).

Where _si is point ( _xi , _yi ), _dij is the distance between point ( _xi , _yi ) and point ( _xj , _yj ), and N( _dij ) is the number of points with a distance of h. Select a suitable theoretical model to fit an optimal theoretical semivariogram curve to more accurately reflect the variation law of the variable. The semivariogram _γij conforms to the first law of geography, and attributes that are similar in space are similar. Its theoretical models include the pure gold nugget effect model, spherical model, exponential model, Gaussian model, etc. It has been proved by formula (2) that the spatial shadow fading coefficient follows exponential decay, so the fitting of the semivariogram adopts an exponential model and is fitted by least squares:

Where h is the distance between any two points; C ₀ is the nugget constant; C ₀ +C is the sill value; a is the step length corresponding to the intersection of the tangent line of the model at the origin and the sill value.

Step S400: construct an adaptive Kriging model, and construct a spectrum map according to the adaptive Kriging model. Specifically, according to steps S200 and S300, select sensors whose distance from the estimated point (x ₀ , y ₀ ) is less than the decorrelation distance d _cor from the sensor sample to establish a sensor estimation group, denoted by Ω ₀ . According to formula (10), the semivariogram values γ _ij between sensors in the estimation group and the semivariogram values between each sensor and the estimation point are calculated. Then, a set of linear equations called the Kriging model is solved by the Lagrange multiplier method to obtain the weight coefficient ω _i , and the linear system is given by the following formula:

Where γ _ij is the semivariogram value between point (x _i , y _i ) and point (x _j , y _j ), φ is the Lagrange multiplier, and the weight coefficient ω _i is the estimated value that satisfies the point (x ₀ , y ₀ ) The optimal set of coefficients with the smallest difference from the true value P ₀ is At the same time, it satisfies the conditions for unbiased estimation γ _io is expressed as the semivariogram value between location i and the estimation point.

Finally, the estimated point value is calculated according to formula (11):

In the formula, is the estimated value of a certain attribute at the point (x ₀ , y ₀ ), and _Pi is the sample value.

It should be noted that in the above formula, i, j, and k only represent serial numbers.

In order to verify that the method of the present application has higher accuracy in constructing spectrum maps than existing methods. In this embodiment, the performance of the proposed spectrum map construction scheme will be evaluated by simulation data and real data. The experiment randomly selects 1000 sensors from all sensors as known sensors. Under different shadow fading standard deviations, the spectrum map construction performance of different algorithms is analyzed and compared. The parameter settings of the simulation data are shown in Table 1.

Table 1 Simulation parameters

parameter value Regional Dimension 100× ^100m2 Signal transmission power 30dBm, 50dBm, 60dBm Signal transmission Cartesian coordinates (20,80), (80,80), (80,20) Signal frequency 5000MHz Shadow fading standard deviation 1dB, 3dB, 6dB

The real data experiment used a data set publicly available on IEEE Dataport. The data is real spectrum data measured at 811MHz and 2630MHz using Rohde & Schwarz (R&S) TSMW, including signal power, signal-to-noise ratio, signal reception strength, etc. Each measurement is synchronized with GPS positioning. The experiment was measured on the campus of the Technical University of Denmark. The mobile spectrum observation equipment traveled about 14km and generated about 60,000 data points. All random experimental results in simulation experiments and real data are the average of 500 random experiments. Accuracy is an important criterion for algorithm performance, so the mean square error (RMSE) is used to analyze the accuracy of the RMSE construction, which can be expressed as:

Where l and w are the length and width of the target area, respectively. is the interpolated estimate, and _Pij is the real data.

As shown in Figures 4, 5 and 6, four different algorithms, including Random-OK, Random-AK, ABC-OK and ABC-AK, are compared and analyzed based on different standard deviations of shadow fading in simulation data to build spectrum maps. It can be seen that the RMSE of the four algorithms increases with the increase of the standard deviation of shadow fading. The performance of ABC-AK is better than that of the other three algorithms, indicating that ABC-AK has strong robustness. When the number of sensors is less than 300, under the same construction method, the spectrum construction performance of sensor optimization selection is better than that of random selection. In the same sensor selection method, adaptive Kriging has better spectrum construction performance than ordinary Kriging.

As shown in Figure 7, the RMSE of spectrum map construction using four different algorithms, including Random-OK, Random-AK, ABC-OK, and ABC-AK, is compared and analyzed based on measured data. It can be seen that: (1) The RMSE of all algorithms decreases with the increase in the number of sensors, and ABC-SLO-SA-AK has the best performance in spectrum map construction. Under sensor optimization selection, the RMSE of ABC-AK is 0.30 dBm lower than that of ABC-OK on average. Under random sensor selection, the RMSE of the Random-AK algorithm is 0.38 dBm lower than that of the Random-OK algorithm. (2) Under ordinary Kriging construction, the RMSE of the ABC-OK algorithm is 0.71 dBm lower than that of Random-OK on average. Under adaptive Kriging construction, the RMSE of the ABC-AK algorithm is 0.63 dBm lower than that of Random-AK on average. In the experiment, the AK algorithm has better performance under the ABC-SLO algorithm. This is because the AK algorithm uses an adaptive estimation group to reduce the impact of low-correlation sensors on interpolation errors, which is more conducive to generating an optimized layout.

As shown in Figure 8, the location of the original map, signal source strength, and spectrum map construction are compared between the results of different spectrum map construction methods when the shadow fading standard deviation is 3 dB and the number of sensors is 100. It can be found that the ABC-SA algorithm performs well in signal source location and source signal strength recovery.

As shown in Figure 9, in order to further prove the widespread effectiveness of the algorithm, this paper compares different spectrum map construction algorithms based on measured data, including ABC-SA, IDW[24], NN[25], and Splines. It can be seen that the RMSE of each algorithm decreases with the increase in the number of sensors, which shows that increasing the sample rate is an important factor in improving the accuracy of spectrum maps. Among the four algorithms, the RMSE of the ABC-AK algorithm is always smaller than that of the other three algorithms and is 1.80dBm, 1.53dBm, and 0.97dBm lower than the RMSE of the Random-NN, Random-Splines, and Random-IDW algorithms, respectively. This proves that in practice, the ABC-SLO-SA-AK algorithm has better spectrum map construction performance than other algorithms.

The present invention proposes a spectrum map construction method based on sensor layout optimization selection and adaptive Kriging model in sensor networks, which realizes high-precision spectrum map construction. A large number of simulation results show that the spectrum map construction performance of the proposed method is improved by 37.56%, 25.32% and 12.89% respectively compared with Rondom-OK performance when the standard deviation of shadow fading is 1dB, 3dB and 6dB.

The above embodiments are only preferred implementation modes of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and equivalent substitutions without departing from the principles of the present invention. These technical solutions after improvements and equivalent substitutions to the claims of the present invention all fall within the protection scope of the present invention.

Claims (2)

1. A spectrum map construction method based on sensor layout optimization and adaptive Kriging model, characterized by comprising: The improved artificial bee colony algorithm is used to optimize the sensor layout; Finding a sensor estimation group from among the preferred sensors; Calculate semivariogram values and fit semivariograms; constructing an adaptive Kriging model, and constructing a spectrum map according to the adaptive Kriging model; Wherein, the improved artificial bee colony algorithm includes improvements to the disturbance mechanism and fitness function, as well as improvements to the artificial bee colony; The improvement of the perturbation mechanism is: the next state is explored by exchanging the selected sensor and the unselected sensor, wherein the selected sensor represents the sensor for interpolation and the unselected sensor represents the sensor to be interpolated; the perturbation mechanism and the fitness function are used to generate a new solution, including: When selecting the sensor to be replaced, consider replacing the sensor that has the least impact on the interpolation accuracy of the current sensor layout; The sensor with the smallest impact on the interpolation accuracy in the current layout is determined by m-times interpolation error calculation. This point will be regarded as the sensor with the upper limit of exploration by the scout bee and will be discarded first in the next state transfer. When selecting the sensors to be inserted, the respective weights η _i are considered according to the RMSE of each sensor; The fitness function is shown in formula (5): In the formula, is the estimated value for the unselected sensor, is the real data, m ^* is the number of sensors; The improvement of the artificial bee colony comprises: The employed bees search for new sensors according to formula (6), that is, generate a new sensor layout and share the sensor layout information with the observing bees, and select the sensor layout with the smallest fitness function value f according to the greedy strategy to maintain the optimal solution: v _ij =η _kj ×x _kj (6) Where, k = 1, 2, ..., NP j = 1, 2, ..., D and k ≠ i, η _kj is the weight matrix; x _ij represents the new solution found by the scout bee; vi _ij represents the new solution found by the employed bee; The observation bee calculates the selection probability p _i of each sensor according to formula (7), and gives priority to sensors with higher weights according to the information shared by the employed bees, thereby improving the convergence speed: The scout bee discards the sensors that have reached the exploration limit and have low weights, and searches for a new valuable sensor according to formula (8) to enhance the ability to escape from the local optimum: In the formula, r _ij is a random number between [0,1]; and Represents the upper and lower limits of the j-th dimension of the problem; The method for finding a sensor estimation group from the selected sensors is as follows: establishing a sensor estimation group Ω ₀ of an unknown point s ₀ according to a decorrelation distance d _cor , wherein the decorrelation distance of the unknown point is defined by a Moran index; The semivariance value is calculated using the following formula: Where _si is the point ( _xi , _yi ), _dij is the distance between the point ( _xi , _yi ) and the point ( _xj , _yj ), and N( _dij ) is the number of points with a distance h between them; The fitting of the semivariogram adopts an exponential model and is performed by least squares fitting; The method for constructing the adaptive Kriging model is: solving a set of linear equations called the Kriging model by the Lagrange multiplier method to obtain the weight coefficient ω _i , and the linear system is given by formula (12): Where γ _ij is the semivariogram value between point (x _i , y _i ) and point (x _j , y _j ), φ is the Lagrange multiplier, and the weight coefficient ω _i is the estimated value that satisfies the point (x ₀ , y ₀ ) The optimal set of coefficients with the smallest difference from the true value P ₀ is At the same time, it satisfies the conditions for unbiased estimation γ _io is expressed as the semivariogram value between location i and the estimation point; According to formula (13), the estimated point value is calculated In the formula, is the estimated value of an attribute at the point (x ₀ ,y ₀ ), and _Pi is the sample value. 2. The method according to claim 1, characterized in that the optimizing and selecting the sensor layout by using the improved artificial bee colony algorithm comprises: Initialize sensor position; Hired bees generate new solutions based on the improved perturbation mechanism; The observer bee generates new solutions from the sensor positions according to probability p _i ; The solution that the scout bee decided to abandon; After multiple iterations, the optimal sensor position is output.