CN113077082A - Mining area mining subsidence prediction method based on improved crow search algorithm - Google Patents

Mining area mining subsidence prediction method based on improved crow search algorithm Download PDF

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CN113077082A
CN113077082A CN202110323901.4A CN202110323901A CN113077082A CN 113077082 A CN113077082 A CN 113077082A CN 202110323901 A CN202110323901 A CN 202110323901A CN 113077082 A CN113077082 A CN 113077082A
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郭庆彪
陈红凯
罗锦
王亮
吕鑫
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Anhui University of Science and Technology
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Abstract

The invention relates to a mining area mining subsidence prediction method based on an improved crow search algorithm, which comprises the following steps of: s1, introducing a Levy flight strategy, a leader strategy and a replacement crow strategy into the crow search algorithm for improvement based on the crow search algorithm to obtain an improved crow search algorithm; and S2, introducing the improved crow search algorithm into probability integral parameter inversion to establish a probability integral parameter inversion model based on the improved crow search algorithm, and performing settlement prediction calculation through the model to obtain a settlement probability predicted value. According to the mining area mining subsidence prediction method based on the improved crow search algorithm, on the basis of the crow search algorithm, a Levy flight strategy, a leader strategy and a replacement crow strategy are introduced, a probability integration method parameter inversion model based on the improved crow search algorithm is constructed, the probability integration method parameter inversion model is superior to a CAS in the aspects of relative errors of control parameters and errors in fitting, and the probability integration method has a certain random error resistance.

Description

Mining area mining subsidence prediction method based on improved crow search algorithm
Technical Field
The invention belongs to the technical field of mining subsidence prediction in a mining area, and particularly relates to a mining subsidence prediction method based on an improved crow search algorithm, wherein the mining subsidence prediction method is based on an improved crow search algorithm and is used for inverting probability integral parameters.
Background
At present, coal is the main energy source in China. Large-scale mining of coal resources can result in large-scale ground subsidence and disastrous effects on the natural environment. Surface subsidence caused by underground mining activities is a serious engineering, economic and environmental problem. In a broad sense, surface subsidence is the inevitable consequence of underground mining activities, reflecting the state of motion of the mine. Ground subsidence has a serious impact on ground structure, service and communications. In the development of construction sites in ground subsidence areas, extensive remedial measures or special building designs are often required. Therefore, mining subsidence prediction has become the focus of attention of scholars at home and abroad.
In the 50 s of the 20 th century, the Polish student J.Litteringzyn (J.Litwiniszyn) introduced the random medium theory into rock formation mobility research, and then the Chinese student Liubao et al continued to develop the theory into probability integration. In China, the probability integration method is one of the most mature and widely applied settlement prediction methods. Parametric errors and model errors are the main sources of error in probability integration applications. The key for improving the prediction precision of the probability integration method is to reduce model errors and parameter errors. The model error mainly comes from the basic assumption of the method and is difficult to improve, so the meaning of reducing the parameter error is more obvious. Accurate mining subsidence prediction should be based on obtaining accurate parameters. The prediction parameter inversion method of the probability integration method roughly goes through the processes of a linear approximation method, a step acceleration method, an intelligent algorithm and an optimization algorithm. The linear approximation parameter method linearizes probability integral by using the idea of linear approximation, and then calculates parameters according to the least square principle. The initial values are orthogonally designed, and then the real values of the parameters are quickly approximated in a small amount of experiments by utilizing a linear approximation parameter method. However, the method is complicated in calculation process and difficult to popularize. The GE applies a model vector method (step acceleration method) to obtain prediction parameters of mining subsidence. The method solves the problems of acquiring parameters by utilizing the actual measurement data of the mining of the working face with any shape and utilizing the dynamic measurement data. The solving process of the step-size acceleration method can be trapped in a local extreme value trap, and the local optimal solution can be mistaken as the global optimal solution. A probability integral parameter inversion model based on a genetic algorithm is constructed, and certain accuracy, reliability and stability are achieved in parameter calculation. The particle swarm optimization algorithm is proposed to invert the parameters of the probability integration method, and the method has the advantages of high search speed, high efficiency, simple algorithm and the like.
Through analysis of research results, it can be found that when the search range of the algorithm is not sufficient, the genetic algorithm and the particle swarm optimization algorithm are both in local optimization to a certain extent, so that the algorithm is early and converged.
Disclosure of Invention
The invention aims to solve the problems and provide a mining area mining subsidence prediction method based on an improved crow search algorithm.
The invention realizes the purpose through the following technical scheme:
a mining area mining subsidence prediction method based on an improved crow search algorithm comprises the following steps:
s1, introducing a Levy flight strategy, a leader strategy and a replacement crow strategy into the crow search algorithm for improvement based on the crow search algorithm to obtain an improved crow search algorithm;
s2, introducing the improved crow search algorithm into probability integral parameter inversion to establish a probability integral parameter inversion model based on the improved crow search algorithm, and performing settlement prediction calculation through the model to obtain a settlement probability predicted value;
the specific process of introducing the improved crow search algorithm into the probability integral parameter inversion is as follows:
1) setting the maximum number of iterations tmaxPerception probability AP, flight radius riGiving a center value X of a probability integral parameter0＝[q，tanβ，b，θ，s1，s2，s3，s4]And the fluctuation range DeltaX ═ Deltaq, Deltatanβ，Δb，Δs1，Δs2，Δs3，Δs4]Generating an initial crow population
Figure BDA0002993830530000031
And recording the initial crow group position as the memory position M of the crow groupi；
2) Setting a fitness function for judging whether the crow position is good or bad:
Figure BDA0002993830530000032
wherein T is the number of observation stations, Wj、UjAre each XiAs the expected sinking and horizontal displacement values of the probability integral parameters at observation station j,
Figure BDA0002993830530000033
respectively an actually measured sinking value and an actually measured horizontal displacement value on an observation station j;
3) updating the positions of the crows, and searching each crow in the population according to a crow searching formula after introducing a Levy flight strategy and a leader strategy;
4) generating a substitute crow according to a crow search formula after introducing a substitute crow strategy, replacing the crow position beyond a solution space, and updating the crow position;
5) calculating the fitness of the updated crow memory position, and updating the memory position of the crow according to a crow memory position updating formula;
6) and repeating the steps 3) to 5) until the maximum iteration times are reached or the precision condition is met, and outputting the fitness function optimal value in the crow memory value as a result.
As a further optimization scheme of the present invention, the crow search algorithm specifically comprises: assuming that N crows fly in a defined D-dimension search range, the position of food is searched, and a better fitness function value f (X) of the position of the food is foundi，t) Low, where the position of crow i in the t iteration is:
Figure BDA0002993830530000041
wherein i ∈ [1, N ]]，t∈[1，tmax]，tmaxRepresenting the maximum number of iterations;
the best position found by the t iteration of the crow i, namely the memory position of the crow is as follows:
Figure BDA0002993830530000042
in the searching process, the crow has two different modes to update the position of the crow, the crow i randomly follows the crow j, the memory position of the crow j is tried to be found, the crow j has certain perception probability to find that the crow j is tracked, if the crow j is not found, the memory position of the crow j is obtained by the crow i, the state is a first state, if the crow j is found, the crow i is taken to a random position, the state is a second state, and the expression formula of the searching process is as follows:
Figure BDA0002993830530000043
wherein the flight radius riObeying the uniform distribution between 0 and 1, wherein AP represents the perception probability of the crow j, and pl is the flight distance;
after the search is finished, the fitness of the new position of the crow i is compared with the fitness of the memory value of the crow i, the memory position of the crow is updated, and the expression formula is as follows:
Figure BDA0002993830530000044
and after the iteration is finished, taking the crow memory value with the minimum fitness function value as the optimal parameter solution for output.
As a further optimization scheme of the invention, a Levy flight strategy introduced when improving based on a crow search algorithm is specifically as follows:
Figure BDA0002993830530000051
wherein S is the step length, mu and v are normal distribution,
Figure BDA0002993830530000052
Figure BDA0002993830530000053
σv＝1
wherein the value of beta is 1.5;
the crow search formula introduced in the Levy flight strategy is as follows:
Figure BDA0002993830530000054
as a further optimization scheme of the invention, a leader strategy introduced when improving based on a crow search algorithm is specifically as follows: randomly selecting N/2 crows, and taking the memory value of the crows with the optimal fitness as the position M of the leaderleader，tWhen the execution state is one, selecting a leader position for tracking;
the crow search formula after introducing the Levy flight strategy and the leader strategy is as follows:
Figure BDA0002993830530000055
as a further optimization scheme of the invention, a replacement crow strategy introduced when improving based on a crow search algorithm is specifically as follows: when a crow position outside a solution space range is generated in the searching process, a new crow position is randomly generated in the solution space to replace the position to participate in the next iterative calculation;
the crow search formula after introducing the replacement crow strategy is as follows:
Figure BDA0002993830530000056
the invention has the beneficial effects that:
1) on the basis of a crow search algorithm, a Levy flight strategy, a leader strategy and a replacement crow strategy are introduced, a probability integration method parameter inversion model based on an improved crow search algorithm is constructed, a simulation test is designed to discuss the inversion capability of the model, and the results of the simulation test show that: relative errors of ICAS inversion parameters q, tan beta, b and theta are respectively 0.12%, 0.39%, 0.54% and 0.15%, relative errors of inflection point offset distance are not more than 2.8% at most, and comparative analysis proves that ICAS is superior to CAS in the aspects of relative errors of control parameters and errors in fitting; (ii) a
2) The invention designs an observed value with random errors to verify the anti-interference capability of the model, and the result shows that: under the interference of random errors, although the relative errors of the parameter fitting results and the errors in fitting are increased slightly, the accuracy and precision are still kept at a higher level, which shows that the parameter inversion model introduced based on the improved crow search algorithm has certain random error resistance.
Drawings
FIG. 1 is a flow chart of the improved crow search algorithm inverting probability integral parameters of the present invention;
FIG. 2 is a Levy flight trajectory diagram of the invention;
FIG. 3 is a diagram of a simulation experiment working surface of the present invention;
FIG. 4 is a diagram of the absolute error analysis data of ICAS and CAS predicted values of the present invention.
Detailed Description
The present application will now be described in further detail with reference to the drawings, it should be noted that the following detailed description is given for illustrative purposes only and is not to be construed as limiting the scope of the present application, as those skilled in the art will be able to make numerous insubstantial modifications and adaptations to the present application based on the above disclosure.
Example 1
As shown in fig. 1-2, a mining area mining subsidence prediction method based on an improved crow search algorithm includes the following steps:
s1, introducing a Levy flight strategy, a leader strategy and a replacement crow strategy into the crow search algorithm for improvement based on the crow search algorithm to obtain an improved crow search algorithm;
s2, introducing the improved crow search algorithm into probability integral parameter inversion to establish a probability integral parameter inversion model based on the improved crow search algorithm, and performing settlement prediction calculation through the model to obtain a settlement probability predicted value;
the probability integration method is used for calculating the expected value of mining subsidence and the horizontal movement value of any point A (x, y) on the earth's surface according to the following formula:
Figure BDA0002993830530000071
wherein the content of the first and second substances,
W0＝mq cosα
Figure BDA0002993830530000072
Figure BDA0002993830530000073
in the formula, D1And D3Respectively the inclined length and the strike length of a mining working face, m is the average mining thickness of the working face, q is a sinking coefficient, alpha is the inclination angle of the working face, tan beta is the main influence angle tangent, H, H1、H2Respectively including the mining depth at the main broken line position, the mining depth at the upper boundary and the mining depth at the lower boundary of the working face3Calculating the length, l, for the working face run3＝D3-S3-S4，l1The length is calculated for the working face trend,
Figure BDA0002993830530000074
wherein S is1、S2、S3、S4The inflection point offset distance of the rising mountain, the inflection point offset distance of the falling mountain, the inflection point offset distance of the open-cut eye and the inflection point offset distance of the stoping line are respectively.
Arbitrary point A (x, y) of the earth's surface
Figure BDA0002993830530000081
(angular value of positive counterclockwise of x-axis to specified direction) horizontal displacement in direction:
Figure BDA0002993830530000082
wherein r is the major influence radius, b is the horizontal shift coefficient,
Figure BDA0002993830530000083
to sink W (x, y) in
Figure BDA0002993830530000084
The directional derivative of direction, i.e.
Figure BDA0002993830530000085
The method is characterized in that a crow searching algorithm proposed by simulating foraging behavior of crow is assumed to have four points, wherein one point is that the crow lives in a social form, the other point is that the crow hides own food and remembers the position of the crow, the third point is that the crow tracks other crow and tries to find the food position of other crow, and the fourth point is that the crow senses that the crow is tracked by a certain probability and brings a tracker to a random position.
The crow search algorithm based on the four-point hypothesis specifically comprises the following steps: assuming that N crows fly in a defined D-dimension search range, the position of food is searched, and a better fitness function value f (X) of the position of the food is foundi，t) Low, where the position of crow i in the t iteration is:
Figure BDA0002993830530000086
wherein i ∈ [1, N ]]，t∈[1，tmax]，tmaxRepresenting the maximum number of iterations;
the best position found by the t iteration of the crow i, namely the memory position of the crow is as follows:
Figure BDA0002993830530000087
in the searching process, the crow has two different modes to update the position of the crow, the crow i randomly follows the crow j, the memory position of the crow j is tried to be found, the crow j has certain perception probability to find that the crow j is tracked, if the crow j is not found, the memory position of the crow j is obtained by the crow i, the state is a first state, if the crow j is found, the crow i is taken to a random position, the state is a second state, and the expression formula of the searching process is as follows:
Figure BDA0002993830530000091
wherein the flight radius riObeying the uniform distribution between 0 and 1, wherein AP represents the perception probability of the crow j, and pl is the flight distance;
after the search is finished, the fitness of the new position of the crow i is compared with the fitness of the memory value of the crow i, the memory position of the crow is updated, and the expression formula is as follows:
Figure BDA0002993830530000092
and after the iteration is finished, taking the crow memory value with the minimum fitness function value as the optimal parameter solution for output.
The Levy flight strategy introduced when improving based on the crow search algorithm is specifically as follows:
Figure BDA0002993830530000093
wherein S is the stepLong, mu, v are normally distributed,
Figure BDA0002993830530000094
Figure BDA0002993830530000095
σv＝1
wherein the value of beta is 1.5;
the crow search formula introduced in the Levy flight strategy is as follows:
Figure BDA0002993830530000096
the leader strategy introduced when improving based on the crow search algorithm is specifically as follows: randomly selecting N/2 crows, and taking the memory value of the crows with the optimal fitness as the position M of the leaderleader，tWhen the execution state is one, selecting a leader position for tracking;
the crow search formula after introducing the Levy flight strategy and the leader strategy is as follows:
Figure BDA0002993830530000101
the replacement crow strategy introduced when improving based on the crow search algorithm is specifically as follows: when a crow position outside a solution space range is generated in the searching process, a new crow position is randomly generated in the solution space to replace the position to participate in the next iterative calculation;
the crow search formula after introducing the replacement crow strategy is as follows:
Figure BDA0002993830530000102
when the improved crow search algorithm is introduced into the probability integral parameter inversion, the method specifically comprises the following steps:
1) setting the maximum number of iterations tmaxPerception probability AP, flight radius riGiving a center value X of a probability integral parameter0＝[q，tanβ，b，θ，s1，s2，s3，s4]And a fluctuation range Δ X ═ Δ q, Δ tan β, Δ b, Δ s1，Δs2，Δs3，Δs4]Generating an initial crow population
Figure BDA0002993830530000103
And recording the initial crow group position as the memory position M of the crow groupi；
2) Setting a fitness function for judging whether the crow position is good or bad:
Figure BDA0002993830530000104
wherein T is the number of observation stations, Wj、UjAre each XiAs the expected sinking and horizontal displacement values of the probability integral parameters at observation station j,
Figure BDA0002993830530000105
respectively an actually measured sinking value and an actually measured horizontal displacement value on an observation station j;
3) updating the positions of the crows, and searching each crow in the population according to a crow searching formula after introducing a Levy flight strategy and a leader strategy;
4) generating a substitute crow according to a crow search formula after introducing a substitute crow strategy, replacing the crow position beyond a solution space, and updating the crow position;
5) calculating the fitness of the updated crow memory position, and updating the memory position of the crow according to a crow memory position updating formula;
6) and repeating the steps 3) to 5) until the maximum iteration times are reached or the precision condition is met, and outputting the fitness function optimal value in the crow memory value as a result.
Experimental example 1
In order to verify the feasibility and the inversion accuracy of the improved crow algorithm and verify the feasibility and the inversion accuracy of the improved crow algorithm, a simulation experiment is designed, and the working surface of the simulation experiment is established as follows: rectangular working face trend length D3800m, inclined mining length D1The average mining thickness m of the coal seam is 3.0m, the dip angle alpha of the coal seam is 5 degrees, the average mining depth H is 400m, a roof is managed by adopting a caving method, and monitoring points (E1-E51) are arranged on a main section of the strike at intervals of 30m in a simulated mode; monitoring points (N52-N92) are arranged on the inclined main section at intervals of 30m simulation. The prediction parameters of the probability integration method are respectively as follows: the subsidence coefficient q is 0.8, the horizontal movement coefficient b is 0.3, the main influence tangent tan β is 2.0, the mining influence propagation angle θ is 87 °, the inflection offset S1 is S2, S3, S4 is 0.1H.
The simulated work surface is shown in figure 3.
And generating a simulated sinking observation value and a simulated horizontal movement value by using the set probability integral parameters, respectively inverting the probability integral parameters by using an original crow searching algorithm and an improved crow searching algorithm, and comparing the relative error and the medium error of the inversion result. Setting the size N of the crow population as 100, the maximum iteration times as 100, and the flight radius riThe perception probabilities AP are 0.1(CAS) and 0.5(ICAS), respectively, at 1. The results of 10 separate runs are shown in Table 1.
TABLE 1 comparison analysis of stability and accuracy of original crow's feet search algorithm and improved crow's feet search algorithm
Figure BDA0002993830530000121
The experimental results in table 1 show that:
in the aspect of parameter relative errors, the relative error of the inversion parameters of the original crow searching algorithm is not more than 8.7%, the relative error of the inversion parameters of the improved crow searching algorithm is controlled within 2.8%, and the relative errors of the parameters inverted by the improved crow searching algorithm are all smaller than those of the original crow searching algorithm.
In the aspect of errors in parameter fitting, except that the errors in fitting of the horizontal movement coefficient b and the horizontal movement coefficient b are not large, the errors in fitting of other improved crow search algorithm inversion parameters are better than those of the original crow search algorithm, the errors in parameter fitting of the original crow search algorithm are not more than 6.12, and the errors in parameter fitting of the improved crow search algorithm are not more than 5.46, so that the improved crow search algorithm is high in parameter precision, and the obtained result is reliable. Simulation experiment results show that compared with the original crow search algorithm, the improved crow search algorithm has more accurate predicted parameters of the inversion probability integration method and higher accuracy of the inversion parameters.
The average value of the 10 times inversion results is used for calculating the expected sinking value and the expected horizontal movement value on each observation station, the absolute error between the expected value and the measured value of the two algorithms is compared, and as can be seen from fig. 4, the absolute error between the expected value and the measured value calculated by the probability integration parameters obtained by ICAS inversion is smaller, and the expected result is more accurate.
In order to research the random error resistance of the improved crow search algorithm probability integral inversion model, on the basis of 3.2 simulation experiments, accidental errors obeying normal distribution N (0,4) and N (0,10) are added to a simulation observation value respectively, 10 times of experiments are carried out in each case, and the experimental results are shown in table 2.
TABLE 2 improved crow search algorithm analysis of random error resistance
Figure BDA0002993830530000131
As can be seen from the data in table 2: after accidental errors of N (0,4) and N (0,10) which obey normal distribution are added, the maximum values of relative errors of the parameters respectively do not exceed 2.8% and 3.5%, and the maximum values of errors in parameter fitting respectively do not exceed 5.5 and 5.8, which shows that under the interference of random errors, although the errors of the parameter fitting results are increased, the precision and the accuracy are still kept at a higher level, and the ICAS parameter inversion model has certain random error resistance.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims (5)

1. A mining area mining subsidence prediction method based on an improved crow search algorithm is characterized by comprising the following steps of:
s1, introducing a Levy flight strategy, a leader strategy and a replacement crow strategy into the crow search algorithm for improvement based on the crow search algorithm to obtain an improved crow search algorithm;
s2, introducing the improved crow search algorithm into probability integral parameter inversion to establish a probability integral parameter inversion model based on the improved crow search algorithm, and performing settlement prediction calculation through the model to obtain a settlement probability predicted value;
the specific process of introducing the improved crow search algorithm into the probability integral parameter inversion is as follows:
1) setting the maximum number of iterations tmaxPerception probability AP, flight radius riGiving a center value X of a probability integral parameter0＝[q，tanβ，b，θ，s1，s2，s3，s4]And a fluctuation range Δ X ═ Δ q, Δ tan β, Δ b, Δ s1，Δs2，Δs3，Δs4]Generating an initial crow population
Figure FDA0002993830520000011
And recording the initial crow group position as the memory position M of the crow groupi；
2) Setting a fitness function for judging whether the crow position is good or bad:
Figure FDA0002993830520000012
wherein T is the number of observation stations, Wj、UjAre each XiEstimated dip as a probability integral parameter at observation station jValue and horizontal displacement value, Wj 0、
Figure FDA0002993830520000013
Respectively an actually measured sinking value and an actually measured horizontal displacement value on an observation station j;
3) updating the positions of the crows, and searching each crow in the population according to a crow searching formula after introducing a Levy flight strategy and a leader strategy;
4) generating a substitute crow according to a crow search formula after introducing a substitute crow strategy, replacing the crow position beyond a solution space, and updating the crow position;
5) calculating the fitness of the updated crow memory position, and updating the memory position of the crow according to a crow memory position updating formula;
6) and repeating the steps 3) to 5) until the maximum iteration times are reached or the precision condition is met, and outputting the fitness function optimal value in the crow memory value as a result.
2. The mining area mining subsidence prediction method based on the improved crow search algorithm is characterized in that the crow search algorithm specifically comprises the following steps: assuming that N crows fly in a defined D-dimension search range, the position of food is searched, and a better fitness function value f (X) of the position of the food is foundi，t) Low, where the position of crow i in the t iteration is:
Figure FDA0002993830520000021
wherein i ∈ [1, N ]]，t∈[1，tmax]，tmaxRepresenting the maximum number of iterations;
the best position found by the t iteration of the crow i, namely the memory position of the crow is as follows:
Figure FDA0002993830520000022
in the searching process, the crow has two different modes to update the position of the crow, the crow i randomly follows the crow j, the memory position of the crow j is tried to be found, the crow j has certain perception probability to find that the crow j is tracked, if the crow j is not found, the memory position of the crow j is obtained by the crow i, the state is a first state, if the crow j is found, the crow i is taken to a random position, the state is a second state, and the expression formula of the searching process is as follows:
Figure FDA0002993830520000023
wherein the flight radius riObeying the uniform distribution between 0 and 1, wherein AP represents the perception probability of the crow j, and pl is the flight distance;
after the search is finished, the fitness of the new position of the crow i is compared with the fitness of the memory value of the crow i, the memory position of the crow is updated, and the expression formula is as follows:
Figure FDA0002993830520000031
and after the iteration is finished, taking the crow memory value with the minimum fitness function value as the optimal parameter solution for output.
3. The mining area mining subsidence prediction method based on the improved crow search algorithm as claimed in claim 2, wherein the Levy flight strategy introduced when the improvement is carried out based on the crow search algorithm is specifically as follows:
Figure FDA0002993830520000032
wherein S is the step length, mu and v are normal distribution,
Figure FDA0002993830520000033
Figure FDA0002993830520000034
σv＝1
wherein the value of beta is 1.5;
the crow search formula introduced in the Levy flight strategy is as follows:
Figure FDA0002993830520000035
4. the mining area mining subsidence prediction method based on the improved crow search algorithm as claimed in claim 2, characterized in that the leader strategy introduced when improving based on the crow search algorithm is specifically: randomly selecting N/2 crows, and taking the memory value of the crows with the optimal fitness as the position M of the leaderleader，tWhen the execution state is one, selecting a leader position for tracking;
the crow search formula after introducing the Levy flight strategy and the leader strategy is as follows:
Figure FDA0002993830520000036
5. the mining area mining subsidence prediction method based on the improved crow's foot search algorithm as claimed in claim 2, characterized in that the replacement crow strategy introduced when improving based on the crow's foot search algorithm is specifically: when a crow position outside a solution space range is generated in the searching process, a new crow position is randomly generated in the solution space to replace the position to participate in the next iterative calculation;
the crow search formula after introducing the replacement crow strategy is as follows:
Figure FDA0002993830520000041
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