Metaheuristic parameter optimization algorithm based on variation chain search

Abstract

The invention belongs to the field of parameter optimization algorithms, discloses a meta-heuristic parameter optimization algorithm based on variation chain search, and particularly relates to a meta-heuristic evolutionary parameter optimization algorithm for variation chain search based on individual characteristics of sample points and overall generality of a sample point set. The method comprises the following specific processing steps: (1) hydrological model parameter determination and hierarchical division; (2) collecting an initial sample group; (3) extracting the optimal evolution direction (acceleration) of the individual; (4) optimizing subgroup division; (5) generating an optimization speed vector; (6) determining a search direction; and (7) convergence conditions. According to the method, on the basis of the similarity and anisotropy between the sample points in the hydrological model parameter optimization process, the sample points are updated and iterated through similarity analysis and a spatial clustering method, and a new thought is provided for the optimization method of the hydrological model.

Description

Technical Field

[0001] The present invention belongs to the field of parameter optimization algorithms, in particular to a parameter calibration method for complex hydrological models. Background Art

[0002] Hydrology studies the relationship and overall nature of Earth's water generation, circulation, distribution, and interactions with the environment. Rapid urbanization and industrialization have led to various changes in hydrological systems, including deforestation, land cover change, and irrigation. Hydrological models are important tools for studying the impacts of climate, soil properties, and other factors on water resources, and they play a crucial role in guiding decision-making related to water resources and the environment. Model parameters determine the quality and usability of simulation results. However, parameter determination methods such as field measurements are prohibitively expensive in terms of both cost and time. Parameter optimization algorithms, as fast and inexpensive parameter determination solutions, are key to reducing parameter uncertainty and improving the practicality of model simulation results.

[0003] Current parameter optimization algorithms can be broadly categorized into two main categories: evolutionary algorithms and traditional parameter optimization algorithms. Evolutionary algorithms are more suitable for parameter optimization in hydrological models. Evolutionary algorithms generally consist of two steps: initial sample point selection and the optimization phase. Existing algorithms primarily use random selection or spatial constraints to limit the sampling range for initial sample points. These approaches can exclude potential optimal solutions, ultimately impacting optimization accuracy. They also focus solely on the variation characteristics of a single parameter dimension, ignoring the correlations between parameter combinations. During the optimization phase, the inherent optimization directionality and uniformity of parameter combination optimization rules inherent in existing optimization algorithms can affect the efficiency and accuracy of parameter optimization. Finding an optimization algorithm that considers the correlations between groups of parameter combinations while also focusing on the characteristics of individual parameter combinations and adopting differentiated optimization strategies to update sample points would be a promising approach that balances accuracy and efficiency.

[0004] Therefore, this study proposes a meta-heuristic evolutionary parameter optimization algorithm (IDTO) based on the mutation chain search of individual sample points and the overall commonality of the sample point set, similar to the transmission pathway of infectious diseases, to meet the requirements of parameter optimization of complex hydrological models. Summary of the Invention

[0005] Purpose of the invention: The present invention provides a new approach to the existing field of evolutionary parameter optimization, and studies and implements a meta-heuristic evolutionary parameter optimization algorithm based on mutation chain search based on the individual characteristics of sample points and the overall commonality of sample point sets.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A meta-heuristic parameter optimization algorithm based on mutation chain search includes the following steps:

[0008] (1) Determine the range of hydrological parameters: Based on the experimental data of basic geology, hydrogeology, topography and geomorphology in the karst area and karst survey, determine the range of simulation parameters of the hydrological model (hydrological model examples include the modular groundwater flow model MODFLOW developed by the United States Geological Survey and the conceptual hydrological model Hymod developed by British hydrologists) and give the initial value x0 of the parameter, i.e., the seed point;

[0009] (2) Determination of the first-layer sampling space and sample point collection: In order to ensure that the collected sample points can be spread over the entire parameter range as much as possible and improve the accuracy of the subsequent optimization process, this algorithm adopts a stratified sampling strategy; according to the seed point, the parameter range is stratified to determine the first-layer sampling space r c , and randomly select m sampling points in this space to form the first-layer sample point set CP={x0,x1,x2,…,x m}, x is the sample point in the first layer;

[0010] (3) Determine the secondary sampling space and sample point collection; determine the secondary sampling space r of each sample point in the first layer s , and randomly select n sample points in this space to generate a secondary sample point set SP for each sample point = {x i1 ,x i2 ,x i3 ,…,x in |i=1,…,m},x i1 represents the first sub-layer sample point of the i-th first-layer sample point;

[0011] (4) Determination of the initial sample group: The initial sample points are generated by merging the first-layer sample point set and the second-layer sample point set, and each sample point is brought into the hydrological model to calculate the objective function value. According to the calculation results, the corresponding sample points are rearranged from small to large, and the sample point with the largest current function value is removed to form the initial sample point set P = {x1, x2, x3, ..., x m×n};

[0012] (5) The variation of each sample point is determined; the variation means the optimization direction that each sample point is most likely to obtain a better advantage; using the similarity analysis formula, according to the Pearson correlation coefficient of each dimension, the mean of the standard covariance between the dimensions is calculated to generate the similarity coefficient matrix of the sample points. And find each sample point x i The corresponding sample point x is smaller than the calculated value of the objective function and has the largest similarity coefficient j , with the similarity coefficient c of the two ij As the sample point xi The amount of variation;

[0013] (6) Sample point subgroup division: In order to reduce the optimization burden, the sample points are divided into nopt sample subgroups PS = {S1, S2, S3, ..., S nopt}, and assign the top nopt sample points that are currently the best to each subgroup in turn, that is, x1 is assigned to S1 as the base point, x2 is assigned to S2 as the base point, and so on; then cluster the remaining points according to the Euclidean distance and enter each sample subgroup respectively;

[0014] (7) Determine the search direction: In each sample subgroup, find the n+1 sample points with the highest similarity as the minimum optimization unit, and consider the variation of each sample point to form a variation chain. Then, determine the velocity vector of this variation chain based on the similarity analysis of the sample point with the largest objective function value in this variation chain.

[0015] (8) Update the sample points; combine the sample speed and the variation to form the sample point update formula (8), generate new sample points, and bring them into the hydrological model to calculate the objective function value. Compare this function value with the maximum objective function value in the current variation chain. If it is less than the current maximum objective function value, directly replace the sample point in the variation chain. Otherwise, continue to use formula (9) to generate new sample points again and replace them.

[0016] (9) Update the variation; through step (4), each newly generated replacement sample point generates a new variation;

[0017] (10) Check convergence; set two types of convergence conditions; the first type is whether the iteration count has reached the maximum iteration requirement; the second type is whether the rate of change of the parameter optimization result is lower than the threshold; if these convergence conditions are met, output the global optimal solution and the corresponding sample point information; otherwise, continue to step (5);

[0018] (11) Result output and comparative analysis: The optimal solution that meets the convergence requirements is output and compared with the existing parameter optimization algorithm in terms of accuracy and efficiency.

[0019] As a further preferred embodiment, step (2) includes:

[0020] (2-1) Determine the first floor space coefficient (a) to be 0.5, and use the maximum value of the global optimization range up r , and the minimum value low r , according to formula (1) to determine the first floor space radius r c :

[0021] r c =a×(up r -lowr ) Formula (1)

[0022] (2-2) According to the initial value of the parameter x0 and formulas (2) and (3), determine the upper boundary (up c ) and the lower boundary (low c ):

[0023] up c =x0+r c Formula (2)

[0024] low c =x0-r c Formula (3)

[0025] (2-3) in low c -up c Randomly select m sample points CP={x0,x1,x2,…,x m}.

[0026] As a further preferred embodiment, step (3) includes:

[0027] (3-1) Select the appropriate sub-layer space coefficient (b) and use the maximum value up in the global optimization range r , and the minimum value low r , according to formula (4) to determine the radius r of the sub-layer space range s :

[0028] r s =b×(up r -low r ) Formula (4)

[0029] (3-2) Take out each sample point x in the first layer sample point set CP in turn i , and according to formulas (5) and (6), determine the upper boundary of the sampling range of the sub-layer space (up s ) and the lower boundary (low s ):

[0030] up s =x i +r s Formula (5)

[0031] low s =x i -r s Formula (6)

[0032] (3-3) in low s -up s Randomly select n sample points SP={x i1 ,xi2 ,x i3 ,…,x in |i=1,…,m}.

[0033] As a further preferred embodiment, step (6) includes:

[0034] (6-1) Determine the base point of each sample point subgroup; divide the sample points into nopt sample subgroups PS = {S1, S2, S3, ..., S nopt}, and assign the current optimal first nopt sample points to each subgroup in turn, that is, x1 is assigned to S1 as the base point, and x2 is assigned to S2 as the base point;

[0035] (6-2) Allocate the remaining sample points {x nopt+1 ,x nopt+2 ,x nopt+3 ,…,x m×n}, according to formula (7), find the remaining sample points and the base point of each sample subgroup to calculate the discreteness, and select the sample subgroup with the smallest discreteness to enter;

[0036] S i =

[0037] {min i＝1, … ,nopt [abs(x k -x i )]|k=nopt+1,…,m×n+1; i=1,…,nopt}

[0038] Formula (7).

[0039] As a further preferred embodiment, step (7) includes:

[0040] (7-1) In each sample subgroup, use the similarity analysis formula to generate the similarity coefficient matrix within the sample subgroup

[0041] (7-2) Find n+1 sample points with the largest overall similarity coefficient in Sbu_CM to form a mutation chain.

[0042] As a further preferred embodiment, step (8) includes:

[0043] (8-1) In the variant chain, the velocity vector v is the worst point s in the chain. w The similarity coefficient in the chain, the acceleration vector is the variation a of the worst point in the chain;

[0044] (8-2) Determine the geometric center point s in the mutation chain ce , and the optimal point s b, take the random number t as the mutation factor in the update to ensure the variability of each update;

[0045] (8-3) The mutation chain formula (8) is as follows:

[0046] x new =s ce +v×t×(s b -s w )+a×t 2 ×(s b -s w ) formula (8).

[0047] As a further preferred embodiment, step (9) includes:

[0048] (9-1) x new The sample is brought into the target model to calculate the function value y new , compared with y new With s w The corresponding function value y w The size of y new <y w , then x w Replace with x new ;

[0049] (9-2) If y new >y w , then continue to regenerate a new point x according to formula (9) new , covering the original x calculated by formula (9-1) new , and the new point x new To replace s w ;

[0050] x new =s w +(|v|×t×(s b -s w )+|a|×t 2 ×(s b -s w ))×0.5 formula (9).

[0051] Beneficial effects

[0052] This study is based on the similarities and differences between sample points in the process of hydrological model parameter optimization. A stratified sampling strategy is adopted to ensure the comprehensiveness of sample point sampling. Through similarity analysis and spatial clustering methods, the optimization speed of the sample point group and the spatial variability of the individual sample points are determined to improve the optimization accuracy. The sample points are updated and iterated, providing a new idea for the optimization method of hydrological models. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is the overall flow chart of the method of the present invention;

[0054] Figure 2 is the scope of the study area in this embodiment;

[0055] Figure 3 hydrogeological zoning of aquitards and phreatic aquifers;

[0056] Figure 4 hydrogeological zoning of confined aquifers;

[0057] Figure 5 MODFLOW model sensitivity analysis results;

[0058] Figure 6 Schematic diagram of the algorithm optimization process;

[0059] Figure 7 Comparison results of optimization accuracy of various algorithms of the Hymod model. DETAILED DESCRIPTION

[0060] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0061] The technical solution of the present invention is further described in detail below. This example selects the Baotu Spring area in Jinan City, Shandong Province ( Figure 2 The data sources include 8 observation wells in the area and their long-term groundwater level monitoring sequences, 30m resolution DEM data and fault fracture data ( Figure 3 A groundwater model was constructed based on MODFLOW, and the algorithm was applied to optimize the model parameters. This is further illustrated by describing a specific embodiment in conjunction with the following figures.

[0062] (1) Determination of the range of hydrological parameters. The water-bearing system in this study area mainly includes the Quaternary porous aquifer and the fractured karst aquifer. In this model simulation study, the Jinan spring area is divided into three layers in the vertical direction (phreatic aquifer, weak permeable layer, and confined karst water aquifer), which are generalized as a heterogeneous anisotropic confined three-dimensional unsteady flow.

[0063] The MODFLOW model was designed for spatiotemporal discretization. The simulation timeframe was based on monitoring data, and to avoid the impact of extreme conditions such as drought on groundwater levels, a stress period was selected every 10 days, for a total of 20 stress periods, from October 1, 2013, to April 18, 2014. For spatial discretization, based on the topographic and hydrogeological conditions of the Jinan spring basin, the basin was divided into 120 rows and 110 columns. Each aquifer was divided vertically into three aquifers using a 505x506m grid, as shown in the figure.

[0064] The model parameters are shown in Table 1. Morris sensitivity analysis was used to analyze each parameter to determine the parameter with the greatest impact on parameter optimization. The sensitivity index was based on RMSE.

[0065] Table 1 MODFLOW model parameters to be optimized and their ranges:

[0066]

[0067]

[0068] Note: HK represents horizontal permeability, VK represents vertical permeability, SS represents water storage rate, and SY represents water supply degree. The first number after the parameter, 1, represents phreatic aquifer, 2 represents aquitard, and 3 represents karst aquifer. The second number represents the zone number. For the non-exposed zone of the karst aquifer, the parameter water storage rate is selected, and for the non-exposed zone of the exposed zone, the parameter water supply degree is selected. For example, HK1-1 represents the horizontal permeability of zone 1 of the phreatic aquifer.

[0069] According to the Morris sensitivity results, the five parameters with the highest sensitivity were selected for parameter optimization, and the initial points of each parameter were given, as shown in Table 2.

[0070] Table 2 Final optimization parameters of MODFLOW model and their ranges, initial value determination

[0071]

[0072] (2) Determine the first layer sampling space and collect sample points. Take the initial point x0 = (5, 0.1, 10 -4 ,0.05,2×10 -3 ) as the center, calculate the first layer sampling space radius r c =(4.5,0.45,9.5×10 -5 ,0.145,0.14995), determine the sampling space (x0-r c ,x0+r c ) Randomly select m = 20 sampling points to form the first layer sample point set CP = {x0, x1, x2, ..., x 20}.

[0073] (3) Determine the secondary sampling space and collect sample points. Take each point x in the first layer sample point set as i As the center, determine the secondary sampling space r s =(4.5,0.45,9.5×10 -5 ,0.145,0.14995), determine the sub-layer sampling space (x i -r s ,x i +r s ), randomly select n = 10 sample points in each range and generate a set of secondary sample points for each sample point.

[0074] The internal parameter settings of the optimization algorithm, such as the number of iterations, are shown in Table 3.

[0075] Table 3 Internal parameter settings of IDTO optimization algorithm

[0076]

[0077] (4) Determination of the initial sample point group. Combine the first-level sample point set and the secondary sample point set to generate a complete initial sample point set, and bring each sample point into the constructed MODFLOW model to calculate the model simulation results. According to the calculation results, rearrange the corresponding sample points from small to large, remove the sample point with the largest function value, and form the initial sample point set P = {x1, x2, ..., x 200};

[0078] (5) Calculation of variation. According to the similarity formula, calculate the standard covariance mean between each dimension, generate the similarity coefficient matrix, and determine the value of each sample point x i The corresponding variation;

[0079] (6) Sample point subgrouping. Based on the parameter dimension 6, the sample points are divided into nopt = 6 + 1 = 7 sample subgroups PS = {S1, S2, ..., S7}, and the top 7 optimal sample points are assigned to each subgroup as the base point. The remaining sample points are clustered using the Euclidean distance and assigned to each subgroup.

[0080] (7) Determine the search direction. In each subgroup, determine the six sample points with the highest similarity as the minimum optimization unit to form a mutation chain.

[0081] (8) Update sample points and mutation amounts. According to formulas (8) and (9), generate new sample points and replace the original sample points in the mutation chain. Then recalculate the mutation amount of each sample point through similarity analysis.

[0082] (9) Set the convergence conditions and output the optimization results. In this example, the maximum number of iterations is set to 3000, and the threshold for the change rate of the parameter optimization results is set to 0.01. When both conditions are met, the iteration stops and the results are output.

[0083] (10) Comparison of MODFLOW model optimization results. To further verify the effectiveness of this algorithm, this algorithm is compared with multiple optimization algorithms. The comparison results are shown in Table 4. From the simulation results, the optimization accuracy of this algorithm is improved by an average of 12.3%.

[0084] Table 4: Comparative study of MODFLOW model optimization accuracy:

[0085]

[0086] (11) Applicability study of the conceptual hydrological model Hymod. In order to explore the applicability of the algorithm more extensively, this scheme also applies the conceptual hydrological model Hymod for testing. The data comes from the Hymod model configured by the spotpy library in Python and related collected data. The model parameters are selected as shown in Table 5.

[0087] Table 5: Hymod model optimization parameters and their ranges, initial value settings:

[0088]

[0089] Note: cmax represents the maximum water storage capacity; bexp represents the spatial variation index of water storage capacity; alpha represents the outlet distribution coefficient of the high-flow tank; rs represents the outflow attenuation coefficient of the low-flow tank; rq represents the outflow attenuation coefficient of the high-flow tank;

[0090] It is also compared and analyzed with multiple types of optimization algorithms. The accuracy comparison results are shown in Table 6 and Figure 7 As shown in the results, on the Hymod model, the optimization accuracy of this algorithm is improved by an average of 7.72%.

[0091] Table 6: Comparative study of Hymod model optimization accuracy:

[0092]

[0093] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A meta-heuristic parameter optimization algorithm based on mutation chain search, characterized in that: The following steps are involved: (1) Determine the range of hydrological parameters: According to the experimental data of basic geology, hydrogeology, topography and geomorphology in karst areas and karst investigation, determine the range of hydrological model simulation parameters and give the initial value x0 of the parameter, i.e., the seed point; (2) Determination of the first-layer sampling space and collection of sample points: In order to ensure that the collected sample points can be distributed throughout the entire parameter range as much as possible and improve the accuracy of the subsequent optimization process, this algorithm adopts a stratified sampling strategy; according to the seed point, the parameter range is stratified to determine the first-layer sampling space r c , and randomly select m sampling points in this space to form the sample point set CP = {x0, x1, x2, ..., x m }, x is the sample point in the first layer; (3) Determine the secondary sampling space and collect sample points; determine the secondary sampling space r of each sample point in the first layer s , and randomly select n sample points in this space to generate a secondary sample point set SP = {x i1 ,x i2 ,x i3 ,…,x in |i=1,…,m},x i1 represents the first sub-layer sample point of the i-th first-layer sample point; (4) Determine the initial sample group: combine the first-layer sample point set and the second-layer sample point set to generate the initial sample points, and bring each sample point into the hydrological model to calculate the objective function value. According to the calculation results, rearrange the corresponding sample points from small to large, remove the sample point with the largest function value, and form the initial sample point set P = {x1, x2, x3, ..., x m×n }; (5) The variation of each sample point is determined; the variation means the optimization direction that is most likely to obtain a better advantage for each sample point; Using the similarity analysis formula, according to the Pearson correlation coefficient of each dimension, the mean of the standard covariance between the dimensions is calculated to generate the similarity coefficient matrix of the sample points. And find each sample point x i The corresponding sample point x is smaller than the calculated value of the objective function and has the largest similarity coefficient j , with the similarity coefficient c of the two ij As the sample point x i The amount of variation; (6) Sample point subgroup division: In order to reduce the optimization burden, the sample points are divided into nopt sample subgroups PS = {S1, S2, S3, ..., S nopt }, and assign the current optimal first nopt sample points to each subgroup in turn, that is, x1 is assigned to S1 as the base point, x2 is assigned to S2 as the base point, and so on; then cluster the remaining points according to the Euclidean distance and enter each sample subgroup respectively; (7) Determine the search direction: In each sample subgroup, find the n+1 sample points with the highest similarity as the minimum optimization unit, and consider the variation of each sample point to form a variation chain. Then, determine the velocity vector of this variation chain based on the similarity analysis of the sample point with the largest objective function value in this variation chain. (8) Update sample points; combine the sample speed and variation to form sample points, generate new sample points, and bring them into the hydrological model to calculate the objective function value. Compare this function value with the maximum objective function value in the current variation chain. If it is less than the current maximum objective function value, directly replace the sample point in the variation chain. Otherwise, generate new sample points again and replace them. (9) Update the variation; through step (4), each newly generated replacement sample point generates a new variation; (10) Check convergence; set two types of convergence conditions; the first type is whether the iteration count has reached the maximum iteration requirement; the second type is whether the change rate of the parameter optimization result is lower than the threshold; if these convergence conditions are met, output the global optimal solution and the corresponding sample point information; otherwise, continue to execute step (5); (11) Result output and comparative analysis: The optimal solution that meets the convergence requirements is output, and a comparative analysis is performed on the accuracy and efficiency with the existing parameter optimization algorithms.

2. The meta-heuristic parameter optimization algorithm based on mutation chain search according to claim 1, characterized in that: The step (2) comprises: (2-1) Determine the first floor space coefficient (a) to be 0.5, and use the maximum value up of the global optimization range r , and the minimum value low r , according to formula (1) determine the radius r of the first floor space c : r c =a×(up r -low r ) Formula(1) (2-2) According to the initial value of the parameter x0 and formulas (2) and (3), determine the upper boundary of the first layer sampling space (up c ) and the lower boundary (low c ): up c =x0+r c Formula (2) low c = x0-r c Formula(3) (2-3) in low c -up c Randomly select m sample points within the range CP={x0,x1,x2,…,x m }.

3. The meta-heuristic parameter optimization algorithm based on variation chain search according to claim 1, characterized in that: The step (3) comprises: (3-1) Select the appropriate sub-layer space coefficient (b) and use the maximum value up in the global optimization range r , and the minimum value low r , according to formula (4), determine the radius r of the sub-layer space range s : r s = b × (up r -low r ) Formula(4) (3-2) Take each sample point x in the first layer sample point set CP in turn i , and according to formulas (5) and (6), determine the upper boundary of the sampling range of the sub-layer space (up s ) and the lower boundary (low s ): up s =x i +r s Formula (5) low s = x i -r s Formula(6) (3-3) in low s -up s Randomly select n sample points SP = {x i1 ,x i2 ,x i3 ,…,x in |i=1,…,m}.

4. The meta-heuristic parameter optimization algorithm based on mutation chain search according to claim 1, characterized in that: The step (6) comprises: (6-1) Determine the base point of each sample point subgroup; divide the sample points into nopt sample subgroups PS = {S1, S2, S3, ..., S nopt }, and assign the current optimal first nopt sample points to each subgroup in turn, that is, x1 is assigned to S1 as the base point, and x2 is assigned to S2 as the base point; (6-2) Allocate the remaining sample points {x nopt+1 ,x nopt+2 ,x nopt+3 ,…,x m×n }, according to formula (7), find the remaining sample points and the base point of each sample subgroup to calculate the discreteness, and select the sample subgroup with the smallest discreteness to enter; S i ＝ {min i＝1,…,nopt [abs(x k -x i )]|k=nopt+1,…,m×n+1;i=1,…,nopt} Formula (7).

5. The meta-heuristic parameter optimization algorithm based on mutation chain search according to claim 1, characterized in that: The step (7) comprises: (7-1) In each sample subgroup, the similarity analysis formula is used to generate the similarity coefficient matrix within the sample subgroup (7-2) Find n+1 sample points with the largest overall similarity coefficient in Sbu_CM to form a mutation chain.

6. The meta-heuristic parameter optimization algorithm based on mutation chain search according to claim 1, characterized in that: The step (8) comprises: (8-1) In the variant chain, the velocity vector v is the worst point s in the chain. w The similarity coefficient in the chain, the acceleration vector is the variation a of the worst point in the chain; (8-2) Determine the geometric center point s in the variant chain ce , and the optimal point s b , take the random number t as the mutation factor in the update to ensure the variability of each update; (8-3) The mutation chain formula (8) is as follows: x new =s ce +v×t×(s b -s w )+a×t 2 ×(s b -s w ) formula (8).

7. The meta-heuristic parameter optimization algorithm based on mutation chain search according to claim 1, characterized in that: The step (9) comprises: (9-1) x new The sample is brought into the target model to calculate the function value y new , compared with new With s w The corresponding function value y w The size of y new <y w , then x w Replace with x new ; (9-2) If y new >y w , then continue to regenerate a new point x according to formula (9) new , covering the original x calculated by formula (9-1) new , and the new point x new To replace s w ; x new =s w +(|v|×t×(s b -s w )+|a|×t 2 ×(s b -s w ))×0.5 formula (9).

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