# Research on the Development Support Strategy of Cultural Enterprises Based on Fish Swarm Algorithm under the Background of Public Health

Authors: Lin Yu; Li Hua; Jiaran Ding
Journal: Journal of Environmental and Public Health
 (2022)

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## Abstract

Under the background of public health events, the government needs to adopt reasonable support strategies to help cultural enterprises tide over the crisis. However, the original analytic hierarchy process cannot be comprehensive and accurate analysis, resulting in that the government support strategy cannot play a role. Fish swarm algorithm is a comprehensive intelligent algorithm, which can comprehensively analyze the factors affecting the formulation of supporting strategies for cultural enterprises, and has the advantages of simple operation and strong analysis ability. Under this background, this paper puts forward a fish swarm model; this method is a comprehensive intelligent analysis method, which can help the government find the best support strategy from the perspectives of politics, economy, and society. In order to verify the effectiveness of the fish school model, this paper uses MATLAB software for verification; the results show that, in the support strategy classification, selection accuracy, and selection time, fish school model is superior to the analytic hierarchy process. Therefore, the fish swarm model can help the government to better choose supporting policies and help cultural enterprises tide over the crisis and improve the accuracy of formulating supporting strategies for cultural enterprises.


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## Body

## 1. Introduction

In the case of public health emergencies, the government will increase its support for performing arts enterprises and adopt corresponding support strategies. Too many supporting policies will greatly weaken the government’s economy and affect the support for other enterprises. Too few support strategies are not conducive to performing arts enterprises to survive the crisis [1]. How to choose the support strategy of performing arts enterprises and achieve accurate support is a problem that the government needs to solve at present. Under this background, domestic scholars have increased the research on related topics and made this issue become a research hotspot. From 2010 to 2022, the research literature on performing arts support strategies at home and abroad showed exponential growth, and the relevant results are shown in Table 1.Table 1
Research literature on supporting policies of performing arts enterprises.
YearNumber of documents (articles)YearNumber of documents (articles)2010543.4720171282.602011995.6520182356.5220121143.472019739.1320132408.6920201913.0420141852.1720211434.7820151591.3020221460.8620161004.34Note: the data comes from CNKI, Wanfang, and other websites.Support strategy is an important means for performing arts enterprises to deal with public health events, and it is also the premise for them to play a social role [2]. There are many factors that affect the support strategy, which makes it difficult for performing arts enterprises to choose the support strategy. Some scholars believe that fish swarm model can integrate various influencing factors and improve the level of supporting policy choice [3]. Fish swarm algorithm has the advantage of comprehensive analysis, which can find the main factors of supporting strategies for cultural enterprises among many complex influencing factors and analyze and judge them. The choice of supporting strategies for cultural enterprises needs comprehensive analysis of various factors, so fish swarm algorithm meets its analysis requirements. Some scholars believe that fish swarm model is a comprehensive intelligent algorithm, which can analyze more comprehensively and improve the accuracy of fostering strategy selection. Some scholars believe that fish swarm algorithm can analyze public health events and analyze the support strategies of performing arts enterprises in combination with the impact of public health events [4]. The existing support strategy formulation of cultural enterprises is inaccurate. In order to better formulate the support strategy, the state needs to adopt comprehensive analysis methods. Therefore, the comprehensive research on the support strategy is the development trend in the future. Fish swarm theory is widely used in industry, electric power, and other fields, and good research results are obtained. In the past, the research method of support strategy is relatively single and the research process is complex, which requires a comprehensive intelligent analysis method. Fish swarm algorithm has the advantage of simple analysis process. It can analyze cultural enterprises from multiple angles and improve the accuracy of support strategy formulation.The fish swarm model can comprehensively analyze the factors that support the formulation of strategies and help performing arts enterprises survive the “crisis” of public events. Combining fish swarm algorithm with the influencing factors of public health events can better judge the implementation effect of support strategies and improve the ability of enterprises to deal with public health events. Some scholars compare fish swarm model with analytic hierarchy process and find that fish swarm model has more advantages in multifactor analysis. Some scholars have verified through actual case analysis and found that the comprehensive analysis effect of fish swarm model is better, and multiple factors can be comprehensively analyzed at the same time. Some scholars have verified the case of fish swarm algorithm and found that fish swarm algorithm can analyze massive data, and the analysis effect is ideal. Based on the above background, this paper uses fish swarm algorithm to analyze public health events and compares with analytic hierarchy process to verify the effectiveness of fish swarm algorithm and provide support for the choice of supporting strategies for performing arts enterprises. This paper mainly elaborates the content including: (1) under the public health event cultural enterprise support strategy formulation request as well as the fish school model research present situation; (2) the fish school model principle as well as the concrete application; (3) the example analysis to the cultural enterprise support strategy.


## 2. Overview of Relevant Theories

### 2.1. Fish Swarm Algorithm

Fish swarm algorithm is a stochastic comprehensive statistical method, which mainly analyzes public health events and finds out the supporting strategies of performing arts enterprises by finding influencing factors, clustering influencing factors, and randomly selecting key factors and outputting final results.Suppose 1:Ait is a set of multiangle support strategies, where i supports the aspect of the strategy, y supports the scope of application of the strategy, and x is arbitrary support strategy. Assuming Pix,y=∑i,t=1nlimδx⟶0Ait⇄k|g, k∈1,…,m then Pix,y is the best scope of application of fostering strategy. Because the randomness of the supporting strategy set is normal, Ait=2ϖsintanθt/ρ⟶ is the best in the global position, where ρ⟶ is the minimum policy set.In Theorem1, Pnx,y the local optimal position has an adaptive functionlimδx⟶0F⋅∈Bt, and the overall optimal position is calculated as shown in(1)∫x∈Aij∑i=1nfPix¯<∢θfx^,where the eigenvalue θfx is calculated.Theorem 1.
If the following conditions are satisfied,fx,y<maxx,yfx,y′<maxx,y′, …, then all local eigenvalues are less than within fx,y′, and the error is less than linx,y′.Theorem 2.
Any pointxit in the set of supporting strategies is distributed discretely [6], and the deviation of any point is dx, and its calculation formula is as(2)dx,y=∂2Ω∂u∂vx⟶∞x·tlogPix,y,where dx,y is the projection of deviation; ∂2Ω/∂u∂v is the support function between the government and cultural enterprises.The relation of variation amplitude can be judged by integral, so the deviation projection of supporting strategy set can be used as supporting strategy set. According to Theorem2, the deviation of supporting strategy set x·t/logPix,y¯ can accurately judge the change range. Some scholars have applied fish swarm model to performing arts enterprises to prove their ability to manage uncertainty. Therefore, this paper transforms the data of supporting strategy set to realize multiangle analysis [7].


### 2.2. Fish Swarm Clustering

In this paper, fish swarm model is selected to optimize the supporting strategy set. This method uses the probability of policy change, to divide the clustering degree [8], and constantly revises the relationship between policy sets; fish swarm model uses “IF” judgment condition to determine the level of different support strategies: xi,yi∈Aij, Sx,y=maxxi,yi, and, xi and xi are the boundary points of the set; then S=∑i=1nsxi⇄mink/q¯¯.Among them,k is the weight coefficient of supporting strategies, Aij is the set of supporting strategies, Sx is the best combination of policies and enterprise needs, and maxxi,yi is the maximum supporting strength. Fish swarm model can be used to analyze unstructured data, process it through different fusion degrees, and output the best strategy results [9].Hypothesis 1.
Arbitrary support strategy:xi After sorting by weight S, the fitting relationship between input variables xi and output variables yi can be obtained, as shown in(3)Aij=∑i,j=1n·linxi−yiq∂2Ω∂u2,where q is the fitting center, respectively; linp() is the expected function and Aij is the set of policies.
By fish swarm model analysis of the above expected functions, continuous operators can be obtained, and the calculation results are shown in(4)gij=k⋅∑i,j,k=1ngijtx⟶,where k is the fusion coefficient and t is the adjustment coefficient. According to the fusion situation, the output value is obtained, and the calculation result is shown in(5)y=k⋅±gijtx⇄fPjxmax∑i,j=1nAijtx,y,fish swarm model reduces the processing amount of policies [10] and realizes the orderly arrangement of policies through weights. At the same time, the support strategy has been derived for many times [11], which reduces the influence of uncertain factors on the results and realizes the multiangle analysis of the support strategy set [12].


## 2.1. Fish Swarm Algorithm

Fish swarm algorithm is a stochastic comprehensive statistical method, which mainly analyzes public health events and finds out the supporting strategies of performing arts enterprises by finding influencing factors, clustering influencing factors, and randomly selecting key factors and outputting final results.Suppose 1:Ait is a set of multiangle support strategies, where i supports the aspect of the strategy, y supports the scope of application of the strategy, and x is arbitrary support strategy. Assuming Pix,y=∑i,t=1nlimδx⟶0Ait⇄k|g, k∈1,…,m then Pix,y is the best scope of application of fostering strategy. Because the randomness of the supporting strategy set is normal, Ait=2ϖsintanθt/ρ⟶ is the best in the global position, where ρ⟶ is the minimum policy set.In Theorem1, Pnx,y the local optimal position has an adaptive functionlimδx⟶0F⋅∈Bt, and the overall optimal position is calculated as shown in(1)∫x∈Aij∑i=1nfPix¯<∢θfx^,where the eigenvalue θfx is calculated.Theorem 1.
If the following conditions are satisfied,fx,y<maxx,yfx,y′<maxx,y′, …, then all local eigenvalues are less than within fx,y′, and the error is less than linx,y′.Theorem 2.
Any pointxit in the set of supporting strategies is distributed discretely [6], and the deviation of any point is dx, and its calculation formula is as(2)dx,y=∂2Ω∂u∂vx⟶∞x·tlogPix,y,where dx,y is the projection of deviation; ∂2Ω/∂u∂v is the support function between the government and cultural enterprises.The relation of variation amplitude can be judged by integral, so the deviation projection of supporting strategy set can be used as supporting strategy set. According to Theorem2, the deviation of supporting strategy set x·t/logPix,y¯ can accurately judge the change range. Some scholars have applied fish swarm model to performing arts enterprises to prove their ability to manage uncertainty. Therefore, this paper transforms the data of supporting strategy set to realize multiangle analysis [7].


## 2.2. Fish Swarm Clustering

In this paper, fish swarm model is selected to optimize the supporting strategy set. This method uses the probability of policy change, to divide the clustering degree [8], and constantly revises the relationship between policy sets; fish swarm model uses “IF” judgment condition to determine the level of different support strategies: xi,yi∈Aij, Sx,y=maxxi,yi, and, xi and xi are the boundary points of the set; then S=∑i=1nsxi⇄mink/q¯¯.Among them,k is the weight coefficient of supporting strategies, Aij is the set of supporting strategies, Sx is the best combination of policies and enterprise needs, and maxxi,yi is the maximum supporting strength. Fish swarm model can be used to analyze unstructured data, process it through different fusion degrees, and output the best strategy results [9].Hypothesis 1.
Arbitrary support strategy:xi After sorting by weight S, the fitting relationship between input variables xi and output variables yi can be obtained, as shown in(3)Aij=∑i,j=1n·linxi−yiq∂2Ω∂u2,where q is the fitting center, respectively; linp() is the expected function and Aij is the set of policies.
By fish swarm model analysis of the above expected functions, continuous operators can be obtained, and the calculation results are shown in(4)gij=k⋅∑i,j,k=1ngijtx⟶,where k is the fusion coefficient and t is the adjustment coefficient. According to the fusion situation, the output value is obtained, and the calculation result is shown in(5)y=k⋅±gijtx⇄fPjxmax∑i,j=1nAijtx,y,fish swarm model reduces the processing amount of policies [10] and realizes the orderly arrangement of policies through weights. At the same time, the support strategy has been derived for many times [11], which reduces the influence of uncertain factors on the results and realizes the multiangle analysis of the support strategy set [12].


## 3. The Fish Swarm Model Construct of Supporting Strategy for Performing Arts Enterprises

### 3.1. Coevolution of Initial Parameters

The fish swarm model of supporting strategy selection of performing arts enterprises constructed in this paper is to realize dynamic strategy analysis and improve the ability of selecting strategic schemes, so it is necessary to carry out multiangle coevolution. Fish swarm model uses convergence threshold and adjustment factor to present a distributed set of supporting strategies [13], realize coevolutionary analysis, and finally get the best scheme.The initial support strategy is randomly distributed and has strong uncertainty, and its strategy analysis process is complicated. Therefore, improving the order of supporting strategies, reducing the influence of random supporting strategies on the calculation results, and expanding the number of supporting strategy sets are the keys to the local optimal problem. Fish swarm algorithm can deal with the prop-up strategy orderly and change the randomness of prop-up strategy into the randomness of prop-up strategy set. The results are shown in Figure1.Figure 1
Data processing results of fish school model on supporting strategy.Figure1 shows the analysis of supporting strategies by fish school model. The icon in Figure 1 is the fitting result between theoretical data and actual requirements. The analysis results show that the distribution of supporting strategies is relatively uniform, mainly concentrated between 0.2 and 0.25. Therefore, the initial data processing effect of fish school model is good, which can provide support for later calculation [8].


#### 3.1.1. Analysis of Supporting Strategies under Different Conditions

The choice of supporting strategies for performing arts enterprises should adapt to different conditions, so as to improve the accuracy of analysis and shorten the analysis time. Below, according to different situations, the assignment strategy is analyzed.(1)
The choice of internal support strategies for performing arts enterprises: the results are shown in(6)yijt+1=k·yijt+w1·k⋅∑i,j,k=1nAijkxt⇔fPjxtmean∑i,j=1ngijkxt.(2)
The choice of supporting strategies among different industries: the result is shown in(7)yijΔt=yijt+w2k⋅∑i,j=1nAijtxt⇔fPjxtmax∑i,j=1ngijtxt.(3)
The choice of supporting strategies under public health events: the results are shown in(8)yijΔt+1=w·δ⋅∑i,j=1ngijtxt¬fPjxt∀∑i,j=1nAijtxt+1.Among them,wi is the choice weight of different supporting strategies, k is the clustering degree of different supporting strategies, and n is the number of different supporting strategies [14].


#### 3.1.2. Collaboration Strategies from Different Angles

The government should adopt different support strategies for different performing arts enterprises, so it is necessary to comprehensively analyze enterprises from different angles. The fish swarm model clusters the supporting strategies from different angles and iteratively calculates them. Calculate support strategies from different angles to improve the accuracy of support strategies [15].


### 3.2. Selection of Supporting Strategy for Performing Arts Enterprises Based on Fish Swarm Model

Fish swarm model can realize the coevolution of angles and optimize the initial values, thresholds, and parameters of the supporting strategy set [16] to obtain the optimal strategy and the shortest calculation time. The calculation results are shown in Figure 2.Step 1: Determine the angle and strategy structure of supporting strategy collection, and determine the strategy structure of time series according to the strategy characteristics of supporting strategy selection of performing arts enterprises. The initial weights of the whole strategy are formed into different strategy sets, and each strategy set is arranged according to angle, weight, and threshold [17].Step 2: Policy initialization. Randomly initializes the related parameters of the support policy set. Let the number of supporting strategy setsn = 50, the maximum weight wmax = 0.1, the minimum weight wmin = 0.3, and the maximum iteration times D = 100.Step 3: Calculate the moderation function value. Fish swarm model is used to generate initial sequences from different angles and according to initial weights and thresholds. According to the calculation of formulas (2)∼(4), the moderate function is calculated.Step 4: Select the global optimal strategy, and randomly use the fitness ratio of the strategies in 5 to record the optimal global strategy.Step 5: Determine whether the maximum number of iterations has been reached. If it has been reached, the calculation will be stopped and the best strategy will be returned [16].Figure 2
Selection process of supporting strategy of performing arts enterprises based on fish swarm model.


## 3.1. Coevolution of Initial Parameters

The fish swarm model of supporting strategy selection of performing arts enterprises constructed in this paper is to realize dynamic strategy analysis and improve the ability of selecting strategic schemes, so it is necessary to carry out multiangle coevolution. Fish swarm model uses convergence threshold and adjustment factor to present a distributed set of supporting strategies [13], realize coevolutionary analysis, and finally get the best scheme.The initial support strategy is randomly distributed and has strong uncertainty, and its strategy analysis process is complicated. Therefore, improving the order of supporting strategies, reducing the influence of random supporting strategies on the calculation results, and expanding the number of supporting strategy sets are the keys to the local optimal problem. Fish swarm algorithm can deal with the prop-up strategy orderly and change the randomness of prop-up strategy into the randomness of prop-up strategy set. The results are shown in Figure1.Figure 1
Data processing results of fish school model on supporting strategy.Figure1 shows the analysis of supporting strategies by fish school model. The icon in Figure 1 is the fitting result between theoretical data and actual requirements. The analysis results show that the distribution of supporting strategies is relatively uniform, mainly concentrated between 0.2 and 0.25. Therefore, the initial data processing effect of fish school model is good, which can provide support for later calculation [8].


### 3.1.1. Analysis of Supporting Strategies under Different Conditions

The choice of supporting strategies for performing arts enterprises should adapt to different conditions, so as to improve the accuracy of analysis and shorten the analysis time. Below, according to different situations, the assignment strategy is analyzed.(1)
The choice of internal support strategies for performing arts enterprises: the results are shown in(6)yijt+1=k·yijt+w1·k⋅∑i,j,k=1nAijkxt⇔fPjxtmean∑i,j=1ngijkxt.(2)
The choice of supporting strategies among different industries: the result is shown in(7)yijΔt=yijt+w2k⋅∑i,j=1nAijtxt⇔fPjxtmax∑i,j=1ngijtxt.(3)
The choice of supporting strategies under public health events: the results are shown in(8)yijΔt+1=w·δ⋅∑i,j=1ngijtxt¬fPjxt∀∑i,j=1nAijtxt+1.Among them,wi is the choice weight of different supporting strategies, k is the clustering degree of different supporting strategies, and n is the number of different supporting strategies [14].


### 3.1.2. Collaboration Strategies from Different Angles

The government should adopt different support strategies for different performing arts enterprises, so it is necessary to comprehensively analyze enterprises from different angles. The fish swarm model clusters the supporting strategies from different angles and iteratively calculates them. Calculate support strategies from different angles to improve the accuracy of support strategies [15].


## 3.1.1. Analysis of Supporting Strategies under Different Conditions

The choice of supporting strategies for performing arts enterprises should adapt to different conditions, so as to improve the accuracy of analysis and shorten the analysis time. Below, according to different situations, the assignment strategy is analyzed.(1)
The choice of internal support strategies for performing arts enterprises: the results are shown in(6)yijt+1=k·yijt+w1·k⋅∑i,j,k=1nAijkxt⇔fPjxtmean∑i,j=1ngijkxt.(2)
The choice of supporting strategies among different industries: the result is shown in(7)yijΔt=yijt+w2k⋅∑i,j=1nAijtxt⇔fPjxtmax∑i,j=1ngijtxt.(3)
The choice of supporting strategies under public health events: the results are shown in(8)yijΔt+1=w·δ⋅∑i,j=1ngijtxt¬fPjxt∀∑i,j=1nAijtxt+1.Among them,wi is the choice weight of different supporting strategies, k is the clustering degree of different supporting strategies, and n is the number of different supporting strategies [14].


## 3.1.2. Collaboration Strategies from Different Angles

The government should adopt different support strategies for different performing arts enterprises, so it is necessary to comprehensively analyze enterprises from different angles. The fish swarm model clusters the supporting strategies from different angles and iteratively calculates them. Calculate support strategies from different angles to improve the accuracy of support strategies [15].


## 3.2. Selection of Supporting Strategy for Performing Arts Enterprises Based on Fish Swarm Model

Fish swarm model can realize the coevolution of angles and optimize the initial values, thresholds, and parameters of the supporting strategy set [16] to obtain the optimal strategy and the shortest calculation time. The calculation results are shown in Figure 2.Step 1: Determine the angle and strategy structure of supporting strategy collection, and determine the strategy structure of time series according to the strategy characteristics of supporting strategy selection of performing arts enterprises. The initial weights of the whole strategy are formed into different strategy sets, and each strategy set is arranged according to angle, weight, and threshold [17].Step 2: Policy initialization. Randomly initializes the related parameters of the support policy set. Let the number of supporting strategy setsn = 50, the maximum weight wmax = 0.1, the minimum weight wmin = 0.3, and the maximum iteration times D = 100.Step 3: Calculate the moderation function value. Fish swarm model is used to generate initial sequences from different angles and according to initial weights and thresholds. According to the calculation of formulas (2)∼(4), the moderate function is calculated.Step 4: Select the global optimal strategy, and randomly use the fitness ratio of the strategies in 5 to record the optimal global strategy.Step 5: Determine whether the maximum number of iterations has been reached. If it has been reached, the calculation will be stopped and the best strategy will be returned [16].Figure 2
Selection process of supporting strategy of performing arts enterprises based on fish swarm model.


## 4. Case Analysis of Supporting Strategy Choice of Performing Arts Enterprises

### 4.1. Validity Judgment of Fish Swarm Model

To verify the accuracy of the results, the common detection functionsρx, ϑx, and φx were used for analysis and comparison [18].The data processing functionρx mainly tests the data processing ability of the supporting strategy, and the result is shown in(9)ρx=w·∑i=1nx,y^.The detection functionϑx is the processing time of the detected data, and the result is shown in(10)ϑx=∑i=1nlimδx⟶0xi2−max2πxi,φx is a comprehensive analysis function, which comprehensively analyzes the test results of fish school model and judges whether it can cope with public health events [19]. The result is shown in(11)φx=klimδx⟶0∑i=1n∑i=1nxi⟶yi⟺limδx⟶0∑i=1ncosθxi^,where n is the number of samples of the support strategy set; xi is any support strategy.In order to facilitate the calculation, the number of supporting strategy setsn = 100, the iteration times D = 100, and 4 angles and 3 test functions are analyzed. For the accuracy of the results, take multiple averages, and the specific calculation results are shown in Table 2.Table 2
Test results of test function.
Detection functionValue rangeAverage differenceStandard deviationTest resultsρx2.28E − 019.11E − 015.69E − 01Better1.03E + 001.25E + 001.03E + 00ϑx1.03E + 007.97E − 011.25E + 00Good1.14E + 004.56E − 017.97E − 01φx6.83E − 019.11E − 015.69E − 01Better7.97E − 019.11E − 011.25E + 00Note: the data in the table are abbreviations of decimal point.It can be seen from Table1 that the global optimal strategy of ρx and ϑx test functions is better, while φx is good, and both standard deviation and mean meet the test requirements. In terms of average deviation and standard deviation, the calculated results of fish school model meet the requirement [20]. The convergence degree of fish school model is shown in Figures 3–5.Figure 3
Convergence result ofρx function optimization.Figure 4
Convergence result ofϑx function optimization.Figure 5
Optimization time ofφx function.As can be seen from Figure3, the optimization amplitude and error rate of ρx function are shrinking [19], which shows that the ρx function inspection effect of fish swarm model is better. However, the convergence results of ρx function optimization show volatility, which mainly changes from global selection to local selection. Relatively speaking [21], the convergence result of ϑx function optimization is shown in Figure 4.As can be seen from Figure4, the error rate of ϑx function is shrinking, which shows that the ϑx function of fish swarm model has a good checking effect and the local strategy selection result is stable. Compared with other test functions [22], the optimization time of φx function is shown in Figure 5.As can be seen from Figure5, the error rate of φx is shrinking, which shows that the selection time of ϑx function of fish swarm model is short. At the same time, the function also shows volatility, which is due to the shift from global selection to local selection [23].


### 4.2. Case Introduction of Supporting Policy Choice Strategy Choice

In this paper, under the public health events from 2019 to 2022, performing arts enterprises’ support selection strategies are selected as samples to analyze the results of strategy selection. Strategic choices include economy, technology, politics, and so on [24]. The evaluation criteria of strategy selection refer to “National Measures for Supporting Performing Arts Enterprises” and “Standards for Supporting Performing Arts Enterprises.” There are five levels of strategy selection, which are completely consistent, partially consistent, average, nonconsistent, and completely nonconsistent. The results are shown in Table 3.Table 3
Division results of supporting strategies.
Policy levelPolicy quantity (s)Proportion (%)Completely coincidence120220.82Partial coincidence4327.48General203235.19Inconsistent104118.03Completely inconsistent106718.48


### 4.3. Test Results

In order to verify the effectiveness of fish swarm model proposed in this paper, compared with the questionnaire, the change direction, adaptation range, and fusion level are shown in Figure6.Figure 6
Accuracy of support strategy analysis by different models.As can be seen from Figure6, the calculation time of fish swarm model is less than that of questionnaire, which shows that the calculation efficiency of fish swarm model is higher, and the time change range of questionnaire is large [25]. The calculation accuracy and time of both are shown in Table 4.Table 4
Judgment accuracy and time of different grades.
Analysis modelJudgment accuracy of different strategy levels (%)Calculation time (seconds)Completely coincidencePartial coincidenceGeneralInconsistentCompletely inconsistentFish swarm model97.9698.9898.9898.9699.1612.33Analytic hierarchy process model95.9297.9696.9497.9296.9422.92It can be seen from Table4 that the accuracy of supporting policy selection of fish swarm model is more than 98%, while the accuracy of supporting policy selection of questionnaire is about 90%. Therefore, fish swarm model has better accuracy. The reason is that fish swarm model uses weight and convergence factor to analyze policy, technology, and environment, which makes the calculation result better.


## 4.1. Validity Judgment of Fish Swarm Model

To verify the accuracy of the results, the common detection functionsρx, ϑx, and φx were used for analysis and comparison [18].The data processing functionρx mainly tests the data processing ability of the supporting strategy, and the result is shown in(9)ρx=w·∑i=1nx,y^.The detection functionϑx is the processing time of the detected data, and the result is shown in(10)ϑx=∑i=1nlimδx⟶0xi2−max2πxi,φx is a comprehensive analysis function, which comprehensively analyzes the test results of fish school model and judges whether it can cope with public health events [19]. The result is shown in(11)φx=klimδx⟶0∑i=1n∑i=1nxi⟶yi⟺limδx⟶0∑i=1ncosθxi^,where n is the number of samples of the support strategy set; xi is any support strategy.In order to facilitate the calculation, the number of supporting strategy setsn = 100, the iteration times D = 100, and 4 angles and 3 test functions are analyzed. For the accuracy of the results, take multiple averages, and the specific calculation results are shown in Table 2.Table 2
Test results of test function.
Detection functionValue rangeAverage differenceStandard deviationTest resultsρx2.28E − 019.11E − 015.69E − 01Better1.03E + 001.25E + 001.03E + 00ϑx1.03E + 007.97E − 011.25E + 00Good1.14E + 004.56E − 017.97E − 01φx6.83E − 019.11E − 015.69E − 01Better7.97E − 019.11E − 011.25E + 00Note: the data in the table are abbreviations of decimal point.It can be seen from Table1 that the global optimal strategy of ρx and ϑx test functions is better, while φx is good, and both standard deviation and mean meet the test requirements. In terms of average deviation and standard deviation, the calculated results of fish school model meet the requirement [20]. The convergence degree of fish school model is shown in Figures 3–5.Figure 3
Convergence result ofρx function optimization.Figure 4
Convergence result ofϑx function optimization.Figure 5
Optimization time ofφx function.As can be seen from Figure3, the optimization amplitude and error rate of ρx function are shrinking [19], which shows that the ρx function inspection effect of fish swarm model is better. However, the convergence results of ρx function optimization show volatility, which mainly changes from global selection to local selection. Relatively speaking [21], the convergence result of ϑx function optimization is shown in Figure 4.As can be seen from Figure4, the error rate of ϑx function is shrinking, which shows that the ϑx function of fish swarm model has a good checking effect and the local strategy selection result is stable. Compared with other test functions [22], the optimization time of φx function is shown in Figure 5.As can be seen from Figure5, the error rate of φx is shrinking, which shows that the selection time of ϑx function of fish swarm model is short. At the same time, the function also shows volatility, which is due to the shift from global selection to local selection [23].


## 4.2. Case Introduction of Supporting Policy Choice Strategy Choice

In this paper, under the public health events from 2019 to 2022, performing arts enterprises’ support selection strategies are selected as samples to analyze the results of strategy selection. Strategic choices include economy, technology, politics, and so on [24]. The evaluation criteria of strategy selection refer to “National Measures for Supporting Performing Arts Enterprises” and “Standards for Supporting Performing Arts Enterprises.” There are five levels of strategy selection, which are completely consistent, partially consistent, average, nonconsistent, and completely nonconsistent. The results are shown in Table 3.Table 3
Division results of supporting strategies.
Policy levelPolicy quantity (s)Proportion (%)Completely coincidence120220.82Partial coincidence4327.48General203235.19Inconsistent104118.03Completely inconsistent106718.48


## 4.3. Test Results

In order to verify the effectiveness of fish swarm model proposed in this paper, compared with the questionnaire, the change direction, adaptation range, and fusion level are shown in Figure6.Figure 6
Accuracy of support strategy analysis by different models.As can be seen from Figure6, the calculation time of fish swarm model is less than that of questionnaire, which shows that the calculation efficiency of fish swarm model is higher, and the time change range of questionnaire is large [25]. The calculation accuracy and time of both are shown in Table 4.Table 4
Judgment accuracy and time of different grades.
Analysis modelJudgment accuracy of different strategy levels (%)Calculation time (seconds)Completely coincidencePartial coincidenceGeneralInconsistentCompletely inconsistentFish swarm model97.9698.9898.9898.9699.1612.33Analytic hierarchy process model95.9297.9696.9497.9296.9422.92It can be seen from Table4 that the accuracy of supporting policy selection of fish swarm model is more than 98%, while the accuracy of supporting policy selection of questionnaire is about 90%. Therefore, fish swarm model has better accuracy. The reason is that fish swarm model uses weight and convergence factor to analyze policy, technology, and environment, which makes the calculation result better.


## 5. Concluding Remarks

In this paper, fish swarm model and analytic hierarchy process model are integrated to achieve multidimensional coevolution of supporting strategies for performing arts enterprises. The research results show that the calculation time of fish swarm model is less than that of questionnaire, which shows that the calculation efficiency of fish swarm model is higher, and the time change range of questionnaire is large. The accuracy of supporting policy selection of fish swarm model is more than 98%, while the accuracy of supporting policy selection of questionnaire is about 90%. Therefore, fish swarm model has better accuracy. However, in this model, the multidimensional collaborative strategy pays too much attention to the global selection ability, which leads to the relative decline in the accuracy of the analysis results, and ignores the correlation between the supporting strategy indicators of performing arts enterprises. Therefore, in the future research, the strategy adjustment coefficient of fish swarm model will be increased to improve.



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*Source: 6470147-2022-06-27.xml*