# Evaluation of the Effectiveness of Collusion Control Policy Implementation by BP Neural Network Based on Annealing Algorithm Optimization

Authors: Chongsen Ma; Yun Chen; Zeyang Lei
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Due to the national economic development form and social development demand, in recent years, the government has been vigorously promoting the control of government-enterprise collusion in the bidding process of government projects in order to promote the standardization of the market. How to predict the vertical collusion behavior under different internal and external environments has become an important research content. Although the prediction of individual behavior is difficult to achieve, the prediction of group behavior has certain possibilities. In this paper, we propose a method for predicting and evaluating the vertical collusion behavior of government investment project bidding based on BP neural network analysis optimized by an annealing algorithm. First, drawing on the traditional evaluation model, the evaluation index system of government-enterprise collusion behavior is constructed from five dimensions: internal environment, external environment, policy development, enforcement effort, and feedback channel. Secondly, a machine learning method based on BP neural network optimized by an annealing algorithm is introduced to evaluate the influence of the change of initial conditions on the bidding collusion behavior. This study has certain significance for government managers to discover the problems and causes in policy formulation, which in turn can support the government in further improving the policy utility.


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## Body

## 1. Introduction

Policy formulation and evaluation of management effectiveness is a systematic and complex task, and with the continuous development of China's engineering construction field, the management of corrupt practices in the bidding process of government projects has become increasingly strict [1, 2]. However, the same control policy under different external conditions can lead to different strategies adopted by each participant in the bidding of government investment engineering projects [3]. Therefore, it is of greater practical significance to predict the vertical collusion behavior of each group in the bidding of government investment engineering projects and to carry out targeted control according to the prediction results.Vertical collusion in bidding for engineering projects can bring high economic benefits to each stakeholder, and all parties tend to maximize their profit in the process of project execution [4]. At the same time, in the vertical hierarchical relationship, some actors in the information disadvantage have the information demand, while another actor in the information advantage has the information rent-seeking supply, so the information asymmetry motivates the vertical actor to reach the vertical collusion based on information trading [5]. In the absence of additional costs, collusion is likely to occur between stakeholders in bidding for engineering projects regardless of whether the cost of vertical collusion is symmetrical or not; the possibility of collusion is higher when the cost of collusion is symmetrical; in the presence of additional costs, it can promote the occurrence of collusion in the case of asymmetrical cost of collusion [6]. Therefore, the prediction of changes in regional collusion behavior through reasonable external conditions and the environment in which collusion occurs can help relevant policies and targeted management behavior.There are many influencing factors that affect the change of vertical collusion behavior. By utilizing these factors, it is possible to effectively remedy the deficiencies in policy formulation, save management efforts, and optimize the implementation to improve the science of policy formulation [7]. For example, taking the number of government project bidding collusion cases in a city as the research object, the BP neural network model and algorithm based on annealing algorithm optimization can be used to analyze the relationship between the changes in the number of cases and the external economic environment, the tension between supply and demand in the market, and the government's enforcement efforts. Meanwhile, by decomposing these relationships into optimization problems, and through the solution of the optimization problems, more adaptive policies can be formulated. The paper is based on the Chinese Comprehensive Social Survey (CCS).The paper analyzes and mines the data based on the Chinese General Social Survey (CGSS) [8] and the relevant data from the National Bureau of Statistics. The paper provides more governmental governance of collusion between government and enterprises with decision support by evaluating the degree of collusion between government and enterprises in the bidding field of government investment projects and analyzing the degree of change in collusion behavior under different environmental combinations.The innovation points of this paper are mainly reflected in(1)
A prediction model about vertical collusion behavior in government investment engineering project bidding based on the BP neural network optimized by the annealing algorithm is established.(2)
In the evaluation process, evaluation indexes such as market collusion tendency and government integrity degree on collusion behavior are added to make the evaluation model more realistic.The research in this paper mainly addresses the following issues.(1)
In the process of policy formulation for the prevention of collusion in bidding, the implementation effects of the same policies in different cities differ greatly. Therefore, how to determine the policies that are more adapted to the local economic development status and actual conditions before the policies are promulgated.(2)
How to evaluate the effects of policies already promulgated and optimize the relevant policies.


## 2. Literature Review

### 2.1. Vertical Collusion in Bidding for Government Investment Projects

Due to information asymmetry among parties, disorderly competition among enterprises, imperfect regulatory mechanisms, and the bidding process, the market is highly competitive and most enterprises cannot obtain fair competition [9]. The engineering bidding process includes multiple types of participating subjects, such as bidders, agencies, and supervisory bodies [10]. Due to the complex relationship among the participating subjects, collusion in the bidding process has various types [11, 12]. Vertical collusion refers to the existence of hierarchical differences between colluders, similar to those between superiors and subordinates. Vertical collusion mainly includes vertical collusion between bidders, collusion between agencies and bidders, collusion between bid evaluation experts and bidders, collusion between supervisory agencies and bidders, and multiparty collusion. The emergence of vertical collusion has indirectly promoted the proliferation and development of bidding irregularities. Therefore, it is of great significance to predict collusion through the external environment and local market atmosphere. Thus, how to detect and govern this bidding behavior is also a hot issue being studied by many scholars [13]. Due to the strong randomness of individual behavior, the accuracy and significance of predicting individual decision-making behavior are low. However, the prediction of group behavior can effectively reduce the influence of individual random behavior on the results. By predicting the changes of the internal and external environment on the vertical collusion behavior in the bidding process, the collusion behavior can be effectively controlled. Sirui Nie et al. pointed out that the vertical collusion of bidding will lead to a decline in the quality of the project and various negative effects, while the occurrence of collusion [14] is relatively hidden and difficult to identify. Therefore, an effective and rapid method is necessary to measure the tendency of vertical collusion in bidding to discover vertical collusion in bidding [15].


### 2.2. Factors Influencing Vertical Collusion in Bidding for Government Investment Projects

The collusive behavior of bidding is formed by a combination of influencing factors. The incomplete implementation of the bidding system is an important reason for the prevalence of collusion in government investment projects [16]. This is actually a reflection of the long-standing lack of policy implementation in the bidding field. For a long time, local governments and competent officials have tended to adopt alternative strategies to deal with the implementation of laws and policies. Meanwhile, the implementers choose to adapt the implementation of policies that are not profitable so that indicators such as the level of corruption in the government of the bidding place and the tendency of local collusion have a greater impact on the generation of vertical collusion.Economic motivation is also one of the important reasons for collusion in the bidding process [17]. The reason for this is that the costs and risks of collusion are low compared to the benefits. The cost includes not only the implementation cost of collusion but also the implementation cost and the risk cost. At the same time, the profit-seeking and competition caused by the market economy also contribute to the creation of power and money transactions and collusion in the bidding process in disguise. The local economic development and the degree of competition in the market will have an impact on the collusion. Through research, Henke believes that in the existing bidding model, refusing bribes will increase the participation costs of “honest agents,” has negative externalities and leads to potential corrupt practices [18].


### 2.3. BP Neural Network and Simulated Annealing Algorithm

The BP algorithm originated in the 1980s, has the error back propagation training discovered by David Rumelhart et al. [19]. The algorithm is a model that mimics the neurons of the brain to deal with uncertainty problems. The standard BP neural network is trained twice by the error back propagation algorithm and belongs to a three-layer feedforward network that consists of an input layer, a hidden layer, and an output layer. The main features are that the signal is forward propagation and the error is backward propagation. The BP neural network has better prediction results for highly uncertain problems. The BP algorithm takes the square of the network error as the objective function and uses the gradient descent method to calculate the minimum value of the objective function.BP neural network is essentially a simplified biological model, where the output and input structure on the neural network is a single-layer structure, while the hidden layer is a multilayer structure. All components are connected. The input layer passes the information to the hidden layer after getting the stimulus, and the hidden layer passes the weight information to the output layer according to the calculation rules, and the output layer compares the results and adjusts the weights if the results are incorrect. In other words, the BP neural network uses the backpropagation algorithm to calculate the model for several iterations given the training set D. Finally, the parameters of the training neural network model are determined according to the error requirements. A schematic diagram of the structure of the BP neural network is shown in Figure1.Figure 1
Network structure diagram.


### 2.4. Application of BP Neural Network in the Evaluation Field

BP neural networks have a wide range of applications in nonlinear modeling, system identification, etc. While general neural networks have a predetermined number of network layers, BP neural networks do not require predetermination. Two-layer BP networks achieve the fitting of arbitrary functions without limiting the number of hidden nodes. Therefore, in practical applications, BP neural networks are usually selected with 2 layers.In 2015, Yang Baoan et al. combined BP neural networks with corporate financial analysis and demonstrated the applicability of neural networks in financial analysis [20]. Zeng Zhongdong, on the other hand, found that a neural network model can be useful for establishing a dynamic early warning mechanism for companies in the insurance industry [21]. Fu et al. combined BP neural network with hierarchical analysis to analyze green marketing and found that a high prediction accuracy could be achieved [19]. Yang et al. used a BP neural network to predict the level of teaching management and provide help to improve teaching [22]. Yu et al. found that campus congestion could be better predicted using the BP neural network [23]. Liu Qi et al. found that BP neural networks have high feasibility for application in the field of GEM enterprise value assessment [24]. Wang et al. used the autoregressive integrated moving average (ARIMA) method and the back propagation neural network (BPNN) method to forecast carbon emissions in China, India, the United States, and the European Union in the absence of COVID-19 [25]. Lyu et al. utilized the GA-NN algorithm predicting the torsional strength of reinforced concrete (RC) beams [26]. In summary, it can be found that BP neural networks have high application value and applicability in the field of multiindustry evaluation. Therefore, the introduction of this method in the field of policy adaptability evaluation has high rationality.


### 2.5. Simulated Annealing Algorithm

The simulated annealing (SA) algorithm is derived from the process of temperature change, and the SA algorithm has a strong local search capability [23]. The process is similar to physical annealing, also known as system temperature, by accepting an increase in the objective function through the standard probability rules of Metropolis. SA obtains the global optimal solution to the problem by repeating the sampling during the decrease of the system temperature.


## 2.1. Vertical Collusion in Bidding for Government Investment Projects

Due to information asymmetry among parties, disorderly competition among enterprises, imperfect regulatory mechanisms, and the bidding process, the market is highly competitive and most enterprises cannot obtain fair competition [9]. The engineering bidding process includes multiple types of participating subjects, such as bidders, agencies, and supervisory bodies [10]. Due to the complex relationship among the participating subjects, collusion in the bidding process has various types [11, 12]. Vertical collusion refers to the existence of hierarchical differences between colluders, similar to those between superiors and subordinates. Vertical collusion mainly includes vertical collusion between bidders, collusion between agencies and bidders, collusion between bid evaluation experts and bidders, collusion between supervisory agencies and bidders, and multiparty collusion. The emergence of vertical collusion has indirectly promoted the proliferation and development of bidding irregularities. Therefore, it is of great significance to predict collusion through the external environment and local market atmosphere. Thus, how to detect and govern this bidding behavior is also a hot issue being studied by many scholars [13]. Due to the strong randomness of individual behavior, the accuracy and significance of predicting individual decision-making behavior are low. However, the prediction of group behavior can effectively reduce the influence of individual random behavior on the results. By predicting the changes of the internal and external environment on the vertical collusion behavior in the bidding process, the collusion behavior can be effectively controlled. Sirui Nie et al. pointed out that the vertical collusion of bidding will lead to a decline in the quality of the project and various negative effects, while the occurrence of collusion [14] is relatively hidden and difficult to identify. Therefore, an effective and rapid method is necessary to measure the tendency of vertical collusion in bidding to discover vertical collusion in bidding [15].


## 2.2. Factors Influencing Vertical Collusion in Bidding for Government Investment Projects

The collusive behavior of bidding is formed by a combination of influencing factors. The incomplete implementation of the bidding system is an important reason for the prevalence of collusion in government investment projects [16]. This is actually a reflection of the long-standing lack of policy implementation in the bidding field. For a long time, local governments and competent officials have tended to adopt alternative strategies to deal with the implementation of laws and policies. Meanwhile, the implementers choose to adapt the implementation of policies that are not profitable so that indicators such as the level of corruption in the government of the bidding place and the tendency of local collusion have a greater impact on the generation of vertical collusion.Economic motivation is also one of the important reasons for collusion in the bidding process [17]. The reason for this is that the costs and risks of collusion are low compared to the benefits. The cost includes not only the implementation cost of collusion but also the implementation cost and the risk cost. At the same time, the profit-seeking and competition caused by the market economy also contribute to the creation of power and money transactions and collusion in the bidding process in disguise. The local economic development and the degree of competition in the market will have an impact on the collusion. Through research, Henke believes that in the existing bidding model, refusing bribes will increase the participation costs of “honest agents,” has negative externalities and leads to potential corrupt practices [18].


## 2.3. BP Neural Network and Simulated Annealing Algorithm

The BP algorithm originated in the 1980s, has the error back propagation training discovered by David Rumelhart et al. [19]. The algorithm is a model that mimics the neurons of the brain to deal with uncertainty problems. The standard BP neural network is trained twice by the error back propagation algorithm and belongs to a three-layer feedforward network that consists of an input layer, a hidden layer, and an output layer. The main features are that the signal is forward propagation and the error is backward propagation. The BP neural network has better prediction results for highly uncertain problems. The BP algorithm takes the square of the network error as the objective function and uses the gradient descent method to calculate the minimum value of the objective function.BP neural network is essentially a simplified biological model, where the output and input structure on the neural network is a single-layer structure, while the hidden layer is a multilayer structure. All components are connected. The input layer passes the information to the hidden layer after getting the stimulus, and the hidden layer passes the weight information to the output layer according to the calculation rules, and the output layer compares the results and adjusts the weights if the results are incorrect. In other words, the BP neural network uses the backpropagation algorithm to calculate the model for several iterations given the training set D. Finally, the parameters of the training neural network model are determined according to the error requirements. A schematic diagram of the structure of the BP neural network is shown in Figure1.Figure 1
Network structure diagram.


## 2.4. Application of BP Neural Network in the Evaluation Field

BP neural networks have a wide range of applications in nonlinear modeling, system identification, etc. While general neural networks have a predetermined number of network layers, BP neural networks do not require predetermination. Two-layer BP networks achieve the fitting of arbitrary functions without limiting the number of hidden nodes. Therefore, in practical applications, BP neural networks are usually selected with 2 layers.In 2015, Yang Baoan et al. combined BP neural networks with corporate financial analysis and demonstrated the applicability of neural networks in financial analysis [20]. Zeng Zhongdong, on the other hand, found that a neural network model can be useful for establishing a dynamic early warning mechanism for companies in the insurance industry [21]. Fu et al. combined BP neural network with hierarchical analysis to analyze green marketing and found that a high prediction accuracy could be achieved [19]. Yang et al. used a BP neural network to predict the level of teaching management and provide help to improve teaching [22]. Yu et al. found that campus congestion could be better predicted using the BP neural network [23]. Liu Qi et al. found that BP neural networks have high feasibility for application in the field of GEM enterprise value assessment [24]. Wang et al. used the autoregressive integrated moving average (ARIMA) method and the back propagation neural network (BPNN) method to forecast carbon emissions in China, India, the United States, and the European Union in the absence of COVID-19 [25]. Lyu et al. utilized the GA-NN algorithm predicting the torsional strength of reinforced concrete (RC) beams [26]. In summary, it can be found that BP neural networks have high application value and applicability in the field of multiindustry evaluation. Therefore, the introduction of this method in the field of policy adaptability evaluation has high rationality.


## 2.5. Simulated Annealing Algorithm

The simulated annealing (SA) algorithm is derived from the process of temperature change, and the SA algorithm has a strong local search capability [23]. The process is similar to physical annealing, also known as system temperature, by accepting an increase in the objective function through the standard probability rules of Metropolis. SA obtains the global optimal solution to the problem by repeating the sampling during the decrease of the system temperature.


## 3. BP Neural Network Optimized by Annealing Algorithm

### 3.1. Determination of Relevant Evaluation Indicators

In the traditional government project bidding process, the evaluation process for the change of collusive behavior usually prefers to select quantitative indicators, but the adoption of quantitative indicators for group behavior prediction does not fully reflect the influence of human subjective factors on behavior. At the same time, in the actual implementation process, the same policy achieves a wide range of effects in different cities. It also indicates that, in addition to the basic external conditions, qualitative indicators also have a certain influence on the implementation effect of the project. Therefore, it is of great practical value to use a more objective method to evaluate the behavior of each decision maker in the bidding collusion process and to optimize it on this basis.By reading the previous literature and analyzing the influencing factors of the bidding collusion process, we finally determined 13 evaluation indexes in 5 categories and selected the number of colluding groups choosing to collude and break the law as the output value to predict the vertical collusion behavior of the groups. Since the implementation of the policy has a certain lag, this paper selects the average growth rate of the first two years of policy implementation, versus the second two years, as evaluation indicators to increase the credibility of the results.In the external environment, the economic level in the year of policy making in the implementation place is mainly considered, including GDP and the intensity of market competition. The internal environment indicators include the degree of local collusion tendency and the perceived degree of government corruption (data from CGSS2015 and CGSS2017 survey data); the policy making environment needs to be clarified for the level of policy making and the main target group of the policy, etc. The different effects of different levels of policies on the control of collusion also have a large difference. Under the same policy and external conditions, if the government's implementation strength is different, it will also have a certain influence on the behavior of collusion subjects. Therefore, we choose to evaluate the policy implementation strength (i.e., whether special control actions were carried out in the same year) and the degree of judicial impartiality and trial impartiality; the feedback of the implementation process is reflected by the indicators of the effectiveness of supervision procedures. The relevant evaluation indicators are shown in Table1.Table 1
Table of influencing factors.
Primary indicatorsSecondary indicatorsSourceInternal environmentPropensity to collude degreeCGSS2017Government corruption perception degreeCGSS2015External environmentEconomic development GDP total (billion yuan)Statistical yearbookDevelopment of private economyStatistical yearbookTotal construction industry output valueStatistical yearbookPolicy developmentNumber of relevant lawsStatistical yearbookLevel of new lawsNational laws and regulations databaseType of policyMain target groupsEnforcement effortsWhether there was a special state action in the current yearGeneral office of the CPC central committee websiteFairness of justiceCGSS2015Fairness of trialCGSS2015Feedback channelsMonitoring the effectiveness of the processCGSS2015Effectiveness evaluationRate of increase percentage of decrease percentage of decreaseJudgmental instruments network


### 3.2. BP Neural Network Based on Annealing Algorithm Optimization

In the SA-BP algorithm, the neural network structure first needs to be determined and subsequently optimized using a degradation algorithm. After the relevant parameters have been determined, the BP neural network is used to make predictions. It is assumed that the BP neural network hasn nodes in the input layer, q nodes in the hidden layer, and m nodes in the output layer, and the weights between the nodes in the input layer to the nodes in the hidden layer are Vij and the weights between the nodes in the hidden layer to the nodes in the output layer are Wjk.In the forward propagation phase, the hidden layer outputOj and the output Ok of the output layer are(1)oj=fnetjf∑i=1nvijxi−θjok=fnetkf∑i=1nwjkoi−δk,where xi is the input layer sample data netj, netk are the net input data of the jth, kth node of the hidden layer. θj, δk are the node thresholds. fnet is the selected training function.The error back propagation phase with error signals is(2)δk=−∂E∂ok·∂ok∂netkθj=f′netj∑k=0m−1δkwjk,where E is the total error.The weighting corrections are(3)Δwjk=ηojdk−okok1−okΔvjk=oj1−oj∑k=0m−1δkwjkoi.η∈0,1 is for learning rates.The steps of the BP neural network operation based on the optimization of the SA algorithm are as follows:(1)
Initialization. Let us determine the problem domain, select certain values as initial weights, determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network, and the initial values of the annealing algorithm; initial temperature, annealing times, crossover probability, and variation probability, and other related parameters. The initial solution is generated randomly, and the objective function value of this solution is calculated.(2)
Let us transform the current solution in the solution space according to the generated perturbation function to generate a new solution and calculate the objective function value of the new solution.(3)
If the new solution outperforms the old solution, then replacement is performed. If not, it is replaced with a certain probability, according to Metropolis.(4)
The solution is judged by whether the requirements are satisfied or not.(5)
Let us end if the maximum number of substitutions is reached. If not, an annealing operation is performed to reduce the temperature.(6)
Let us substitute the optimal node weights obtained by the neural network and train the sample data.(7)
Then we calculate the mean square error (MSE) of the training results and determine whether the requirements are met.The block diagram of the operational flow is shown in Figure2.Figure 2
Block diagram of the operational flow.


## 3.1. Determination of Relevant Evaluation Indicators

In the traditional government project bidding process, the evaluation process for the change of collusive behavior usually prefers to select quantitative indicators, but the adoption of quantitative indicators for group behavior prediction does not fully reflect the influence of human subjective factors on behavior. At the same time, in the actual implementation process, the same policy achieves a wide range of effects in different cities. It also indicates that, in addition to the basic external conditions, qualitative indicators also have a certain influence on the implementation effect of the project. Therefore, it is of great practical value to use a more objective method to evaluate the behavior of each decision maker in the bidding collusion process and to optimize it on this basis.By reading the previous literature and analyzing the influencing factors of the bidding collusion process, we finally determined 13 evaluation indexes in 5 categories and selected the number of colluding groups choosing to collude and break the law as the output value to predict the vertical collusion behavior of the groups. Since the implementation of the policy has a certain lag, this paper selects the average growth rate of the first two years of policy implementation, versus the second two years, as evaluation indicators to increase the credibility of the results.In the external environment, the economic level in the year of policy making in the implementation place is mainly considered, including GDP and the intensity of market competition. The internal environment indicators include the degree of local collusion tendency and the perceived degree of government corruption (data from CGSS2015 and CGSS2017 survey data); the policy making environment needs to be clarified for the level of policy making and the main target group of the policy, etc. The different effects of different levels of policies on the control of collusion also have a large difference. Under the same policy and external conditions, if the government's implementation strength is different, it will also have a certain influence on the behavior of collusion subjects. Therefore, we choose to evaluate the policy implementation strength (i.e., whether special control actions were carried out in the same year) and the degree of judicial impartiality and trial impartiality; the feedback of the implementation process is reflected by the indicators of the effectiveness of supervision procedures. The relevant evaluation indicators are shown in Table1.Table 1
Table of influencing factors.
Primary indicatorsSecondary indicatorsSourceInternal environmentPropensity to collude degreeCGSS2017Government corruption perception degreeCGSS2015External environmentEconomic development GDP total (billion yuan)Statistical yearbookDevelopment of private economyStatistical yearbookTotal construction industry output valueStatistical yearbookPolicy developmentNumber of relevant lawsStatistical yearbookLevel of new lawsNational laws and regulations databaseType of policyMain target groupsEnforcement effortsWhether there was a special state action in the current yearGeneral office of the CPC central committee websiteFairness of justiceCGSS2015Fairness of trialCGSS2015Feedback channelsMonitoring the effectiveness of the processCGSS2015Effectiveness evaluationRate of increase percentage of decrease percentage of decreaseJudgmental instruments network


## 3.2. BP Neural Network Based on Annealing Algorithm Optimization

In the SA-BP algorithm, the neural network structure first needs to be determined and subsequently optimized using a degradation algorithm. After the relevant parameters have been determined, the BP neural network is used to make predictions. It is assumed that the BP neural network hasn nodes in the input layer, q nodes in the hidden layer, and m nodes in the output layer, and the weights between the nodes in the input layer to the nodes in the hidden layer are Vij and the weights between the nodes in the hidden layer to the nodes in the output layer are Wjk.In the forward propagation phase, the hidden layer outputOj and the output Ok of the output layer are(1)oj=fnetjf∑i=1nvijxi−θjok=fnetkf∑i=1nwjkoi−δk,where xi is the input layer sample data netj, netk are the net input data of the jth, kth node of the hidden layer. θj, δk are the node thresholds. fnet is the selected training function.The error back propagation phase with error signals is(2)δk=−∂E∂ok·∂ok∂netkθj=f′netj∑k=0m−1δkwjk,where E is the total error.The weighting corrections are(3)Δwjk=ηojdk−okok1−okΔvjk=oj1−oj∑k=0m−1δkwjkoi.η∈0,1 is for learning rates.The steps of the BP neural network operation based on the optimization of the SA algorithm are as follows:(1)
Initialization. Let us determine the problem domain, select certain values as initial weights, determine the number of nodes in the input layer, hidden layer, and output layer of the BP neural network, and the initial values of the annealing algorithm; initial temperature, annealing times, crossover probability, and variation probability, and other related parameters. The initial solution is generated randomly, and the objective function value of this solution is calculated.(2)
Let us transform the current solution in the solution space according to the generated perturbation function to generate a new solution and calculate the objective function value of the new solution.(3)
If the new solution outperforms the old solution, then replacement is performed. If not, it is replaced with a certain probability, according to Metropolis.(4)
The solution is judged by whether the requirements are satisfied or not.(5)
Let us end if the maximum number of substitutions is reached. If not, an annealing operation is performed to reduce the temperature.(6)
Let us substitute the optimal node weights obtained by the neural network and train the sample data.(7)
Then we calculate the mean square error (MSE) of the training results and determine whether the requirements are met.The block diagram of the operational flow is shown in Figure2.Figure 2
Block diagram of the operational flow.


## 4. Empirical Analysis of Predicting Group Behavior of Vertical Collusion in Bidding for Government Investment Projects

### 4.1. Mixed Stabilisation Strategy for Gaming Subjects

In order to verify the applicability of the algorithm and the effectiveness of the fit to the relevant data, MATLAB simulation was used to simulate the proportional decrease of relevant cases before and after the promulgation of the policy in relevant cities in China. In order to ensure the validity of the data, a total of 166 samples from 31 provinces, cities, and autonomous regions were selected for the simulation from the promulgation of the Measures on Bidding and Tendering for Engineering Construction Projects in 2005 to the end of 2020.The output parameters were the percentage decrease in the growth rate of cases and the percentage decrease in the variance. Before the training started, the maximum number of training cycles was set to 1000, the proportion of validation samples was set to 15%, and the proportion of test samples was set to 15%. The annealing algorithm parameters were set to a start temperature of 97°C, an end temperature of 3°C, and a decay coefficient of 0.8. MATLAB was used for the simulation.As can be seen from Figure3, with the continuous optimization of the simulation degradation algorithm, the current accepted optimal solution is continuously close to the historical optimal solution, the value of the mean error gradually decreases, and the model obtains a higher degree of fit.Figure 3
Annealing effect at reduced temperature.From Figure4, it can be found that the validation sample obtained the best fit after the 6th training session as the number of training sessions continued to increase.Figure 4
Plot of mean squared error of training times.From Figures5 and 6, it can be seen that the actual effect of the test data has a small error with the prediction result. Over 70% of the predicted data is distributed around the 0 error line.Figure 5
Sample regression plots.Figure 6
Error distribution chart.Therefore, the BP neural network optimized based on the simulated annealing algorithm can better predict the effect of government project bidding control policies, providing some reference value for the government to formulate policies. It also provides a basis for how the government formulates policies according to the local external environment, economic conditions, and the level of market development.The simulation results show that changes in vertical collusion in tendering can be better predicted through indicators such as external conditions and the internal environment. It also shows that the above conditions have an impact on the creation of bid collusion. Therefore, the control path of the project can be investigated through the above indicators.For researchers, this model extends the existing research and proposes a vertical collusion behavior prediction model for government investment project bidding based on SA-BP, which provides a new research direction for related research. For the government, before formulating policies on the control of collusion behavior in bidding, it can conduct research on the external environment of the city where the policy is implemented to predict the effect of vertical collusion control after the implementation of the new policy, provide data basis and theoretical support for policy formulation, and improve the pertinence of control policies. For project managers, the degree of control of vertical collusion behavior in the bidding process has a greater impact on the difficulty of project acquisition and project profits. So the model proposed in the research can be used to predict the vertical collusion behavior before the bidding, providing guidance for management work.


## 4.1. Mixed Stabilisation Strategy for Gaming Subjects

In order to verify the applicability of the algorithm and the effectiveness of the fit to the relevant data, MATLAB simulation was used to simulate the proportional decrease of relevant cases before and after the promulgation of the policy in relevant cities in China. In order to ensure the validity of the data, a total of 166 samples from 31 provinces, cities, and autonomous regions were selected for the simulation from the promulgation of the Measures on Bidding and Tendering for Engineering Construction Projects in 2005 to the end of 2020.The output parameters were the percentage decrease in the growth rate of cases and the percentage decrease in the variance. Before the training started, the maximum number of training cycles was set to 1000, the proportion of validation samples was set to 15%, and the proportion of test samples was set to 15%. The annealing algorithm parameters were set to a start temperature of 97°C, an end temperature of 3°C, and a decay coefficient of 0.8. MATLAB was used for the simulation.As can be seen from Figure3, with the continuous optimization of the simulation degradation algorithm, the current accepted optimal solution is continuously close to the historical optimal solution, the value of the mean error gradually decreases, and the model obtains a higher degree of fit.Figure 3
Annealing effect at reduced temperature.From Figure4, it can be found that the validation sample obtained the best fit after the 6th training session as the number of training sessions continued to increase.Figure 4
Plot of mean squared error of training times.From Figures5 and 6, it can be seen that the actual effect of the test data has a small error with the prediction result. Over 70% of the predicted data is distributed around the 0 error line.Figure 5
Sample regression plots.Figure 6
Error distribution chart.Therefore, the BP neural network optimized based on the simulated annealing algorithm can better predict the effect of government project bidding control policies, providing some reference value for the government to formulate policies. It also provides a basis for how the government formulates policies according to the local external environment, economic conditions, and the level of market development.The simulation results show that changes in vertical collusion in tendering can be better predicted through indicators such as external conditions and the internal environment. It also shows that the above conditions have an impact on the creation of bid collusion. Therefore, the control path of the project can be investigated through the above indicators.For researchers, this model extends the existing research and proposes a vertical collusion behavior prediction model for government investment project bidding based on SA-BP, which provides a new research direction for related research. For the government, before formulating policies on the control of collusion behavior in bidding, it can conduct research on the external environment of the city where the policy is implemented to predict the effect of vertical collusion control after the implementation of the new policy, provide data basis and theoretical support for policy formulation, and improve the pertinence of control policies. For project managers, the degree of control of vertical collusion behavior in the bidding process has a greater impact on the difficulty of project acquisition and project profits. So the model proposed in the research can be used to predict the vertical collusion behavior before the bidding, providing guidance for management work.


## 5. Conclusions and Limitations

### 5.1. Conclusions

(1)
In the actual calculation, 166 samples from 31 provinces, cities, and autonomous regions in China were selected for the analysis, covering the changes in vertical collusion in most cities in China after 2005. The introduction of the simulated annealing algorithm avoids the complex process of parameter selection in BP neural networks and facilitates the extension of the method.(2)
The results of the study showed that the use of SA-BP models to predict collusion bidding behavior has a high accuracy rate. The model constructed in this paper can be used to predict changes in bidding behavior, help relevant government departments predict changes in bidding behavior, and provide data support for the government to formulate control policies.(3)
The BP neural network vertical collusion behavior prediction model of government project bidding based on the optimization of the annealing algorithm proposed in this paper effectively solves the problem of policy formulation and implementation mainly relying on subjective judgment and lacking data guidance in the current process of bidding collusion behavior control process by using external conditions to predict the change trend of collusive behavior.


### 5.2. Limitations

(1)
As some of the data collection remained the same during the writing of the thesis, necessary simplifications were made to the indicators in the model building process. In future research, the credibility of the model can be enhanced by increasing the scale of the survey and obtaining relevant data.(2)
In the process of future practice, multiple deep learning models and research methods can be used to predict the behavior of vertical collusion groups, analyze the influence of external conditions on collusion behavior under different circumstances and achieve crossvalidation of the research results.


## 5.1. Conclusions

(1)
In the actual calculation, 166 samples from 31 provinces, cities, and autonomous regions in China were selected for the analysis, covering the changes in vertical collusion in most cities in China after 2005. The introduction of the simulated annealing algorithm avoids the complex process of parameter selection in BP neural networks and facilitates the extension of the method.(2)
The results of the study showed that the use of SA-BP models to predict collusion bidding behavior has a high accuracy rate. The model constructed in this paper can be used to predict changes in bidding behavior, help relevant government departments predict changes in bidding behavior, and provide data support for the government to formulate control policies.(3)
The BP neural network vertical collusion behavior prediction model of government project bidding based on the optimization of the annealing algorithm proposed in this paper effectively solves the problem of policy formulation and implementation mainly relying on subjective judgment and lacking data guidance in the current process of bidding collusion behavior control process by using external conditions to predict the change trend of collusive behavior.


## 5.2. Limitations

(1)
As some of the data collection remained the same during the writing of the thesis, necessary simplifications were made to the indicators in the model building process. In future research, the credibility of the model can be enhanced by increasing the scale of the survey and obtaining relevant data.(2)
In the process of future practice, multiple deep learning models and research methods can be used to predict the behavior of vertical collusion groups, analyze the influence of external conditions on collusion behavior under different circumstances and achieve crossvalidation of the research results.



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*Source: 9238838-2022-03-23.xml*