A method for optimizing the dispatch of traffic police forces

Abstract

This invention belongs to the technical field of urban road network resilience research under traffic accidents. It specifically discloses a method for optimizing the dispatch of traffic police force, comprising the following steps: establishing a MILP model based on the UR network within the patrol duty area of ​​a traffic police detachment; solving the MILP model using the CPLEX and Yalmip libraries to obtain an optimal traffic police dispatch solution, thereby achieving optimized traffic police dispatch. This invention addresses the problem that existing research on improving UR network resilience fails to consider the importance of traffic police in handling traffic accidents. By achieving optimal traffic police dispatch during traffic accidents, the method minimizes the total dispatch cost and shortens the duration of the adverse effects caused by the accident.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban road network resilience research under traffic accidents, and specifically relates to a method for optimizing the dispatching of traffic police forces. Background Art

[0002] Traffic accidents not only disrupt the normal operation of urban road (UR) networks but also cause significant casualties. Traffic police are primarily responsible for traffic management and accident investigation. Therefore, they play a vital role in restoring normal operation of UR networks affected by traffic accidents. In real life, the number of available traffic police is often limited. When there are insufficient traffic police to handle all incidents simultaneously, optimizing the dispatch of traffic police to restore normal operation of the affected UR networks is crucial. The above analysis demonstrates that optimizing the dispatch of traffic police during traffic accidents can improve the ability of affected UR networks to respond to traffic accidents.

[0003] Traffic accidents are one of the most common reasons that affect the normal daily operation of UR networks. To this end, scholars have conducted extensive research on traffic accidents in UR networks. The main research contents include traffic accident prediction, influencing factor analysis, and traffic management during accidents (such as traffic flow prediction). The main purpose of traffic accident prevention research is to avoid traffic accidents, while the purpose of research during traffic accidents is to quickly restore the normal operation of the affected network. In existing research, traffic control system design and vehicle detour guidance have been widely used in traffic accident management. For example, emergency control policies based on traffic signals are used to prevent large-scale congestion caused by traffic accidents. Dynamic adaptive vehicle detour routing strategies are used to reduce the negative impact of traffic congestion on UR networks. Although existing technologies have studied various measures to manage traffic accidents in UR networks from different perspectives, they all emphasize the importance of effective traffic accident management to improve the ability of UR networks to cope with such incidents.

[0004] Despite a large number of studies on improving UR network resilience during traffic accidents, there is still less research on improving UR network resilience by optimizing traffic police dispatch. However, traffic police play an important role in handling traffic accidents, and their impact on restoring normal operations of affected UR networks cannot be ignored. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that existing research on improving UR network resilience does not take into account the importance of traffic police in handling traffic accidents, and proposes a traffic police force optimization scheduling method.

[0006] The technical solution of the present invention is: a method for optimizing the dispatch of traffic police force, comprising the following steps:

[0007] S1. Establish a MILP model based on the urban road network within the patrol area of ​​the traffic police detachment;

[0008] S2. Use the commercial solver CPLEX to solve the MILP model, obtain the optimal traffic police dispatch plan, and complete the optimal dispatch of traffic police force.

[0009] The beneficial effects of the present invention are:

[0010] By establishing a MILP model that takes traffic police into consideration and solving it using CPLEX, the present invention achieves optimal traffic police dispatch during traffic accidents. This can minimize the total dispatch cost, shorten the duration of the adverse effects caused by the accident, and effectively improve the resilience of the UR network.

[0011] Preferably, the objective function of the MILP model in step S1 is expressed as:

[0012]

[0013] Among them, min means minimization, F means the objective function, F1 means the first component, F2 means the second component, represents the model weight, v represents the passenger’s travel time value;

[0014] The first component F1 includes labor costs, police car operating costs and penalty costs for failure to handle traffic accidents in a timely manner. The specific expression formula is:

[0015]

[0016] Among them, A represents the traffic accident set, K represents the available TPT set, ρ k represents the cost of the kth TPT to complete a single task, v represents the value time of the passenger, Indicates whether to dispatch the kth TPT to handle the ith accident, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. represents the travel time of the kth TPT from the starting point o to the i-th accident, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, represents the travel time of the kth TPT from the i-th accident to the destination d, It indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ is the penalty coefficient, p i represents the penalty time of the i-th accident;

[0017] The second component F2 is the latest time for TPT to arrive at the accident scene, and the specific expression formula is:

[0018]

[0019] Among them, max means maximization, w i Represents the total time to handle the i-th accident.

[0020] Preferably, the constraints of the MILP model in step S1 include accident handling rule constraints, time constraints for TPT to arrive at the traffic accident scene, coupling constraints, time constraints for completing the handling of the i-th accident, accident severity constraints, constraints on the earliest and latest traffic accidents handled by TPT, and delayed handling time constraints for accidents.

[0021] Preferably, the accident handling rule constraint is that for the i-th accident, one TPT handles it once, and the specific formula is:

[0022]

[0023] in, Indicates whether to dispatch the kth TPT to handle the ith accident, K represents the available TPT set, and A represents the traffic accident set.

[0024] Preferably, the specific expression formula of the time constraint of the TPT arriving at the traffic accident scene is:

[0025]

[0026] in, represents the time when the kth TPT arrives at the jth accident, represents the time when the kth TPT arrives at the i-th accident, A represents the set of traffic accidents, K represents the set of available TPTs, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. represents the intermediate variable, and T2 represents the maximum value.

[0027] Preferably, the specific expression formula of the coupling constraint is:

[0028]

[0029] in, represents the time when the kth TPT arrives at the i-th accident, T1 represents the minimum vehicle travel time between any given nodes, A represents the set of traffic accidents, K represents the set of available TPTs, Indicates whether to dispatch the kth TPT to handle the ith accident.

[0030] Preferably, the specific expression formula of the processing completion time constraint of the i-th accident is:

[0031]

[0032] Among them, w i represents the total time to handle the i-th accident, K represents the available TPT set, represents the time when the kth TPT arrives at the i-th accident, and A represents the set of traffic accidents.

[0033] Preferably, the specific expression formula of the accident severity constraint is:

[0034]

[0035] Among them, s i represents the severity of the i-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident, M1 and is a constant, s j represents the severity of the j-th accident, K represents the available TPT set, and A represents the traffic accident set.

[0036] Preferably, the specific expression formulas of the earliest and latest traffic accident constraints processed by the TPT are:

[0037]

[0038] in, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, Indicates whether the kth TPT starts from the starting point o, Indicates whether the kth TPT returns to the destination d after handling the i-th accident, Indicates whether the kth TPT processes the i-th accident first, Indicates whether the kth TPT handles the i-th accident last, Indicates whether the kth TPT finally returns to the destination d, A represents the traffic accident set, K represents the available TPT set, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT;

[0039] Whether the kth TPT processes the i-th accident first and whether the kth TPT handles the i-th accident last The following constraints are met:

[0040]

[0041] in, represents the time when the kth TPT arrives at the i-th accident site, M2 and is a constant, G k and H k Indicates intermediate variables, min means minimization, and max means maximization

[0042] Preferably, the specific expression formula of the delayed processing time constraint of the accident is:

[0043]

[0044] Among them, d i represents the delayed processing time of the i-th accident, A represents the set of traffic accidents, w i represents the total time to handle the i-th accident, and γ represents the maximum allowed delay time.

[0045] The beneficial effects of the above preferred solution are:

[0046] 1. By constructing the objective function based on labor costs, police car operating costs, penalty costs for failing to handle traffic accidents in a timely manner, and the latest time for TPTs to arrive at the accident scene, and considering the time for TPTs to arrive at the traffic accident scene, coupling, completion time of handling the i-th accident, accident severity, the earliest and latest traffic accidents handled by TPTs, and the delayed handling time of accidents as constraints, the cost of dispatching traffic police can be minimized and the duration of the impact can be shortened, thereby achieving rapid and effective handling of traffic accidents.

[0047] 2. Expressing the objective function and constraints of the MILP model in linear form facilitates CPLEX's solution, enabling efficient and accurate identification of the optimal traffic police dispatch plan and rapid and effective handling of traffic accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The figure shows a flow chart of a method for optimizing the dispatching of traffic police force provided in Example 1 of the present invention.

[0049] Figure 2 The diagram shows a UR network diagram provided in Example 1 of the present invention.

[0050] Figure 3 The figure shows a schematic diagram of a UR network provided in Example 2 of the present invention.

[0051] Figure 4 Shown is a line graph of the model solution time under different numbers of traffic accidents provided in Example 2 of the present invention.

[0052] Figure 5 Shown is a line graph showing the relationship between the objective function value and model weight of the MILP model provided in Example 2 of the present invention.

[0053] Figure 6 Shown is a line graph showing the relationship between the objective function value of the MILP model provided in Example 2 of the present invention and the cost of calling the second TPT.

[0054] Figure 7 Shown is a line graph showing the relationship between the objective function value and the penalty coefficient of the MILP model provided in Example 2 of the present invention.

[0055] Figure 8 Shown is a line graph showing the relationship between the objective function value and the maximum delay time of the MILP model provided in Example 2 of the present invention.

[0056] Figure 9 Shown is a line graph showing the relationship between the objective function value and VOT of the MILP model provided in Example 2 of the present invention.

[0057] Figure 10 Shown is a line graph showing the relationship between the objective function value of the MILP model provided in Example 2 of the present invention and the vehicle speed. DETAILED DESCRIPTION

[0058] The exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are merely exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0059] Example 1:

[0060] like Figure 1 As shown, a method for optimizing the dispatching of traffic police force includes the following steps:

[0061] S1. Establish a mixed-integer linear programming (MILP) model based on the UR network within the patrol area of ​​the traffic police detachment;

[0062] S2. Combine the commercial solver CPLEX and the Yalmip library, and use MATLAB to solve the MILP model, output the optimal traffic police dispatch plan, and complete the optimized dispatch of traffic police force.

[0063] In this example, rationally arranging traffic police investigation tasks during a traffic accident not only helps reduce the cost of dispatching traffic police but also quickly restores normal operations of the affected UR network. This example only studies the patrol duty area of ​​a single traffic police detachment. This example defines the traffic police handling traffic accidents as a traffic police team (TPT). All solutions proposed in this example are designed based on the TPT.

[0064] The UR network within the patrol duty area of ​​the traffic police detachment is defined as G(N1, N2, E), where N1, N2, and E represent the road intersections and endpoints, the intersections between the road and the patrol duty area, and the road sections, respectively. Figure 2 As shown, the UR network contains 25 nodes, including 16 road intersections and endpoints, and 9 intersections between roads and patrol duty areas. There are four traffic accidents in the UR network, of which accidents 1, 2, and 3 occurred within patrol duty areas. The "+" symbol next to a traffic accident indicates its severity; more "+" symbols indicate a more serious accident.

[0065] Assume that when the above traffic accident occurs, the available TPT is located at node number 15. In order to restore the normal operation of the affected UR network in the area, the command center should dispatch the above TPT to handle traffic accidents 1 to 3 within its jurisdiction. Usually, the command center formulates a dispatch plan based on the severity and location of the traffic accident. Figure 2 As shown in the figure, there are two possible dispatch routes: the red line indicates that TPT handles accident 2 first and accident 3 last; while the green line indicates that TPT handles accident 2 first and accident 1 last. Through analysis, it is found that the red line is better than the green line because it has a shorter vehicle travel distance.

[0066] In summary, formulating a traffic police dispatch plan in the event of a traffic accident requires considering factors such as the available TPTs, the UR network structure, and the severity and location of the traffic accident. In a simple UR network, since the available TPTs and the number of traffic accidents are limited, an enumeration method can be used in this network to obtain the optimal traffic police dispatch plan. However, the complexity of the actual UR network structure and the large number of available TPTs increase the difficulty of using the enumeration method to obtain the optimal plan. Therefore, this embodiment establishes an MILP model to effectively solve the above problem. This model aims to minimize the dispatch cost of traffic police and shorten the duration that the network is affected by traffic accidents. Before establishing the model, the following assumptions are made:

[0067] A1.TPT travels between different places via the shortest route;

[0068] A2. The time required for TPT to handle the incident is not taken into account;

[0069] A3. Detailed information about traffic accidents (e.g., severity) is known before planning and remains constant.

[0070] Therefore, the objective function of the MILP model in step S1 is expressed as:

[0071]

[0072] Among them, min means minimization, F represents the objective function, F1 represents the first component, which formulates the scheduling plan by minimizing the scheduling cost, and F2 represents the second component, which aims to shorten the duration of network impact. represents the model weight, v represents the value time of the passenger;

[0073] The first component F1 includes labor costs, police car operating costs and penalty costs for failure to handle traffic accidents in a timely manner. The specific expression formula is:

[0074]

[0075] Among them, A represents the traffic accident set, K represents the available TPT set, ρ k represents the cost of the kth TPT to complete a single task, v represents the value time of the passenger, Indicates whether to dispatch the kth TPT to handle the ith accident, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. represents the travel time of the kth TPT from the starting point o to the i-th accident, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, represents the travel time of the kth TPT from the i-th accident to the destination d, It indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ is the penalty coefficient, p i represents the penalty time of the i-th accident;

[0076] The second component F2 is the latest time for TPT to arrive at the accident scene, and the specific expression formula is:

[0077]

[0078] Among them, max means maximization, w iRepresents the total time to handle the i-th accident.

[0079] In this embodiment, the constraints of the MILP model described in S1 include accident handling rule constraints, time constraints for the TPT to arrive at the traffic accident scene, coupling constraints, time constraints for completing the handling of the i-th accident, accident severity constraints, constraints on the earliest and latest traffic accidents handled by the TPT, and delayed handling time constraints for accidents.

[0080] In this embodiment, the accident handling rule constraint is that for the i-th accident, one TPT handles it once. The specific formula is:

[0081]

[0082] in, Indicates whether to dispatch the kth TPT to handle the ith accident, K represents the available TPT set, and A represents the traffic accident set.

[0083] In this embodiment, the time when the TPT arrives at the traffic accident scene is related to its departure time and the vehicle's travel time. Therefore, the specific expression formula for the time constraint of the TPT arriving at the traffic accident scene is:

[0084]

[0085] in, represents the time when the kth TPT arrives at the jth accident, represents the time when the kth TPT arrives at the i-th accident, A represents the set of traffic accidents, K represents the set of available TPTs, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident;

[0086] Transform the nonlinear part and get:

[0087]

[0088] in, represents the intermediate variable, and T2 represents the maximum value.

[0089] In this embodiment, the coupling constraint is used to describe and The relationship between them is expressed as follows:

[0090]

[0091] in, represents the time when the kth TPT arrives at the i-th accident, T1 represents the minimum vehicle travel time between any given nodes, A represents the set of traffic accidents, K represents the set of available TPTs, Indicates whether to dispatch the kth TPT to handle the ith accident.

[0092] In this embodiment, the specific expression formula of the processing completion time constraint of the i-th accident is:

[0093]

[0094] Among them, w i represents the total time to handle the i-th accident, K represents the available TPT set, represents the time when the kth TPT arrives at the i-th accident, and A represents the set of traffic accidents.

[0095] In this embodiment, during the actual dispatching and commanding process, the command center usually gives priority to dispatching available TPTs to handle traffic accidents with higher severity. The specific expression formula of the accident severity constraint is:

[0096] Among them, s i represents the severity of the i-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident, M1 and is a constant, M1=1, s j represents the severity of the j-th accident, K represents the available TPT set, and A represents the traffic accident set.

[0097] In this embodiment, the specific expression formulas of the earliest and latest traffic accident constraints processed by the TPT are:

[0098]

[0099] in, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, Indicates whether the kth TPT starts from the starting point o. If the kth TPT starts from the starting point o, then otherwise Indicates whether the kth TPT returns to the destination d after handling the i-th accident, Indicates whether the kth TPT processes the ith accident first. If the kth TPT processes the ith accident first, then otherwise Indicates whether the kth TPT last processed the ith accident. If the kth TPT last processed the ith accident, then otherwise Indicates whether the kth TPT finally returns to the destination d. If the kth TPT finally returns to the destination d, then otherwise A represents the traffic accident set, K represents the available TPT set, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT;

[0100] Whether the kth TPT processes the i-th accident first and whether the kth TPT handles the i-th accident last The following constraints are met:

[0101]

[0102]

[0103] Performing linearization operation, we get:

[0104]

[0105] in, represents the time when the kth TPT arrives at the i-th accident site, M2 and is a constant, M2=100000, G k and H k Indicates intermediate variables, min means minimization, and max means maximization

[0106] In this embodiment, according to the relevant regulations of my country's traffic police in performing accident investigation tasks, the available TPT requires arriving at the traffic accident scene within 15 minutes, so the delayed processing time d of the i-th accident is i is max(0,w i -γ), after linearization, the specific expression formula of the accident delay processing time constraint is obtained:

[0107]

[0108] Among them, d i represents the delayed processing time of the i-th accident, A represents the set of traffic accidents, w i represents the total time to handle the i-th accident, and γ represents the maximum allowed delay time.

[0109] Example 2:

[0110] Based on Example 1, the technical effect of the traffic police force optimization dispatching method proposed by the present invention is described.

[0111] In this embodiment, Figure 3 The UR network shown in Figure 1 is used as an example to verify the effectiveness of the MILP model described in Example 1. Figure 2 The UR network within the patrol duty area consists of 366 nodes (including 322 road intersections and endpoints, and 44 intersections between roads and patrol duty areas) and 314 road sections.

[0112] Assumptions Figure 3 The road grades are consistent, and the average speed of police cars is 50 km / h. The travel time can be calculated based on the distances between different nodes. Traffic accidents are more likely to occur at intersections, so this example focuses on accidents occurring at intersections. The research methods for accidents occurring between road sections are similar to those for accidents at intersections and are not further described in this example. Figure 3 In the figure, circles represent traffic accidents, triangles represent available TPTs, and the decimals near the traffic accident represent the severity of the corresponding accident. For example, the red node and decimal point at intersection 67 indicate that an accident with a severity of 0.51 occurred there.

[0113] In this example, two traffic accidents of different sizes were studied. The first scenario was a small-scale case involving six accidents. In this small-scale case, the accident occurring at node 114 had the highest severity. The second scenario was a large-scale case involving 12 accidents. In this large-scale case, the accident occurring at node 132 was the most serious. Before the accident, the two available TPTs were located at nodes 147 and 365, respectively. After these TPTs completed their investigation tasks for all accidents, they could choose to return to any of the following nodes: 55, 124, 147, 173, or 365.

[0114] The other parameters used in the MILP model in this example are shown in Table 1. The passenger's VOT is set to 60.43 yuan per hour. In real life, due to the limited number of TPTs on duty and the fact that only one TPT is often available for traffic accident investigations, dispatching a second TPT to complete the task is very costly. Therefore, this paper sets the cost per unit of task completed by the first and second TPTs to 1 yuan and 20 yuan, respectively. The model's penalty coefficient and maximum allowable delay are set to 100 and 900 seconds, respectively.

[0115] Table 1 Other parameters used in the MILP model

[0116] parameter Value Passenger travel time value 60.43RMB / h The cost of completing a single task with TPT [1RMB,20RMB] Penalty coefficient 100 Maximum allowed delay time 900s

[0117] The proposed solution method was used to solve the MILP model, resulting in the optimal traffic police dispatching schemes for both small-scale and large-scale cases. Table 2 lists the model solution time, objective function values, and optimal dispatching schemes for different cases. The results shown in Table 2 show that the time required to solve the small-scale and large-scale cases using the model was 1.30 seconds and 6.43 seconds, respectively, demonstrating that the proposed CPLEX-based solution method can efficiently solve the model. Dispatching schemes in Table 2 are represented by a combination of node numbers and dashes. For example, the scheme "TPT 1:147-114-67-222-173" indicates that TPT number 1 first processes the incident at node 114 and then processes the incident at node 222. After completing all assigned tasks, the TPT returns to node 173. The effectiveness of the resulting scheme is illustrated using the optimal solution for the small-scale case. The objective function value of the model in this small-scale case is 113.87 yuan (where the values ​​of the first and second sub-objective functions are 99.41 yuan and 861.48 seconds, respectively). By analyzing the optimal scheduling plan for small-scale cases, it can be found that the command center arranged two available TPTs to handle six traffic accidents. When all accidents were handled, both TPTs returned to node 173.

[0118] Table 2 Computation time, objective function value and optimal traffic police dispatching plan

[0119]

[0120] To further validate the effectiveness of the proposed model, the optimal solution in Table 2 was compared with a basic solution commonly used in real life. In the basic solution, the command center dispatches TPTs based on the severity of the traffic accident. The objective function values ​​obtained using the basic solution were 353.95 yuan for small-scale cases and 5247.16 yuan for large-scale cases, respectively. These results demonstrate that the solution derived from the proposed MILP model outperforms the basic solution. Specifically, the optimal solution obtained by the model reduced the objective function values ​​by 64.87% for small-scale cases and 32.90% for large-scale cases.

[0121] This embodiment assumes that there are two available TPTs for handling traffic accidents. In order to evaluate the impact of the number of available TPTs on the model solution effect, the model objective function values ​​under different numbers of available TPTs are listed in Table 3. The TPT numbered 3 shown in Table 3 is assumed to be located at node 147, and its scheduling cost for completing a unit task is 20 yuan. In small-scale cases, the optimal objective function value is obtained when the number of available TPTs is 2; however, in large-scale cases, as the number of available TPTs increases, the objective function value of the MILP model continues to decrease. The above results show that in areas where multiple traffic accidents may occur at the same time, it is necessary to appropriately increase the number of available TPTs (i.e., increase the number of TPTs on duty). Specifically, based on historical data, the command center can use the model proposed in the present invention to determine the optimal number of available TPTs required in a given patrol duty area.

[0122] Table 3 Impact of the number of schedulable TPTs

[0123]

[0124]

[0125] The model developed by the present invention assumes that TPT will give priority to handling more serious traffic accidents. In order to discuss the impact of the above-mentioned priority on the design of the dispatching plan, taking a small-scale case as an example, Table 4 lists the objective function values ​​with and without considering the impact of the severity of the traffic accident. The results show that the objective function value of the plan formulated without considering the impact of the severity of the accident is lower than the objective function value of the plan formulated with the impact of the severity of the traffic accident. The reason is that when the impact of the severity of the accident on the dispatching plan is ignored, TPT directly completes the investigation and handling of all accidents based on the shortest path. However, in actual operation, the command center usually arranges available TPT to give priority to handling more serious accidents, because more serious accidents usually cause more serious economic losses and casualties. Therefore, the impact of the severity of traffic accidents on the traffic police dispatching plan cannot be ignored.

[0126] Table 4 Objective value with and without considering the impact of accident severity

[0127] Consider the severity? F(RMB) <![CDATA[F1(RMB)]]> <![CDATA[F2(s)]]> yes 113.87 99.41 861.48 no 88.81 75.66 783.29

[0128] This example assumes that the TPT can return to five nodes (i.e., nodes 55, 124, 147, 173, and 365) after completing the task. In order to evaluate the impact of the destination location returned after completing the task on the model's objective function value, a comparative analysis was conducted on traffic police dispatching schemes in which the TPT needs to return to the starting point after completing the task (i.e., TPT 1 and 2 return to nodes 147 and 365, respectively, after completing the task). Table 5 lists the objective function values ​​for schemes in which the TPT does and does not need to return to the starting point. The results shown in Table 5 show that the objective function value of the scheme requiring the TPT to return to the starting point is greater than the objective function value corresponding to the scheme that does not require it to return to the starting point. This indicates that when the TPT must return to the starting point, the cost of dispatching the TPT to complete the traffic accident investigation task will change, indicating that the impact of the destination location on the dispatching scheme design cannot be ignored.

[0129] Table 5 Impact of needing to return to the departure point

[0130]

[0131] To further explore the effectiveness of the proposed solution algorithm for solving the MILP model, a genetic algorithm was used to solve the model. Table 6 lists the computation time and corresponding objective function values ​​of the different algorithms. The results in Table 6 show that the computation time of the genetic algorithm is shorter than the solution time of the proposed algorithm. However, the objective function value obtained by the genetic algorithm is greater than that obtained by the CPLEX-based algorithm. In addition, when the genetic algorithm is used to solve a large-scale case, the model has no solution. These results indicate that the proposed solution algorithm can effectively solve the proposed model.

[0132] Table 6 Comparison of different solution algorithms

[0133]

[0134] The model solution time under different numbers of traffic accidents is as follows Figure 4 As shown in the figure, there is a positive exponential relationship between the model solution time and the number of traffic accidents. For example, when the number of traffic accidents increases from 1 to 13, the solution time of the model increases from 0.31 seconds to 6.27 seconds. The above results show that the computational efficiency of the model solution algorithm proposed in the present invention decreases with the increase in the number of traffic accidents. However, in actual situations, the average number of traffic accidents occurring simultaneously in a city is usually less than 5. For example, in 2023, the total number of traffic accidents in Chengdu was 1,324 (that is, the number of traffic accidents per day was approximately 3.62). Therefore, the model solution algorithm proposed in the present invention can meet the needs of actual traffic police dispatch scheme design.

[0135] In this embodiment, a small-scale case is used as an example to discuss the influence of different parameters on the toughness improvement effect of the model proposed in the present invention using parameter sensitivity analysis. The results are as follows: Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 and Figure 10 shown.

[0136] like Figure 5 As shown in Figure 2, there is a positive correlation between the objective function value of the model and the model weight. The fitting curve between (fitting degree is 1.0), indicating that the weight For every unit increase, the objective function value of the model increases by an average of 14.46 yuan. The results show that the influence of model weight on scheduling scheme design cannot be ignored. Figure 6 The results show the impact of the cost of dispatching a second TPT on the model's objective function. The correlation coefficient between the cost of the second TPT and the objective function is 0.978, indicating a strong positive correlation. Furthermore, the growth rate of the objective function decreases as the cost of the second TPT increases. These results indicate the importance of deploying a sufficient number of TPTs in areas with a high probability of traffic accidents. This measure not only helps quickly restore normal operations to the affected UR network, but also minimizes the costs incurred by dispatching traffic police.

[0137] The impact of the penalty coefficient on the model objective function value is as follows Figure 7 As shown in Figure 3, the results show that the objective function value changes slightly with the increase of the penalty coefficient. This is because all traffic accidents are handled promptly in the small-scale case. However, in the large-scale case, there is a strong positive correlation between the penalty coefficient and the model objective function value. Figure 8 The relationship between the model's objective function value and the maximum allowable delay time is shown. As the maximum allowable delay time increases, the model's objective function value first decreases and then remains constant. The reason for this result is that the total time required for the TPT to complete the task is less than 900 seconds (i.e., 861.48 seconds). Only when the total time required to complete the task exceeds 900 seconds does the maximum allowable delay time affect the model's objective function value. Therefore, in order to minimize the adverse impact of traffic accidents on UR network operations, the command center should reasonably dispatch available TPTs in the event of a traffic accident to quickly restore normal operations of the affected UR network.

[0138] The relationship between the objective function value of the model and the passenger's value of time (VOT) is as follows: Figure 9As shown, there is a strong positive correlation between the two. When VOT increases from 20.43 yuan / hour to 70.43 yuan / hour, the model's objective function value rises from 83.73 yuan to 134.48 yuan, a 60.60% increase. Therefore, when the normal operation of the UR network in a city with high VOT is affected by a traffic accident, the command center should quickly design an effective traffic police dispatch plan to handle the traffic accident and reduce its impact on the UR network operation. Figure 10 The model's objective function value decreases as vehicle speed increases, indicating that the cost of dispatching traffic police to handle traffic accidents can be reduced by increasing vehicle speed. Therefore, for TPTs undertaking traffic accident investigations, they can use emergency lanes to increase vehicle speeds, thereby improving response efficiency.

[0139] In summary, the model and solution algorithm proposed in this invention can obtain the optimal traffic police dispatch plan in a relatively short time during traffic accidents. Compared with the basic solution widely used in actual dispatch, the optimal solution proposed in this invention can reduce the objective function value by 64.87% and 32.90% for small-scale and large-scale cases, respectively. Secondly, the number of available TPTs greatly affects the effectiveness of the solution obtained by the model. The command center can use the model developed in this invention to determine the optimal number of available TPTs within a given patrol duty area based on historical data. In addition, the severity of traffic accidents and the location of the destination cannot be ignored in the design of traffic police dispatch plans. Third, compared with genetic algorithms, the model solution algorithm proposed in this invention can achieve more efficient model solution. In addition, there is an exponential positive correlation between the model's calculation time and the number of traffic accidents. Finally, the impact of various parameters on the model's objective function value was analyzed. The results show that the objective function value is affected by the cost of the TPT execution task, the maximum allowable delay time, the VOT, and the vehicle travel time.

[0140] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for optimizing the dispatch of traffic police force, characterized in that: The method specifically comprises the following steps: S1. Establish a MILP model based on the urban road network within the patrol area of ​​the traffic police detachment; S2. Use the commercial solver CPLEX to solve the MILP model and obtain the optimal traffic police dispatch plan, thus optimizing the dispatch of traffic police forces. The objective function of the MILP model is expressed as follows: Among them, min means minimization, F means the objective function, F1 means the first component, F2 means the second component, represents the model weight, v represents the passenger’s travel time value; The first component F1 includes labor costs, police car operating costs and penalty costs for failure to handle traffic accidents in a timely manner. The specific expression formula is: Among them, A represents the traffic accident set, K represents the available TPT set, TPT represents the traffic police team, ρ k represents the cost of the kth TPT to complete a single task, Indicates whether to dispatch the kth TPT to handle the ith accident, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. represents the travel time of the kth TPT from the starting point o to the i-th accident, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, represents the travel time of the kth TPT from the i-th accident to the destination d, It indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ is the penalty coefficient, p i represents the penalty time for not handling the i-th accident in time; The second component F2 is the latest time for TPT to arrive at the accident scene, and the specific expression formula is: Among them, max means maximization, w i Represents the total time to handle the i-th accident.

2. The traffic police force optimization dispatching method according to claim 1 is characterized in that: The constraints of the MILP model in step S1 include accident handling rule constraints, time constraints for the TPT to arrive at the traffic accident scene, coupling constraints, time constraints for completing the handling of the i-th accident, accident severity constraints, constraints on the earliest and latest traffic accidents handled by the TPT, and delayed handling time constraints for accidents.

3. The traffic police force optimization dispatching method according to claim 2 is characterized in that: The accident handling rule constraint is that for the i-th accident, one TPT handles it once. The specific formula is: in, Indicates whether to dispatch the kth TPT to handle the ith accident, K represents the available TPT set, and A represents the traffic accident set.

4. The traffic police force optimization dispatching method according to claim 2 is characterized in that: The specific expression formula of the time constraint of the TPT arriving at the traffic accident scene is: in, represents the time when the kth TPT arrives at the jth accident site, represents the time when the kth TPT arrives at the i-th accident scene, A represents the traffic accident set, K represents the available TPT set, represents the travel time of the kth TPT from the i-th accident to the j-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. represents the intermediate variable, and T2 represents the maximum value.

5. The traffic police force optimization dispatching method according to claim 2, characterized in that: The specific expression formula of the coupling constraint is: in, represents the time when the kth TPT arrives at the ith accident scene, T1 represents the minimum vehicle travel time between any given nodes, A represents the set of traffic accidents, K represents the set of available TPTs, Indicates whether to dispatch the kth TPT to handle the ith accident.

6. The traffic police force optimization dispatching method according to claim 2, characterized in that: The specific expression formula of the processing completion time constraint of the i-th accident is: Among them, w i represents the total time to handle the i-th accident, K represents the available TPT set, represents the time when the kth TPT arrives at the i-th accident scene, and A represents the set of traffic accidents.

7. The traffic police force optimization dispatching method according to claim 2, characterized in that: The specific expression formula of the accident severity constraint is: Among them, s i represents the severity of the i-th accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident, M1 and is a constant, s j represents the severity of the j-th accident, K represents the available TPT set, and A represents the traffic accident set.

8. The traffic police force optimization dispatching method according to claim 2 is characterized in that: The specific expression formula of the earliest and latest traffic accident constraints processed by TPT is: in, Indicates whether the kth TPT starts from the starting point o to handle the i-th accident, Indicates whether the kth TPT starts from the starting point o, Indicates whether the kth TPT returns to the destination d after handling the i-th accident, Indicates whether the kth TPT processes the i-th accident first, Indicates whether the kth TPT handles the i-th accident last, Indicates whether the kth TPT finally returns to the destination d, A represents the traffic accident set, K represents the available TPT set, O k represents the starting point set of the kth TPT, D k represents the destination set of the kth TPT; Whether the kth TPT processes the i-th accident first and whether the kth TPT handles the i-th accident last The following constraints are met: in, represents the time when the kth TPT arrives at the i-th accident site, M2 and is a constant, G k and H k Represents an intermediate variable, min represents minimization, and max represents maximization.

9. The traffic police force optimization dispatching method according to claim 2, characterized in that: The specific expression formula of the delayed processing time constraint of the accident is: Among them, d i represents the delayed processing time of the i-th accident, A represents the set of traffic accidents, w i represents the total time to handle the i-th accident, and γ represents the maximum allowed delay time.

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