Traffic police optimization scheduling method

Abstract

The invention belongs to the technical field of urban road network toughness research under traffic accidents, and particularly discloses a traffic police strength optimization scheduling method, which comprises the following steps of: establishing an MILP model according to a UR network in a patrol on-duty area of a traffic police support; and solving the MILP model by using CPLEX and a Yalmip library to obtain an optimal traffic police scheduling scheme, and completing traffic police force optimization scheduling. According to the method, the problem that the importance of traffic police in the aspect of processing traffic accidents is not considered in the existing research on improving the UR network toughness is solved, and the total scheduling cost is reduced to the maximum extent by realizing the optimal traffic police scheduling in the traffic accident period, and the duration of adverse effects caused by the accidents is shortened.

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 force. Background Art

[0002] Traffic accidents not only affect the normal operation of the urban road (UR) network, but also cause serious casualties. Traffic police are mainly responsible for traffic management and accident investigation. Therefore, traffic police play a vital role in restoring the normal operation of the UR network affected by traffic accidents. In real life, the number of available traffic police is often limited. When there are not enough traffic police to handle all accidents at the same time, it is of great significance to optimize the dispatch of traffic police to restore the normal operation of the affected UR network. The above analysis shows that the ability of the affected UR network to cope with traffic accidents can be improved by optimizing the dispatch of traffic police during 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 a lot of 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 the management of traffic accidents. For example, emergency control policies based on traffic signals to prevent large-scale congestion caused by traffic accidents. Dynamic adaptive vehicle detour routing strategy to reduce the negative impact of traffic congestion on UR networks. Although the existing technology has 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 under traffic accidents, there are still few studies on improving UR network resilience by optimizing the dispatch of traffic police. However, traffic police play an important role in handling traffic accidents, and their impact on restoring the normal operation of the affected UR network cannot be ignored. Summary of the invention

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

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

[0007] S1. Establish a MILP model based on the UR network in 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] The present invention realizes the optimal traffic police dispatch during traffic accidents by establishing a MILP model taking traffic police into consideration and solving the MILP model using CPLEX. It 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 value time of the passenger;

[0014] The first component F1 includes labor costs, police car operation 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 ith accident to the jth 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 ith accident to the destination d, indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ represents the penalty coefficient, and p i represents the penalty time of the ith 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 ith 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 ith accident to the jth 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 ith 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 ith 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 ith accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. M1 and ò1 are constants. s j represents the severity of the jth accident, K represents the available TPT set, and A represents the traffic accident set.

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

[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 ith accident. Indicates whether the kth TPT handles the i-th accident first, Indicates whether the kth TPT handles the ith 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 handles the ith accident first and whether the kth TPT handles the ith accident last The following constraints are met:

[0040]

[0041] in, represents the time when the kth TPT arrives at the ith accident, M2 and ò2 are constants, 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, and 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 the labor cost, police car operation cost, penalty cost for failing to handle traffic accidents in time, and the latest time for TPT to arrive at the scene of the accident, and considering the time for TPT to arrive at the scene of the traffic accident, coupling, completion time of handling the i-th accident, severity of the accident, earliest and latest traffic accidents handled by TPT, and delayed handling time of the accident as constraints, the cost of dispatching traffic police can be minimized and the duration of the impact can be shortened, so as to achieve rapid and effective handling of traffic accidents.

[0047] 2. Expressing the objective function and constraints of the MILP model in linear form helps CPLEX solve the problem, efficiently and accurately obtain the optimal traffic police dispatch plan, and achieve 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 figure shows a schematic diagram of a UR network provided in Embodiment 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 the 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] Fig. 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] Fig.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 driving speed. DETAILED DESCRIPTION

[0058] Now, exemplary embodiments of the present invention will 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 only exemplary and are intended to explain the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0059] Embodiment 1:

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

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

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

[0063] In this embodiment, the reasonable arrangement of the accident investigation tasks of the traffic police during the traffic accident not only helps to reduce the cost of dispatching the traffic police, but also can quickly restore the normal operation of the affected UR network. This embodiment only studies the patrol duty area of ​​a certain traffic police detachment. This embodiment defines the traffic police who handle traffic accidents as a traffic police team (TPT), and any solution proposed in this embodiment is designed based on TPT.

[0064] The UR network in 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 intervals. Figure 2 As shown in Figure 1, 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 in the patrol duty area. The symbol "+" near the traffic accident indicates the severity, and the more "+"s, the more serious the corresponding traffic accident.

[0065] Assume that when the above traffic accident occurs, the available TPT is located at the node numbered 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 in the 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, the development of traffic police dispatch plans under traffic accidents needs to consider factors such as available TPTs, UR network structure, and the severity and location of traffic accidents. In a simple UR network, since the available TPTs and the number of traffic accidents are limited, the enumeration method can be used in the network to obtain the best 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 solution. Therefore, this embodiment establishes a MILP model to effectively solve the above problems. The model aims to minimize the dispatch cost of traffic police and shorten the duration of the network being 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 is made 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 means the objective function, F1 means the first component, which is to formulate the scheduling plan by minimizing the scheduling cost, and F2 means 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 operation 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 ith accident to the jth 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 ith accident to the destination d, indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ represents the penalty coefficient, and p i represents the penalty time of the ith 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 TPT to arrive at the traffic accident scene, coupling constraints, time constraints for completing the processing of the i-th accident, accident severity constraints, constraints on the earliest and latest traffic accidents processed by TPT, and delayed processing 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, and 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 travel time, so the specific expression formula of 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 ith 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 ith accident to the jth accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident;

[0086] The nonlinear part is transformed to obtain:

[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 can be expressed as follows:

[0090]

[0091] in, represents the time when the kth TPT arrives at the ith 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 ith accident, and A represents the set of traffic accidents.

[0095] In this embodiment, in 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]

[0097] Among them, s i represents the severity of the ith accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. M1 and ò1 are constants, with M1=1, ò1=0.01, s j represents the severity of the jth accident, K represents the available TPT set, and A represents the traffic accident set.

[0098] In this embodiment, the specific expression formulas of the earliest and latest traffic accident constraints processed by the TPT are:

[0099]

[0100] 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 ith 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 eventually returns to the destination d. If the kth TPT eventually 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;

[0101] Whether the kth TPT handles the ith accident first and whether the kth TPT handles the ith accident last The following constraints are met:

[0102]

[0103] Performing linearization operation, we get:

[0104]

[0105] in, represents the time when the kth TPT reaches the ith accident, M2 and ò2 are constants, M2=100000, ò1=1, 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 the traffic police in my country for 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, and w i represents the total time to handle the i-th accident, and γ represents the maximum allowed delay time.

[0109] Embodiment 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 As shown by the blue dotted line in the figure, the UR network in the patrol duty area consists of 366 nodes (including 322 road intersections and endpoints, 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 the police car is 50 km / h, then the travel time can be calculated based on the travel distance between different nodes. Traffic accidents are more likely to occur at road intersections, so this embodiment focuses on the research of accidents occurring at road intersections, and the research method for accidents occurring in road sections is similar to the research method for accidents at road intersections, which will not be repeated in this embodiment. Figure 3 In the figure, a circle represents a traffic accident, a triangle represents the available TPT, and the decimals near the traffic accident represent the severity of the corresponding accident. For example, the red node and decimal point at the intersection 67 indicate that an accident with a severity of 0.51 occurred there.

[0113] In this embodiment, two traffic accidents of different scales are studied. The first scenario is a small-scale case including 6 traffic accidents, in which the accident occurring at node 114 has the highest severity. The second scenario is a large-scale case with 12 traffic accidents, in which the accident occurring at node 132 is the most serious. Before the accident, the two available TPTs are located at nodes 147 and 365 respectively. When the above TPTs complete the investigation tasks of all accidents, they can choose to return to any of the following nodes: 55, 124, 147, 173 or 365.

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

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

[0116]

[0117] The MILP model is solved by the solution method proposed in the present invention, and the optimal traffic police dispatching scheme under small-scale and large-scale cases is obtained, and the model solution time, objective function value and optimal dispatching scheme under different cases are listed in Table 2. The results shown in Table 2 show that the time required for obtaining small-scale and large-scale cases using the model is 1.30 seconds and 6.43 seconds, respectively, indicating that the proposed CPLEX-based solution method can efficiently solve the model. The dispatching scheme in Table 2 is represented by a combination of node numbers and dashes. For example, the scheme "TPT 1:147-114-67-222-173" means that the TPT numbered 1 first processes the accident occurring at node 114, and finally processes the accident occurring at node 222. After completing all the above assigned tasks, the TPT returns to node 173. Taking the optimal scheme of the small-scale case as an example to illustrate the effectiveness of the obtained scheme, the objective function value of the model in the small-scale case is 113.87 yuan (wherein the values ​​of the first and second sub-objective functions are 99.41 yuan and 861.48 seconds, respectively). By analyzing the optimal dispatching 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 Calculation time, objective function value and optimal traffic police dispatching plan

[0119]

[0120]

[0121] In order to further verify the effectiveness of the proposed model, the optimal solution in Table 2 is compared with the basic solution commonly used in real life. In the basic solution, the command center dispatches TPTs according to the severity of the traffic accident. In small-scale cases and large-scale cases, the objective function values ​​obtained according to the basic solution are 353.95 yuan and 5247.16 yuan, respectively. The above results show that the solution obtained by the MILP model proposed in the present invention is better than the basic solution. Specifically, the optimal solution obtained by the model can reduce the objective function values ​​of small-scale and large-scale cases by 64.87% and 32.90%, respectively.

[0122] 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 was obtained when the number of available TPTs was 2; however, in large-scale cases, as the number of available TPTs increased, the objective function value of the MILP model continued 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.

[0123] Table 3 Impact of the number of schedulable TPTs

[0124]

[0125] The model formulated by the present invention assumes that TPT will give priority to more serious traffic accidents. In order to discuss the impact of the above-mentioned priority on the design of the dispatching scheme, 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 scheme formulated without considering the impact of the severity of the accident is lower than the objective function value of the scheme formulated when the impact of the severity of the traffic accident is considered. The reason is that when the impact of the severity of the accident on the dispatching scheme 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 TPTs to give priority to 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]

[0128] This embodiment assumes that 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 objective function value, a comparative analysis is conducted on the traffic police dispatching schemes in which 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), and the objective function values ​​of the schemes in which TPT needs to return to the starting point and does not need to return to the starting point are listed in Table 5. The results shown in Table 5 show that the objective function value of the scheme requiring TPT to return to the starting point is greater than the objective function value corresponding to the scheme not requiring it to return to the starting point, indicating that when TPT must return to the starting point, the cost of dispatching 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] In order to further explore the effectiveness of the solution algorithm proposed in the present invention in solving the MILP model, the genetic algorithm was used to solve the model, and the calculation time and corresponding objective function values ​​of different algorithms are listed in Table 6. The results shown in Table 6 show that the calculation time of the genetic algorithm is less than the solution time of the algorithm proposed in the present invention. However, the objective function value obtained by the genetic algorithm is greater than the objective function value obtained by the algorithm based on CPLEX. In addition, when the genetic algorithm is used to solve large-scale cases, the model has no solution. The above results show that the solution algorithm proposed in the present invention 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, 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 occurring in Chengdu was 1,324 (ie, 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, taking a small-scale case as an example, parameter sensitivity analysis is used to discuss the influence of different parameters on the toughness improvement effect of the model proposed in the present invention. The results are as follows: Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 and Fig.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 the design of scheduling scheme cannot be ignored. Figure 6 The effect of the cost of dispatching the second TPT on the value of the model objective function is shown. The correlation coefficient between the cost of the second TPT performing the task and the objective function is 0.978, indicating a strong positive correlation between the two. In addition, the growth rate of the objective function value decreases as the cost of the second TPT performing the task further increases. The above results indicate that it is crucial to arrange a sufficient number of TPTs in areas with a high probability of traffic accidents. This measure not only helps to quickly restore the normal operation of the affected UR network, but also minimizes the cost of 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 2, the results show that the objective function value changes slightly with the increase of the penalty coefficient. The reason is that all traffic accidents are handled in a timely manner 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 objective function value of the model and the maximum allowable delay time is shown. As the maximum allowable delay time increases, the model objective function value first decreases and then remains unchanged. The reason for the above results is that the total time required for 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, the maximum allowable delay time will affect the objective function value of the model. Therefore, in order to minimize the adverse effects of traffic accidents on the operation of the UR network, the command center should reasonably dispatch available TPTs when traffic accidents occur to quickly restore the normal operation 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: Fig. 9As shown in the figure, there is a strong positive correlation between the two. When VOT increases from 20.43 yuan / hour to 70.43 yuan / hour, the objective function value of the model increases from 83.73 yuan to 134.48 yuan, which is an increase of 60.60%. 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 to reduce its impact on the UR network operation. Fig.10 It shows that the objective function value of the model decreases with the increase of vehicle speed, indicating that the cost of dispatching traffic police to handle traffic accidents can be reduced by increasing vehicle speed. Therefore, for TPTs that undertake traffic accident investigation tasks, they can use emergency lanes to increase vehicle speeds and thus improve response efficiency.

[0139] In summary, the model and solution algorithm proposed in the present invention can obtain the optimal traffic police dispatch plan in a shorter time during traffic accidents. Compared with the basic scheme widely used in actual dispatching, the optimal scheme proposed in the present invention can reduce the objective function values ​​of small-scale and large-scale cases by 64.87% and 32.90%, respectively. Secondly, the number of available TPTs greatly affects the effectiveness of the scheme obtained by the model. The command center can use the model formulated by the present invention to determine the optimal number of available TPTs in a given patrol duty area based on historical data. In addition, the impact of the severity of traffic accidents and the location of the destination on the design of traffic police dispatch plans cannot be ignored. Third, compared with the genetic algorithm, the model solution algorithm proposed in the present invention can achieve more effective model solution. In addition, there is a positive exponential relationship between the calculation time of the model and the number of traffic accidents. Finally, the influence of various parameters on the objective function value of the model was analyzed. The results show that the objective function value is affected by the cost of TPT execution tasks, the maximum allowable delay time, VOT and vehicle driving 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 should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for optimizing the dispatching of traffic police force, characterized in that: The method specifically comprises the following steps: S1. Establish a MILP model based on the UR network in the patrol area of ​​the traffic police detachment; 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.

2. The traffic police force optimization dispatching method according to claim 1 is characterized in that: The objective function of the MILP model in step S1 is expressed as: 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 value time of the passenger; The first component F1 includes labor costs, police car operation 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, 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 ith accident to the jth 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 ith accident to the destination d, indicates whether the kth TPT returns to the destination d after handling the ith accident, ξ represents the penalty coefficient, and p i represents the penalty time of the ith accident; 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.

3. 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 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 for the earliest and latest traffic accidents handled by TPT, and delayed handling time constraints for accidents.

4. The traffic police force optimization dispatching method according to claim 3 is characterized in that: The accident handling rule constraint is that for the i-th accident, one TPT handles it once, and 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.

5. The traffic police force optimization dispatching method according to claim 3 is characterized in that: The specific expression formula of the time constraint of TPT arriving at the traffic accident scene is: in, represents the time when the kth TPT arrives at the jth accident, represents the time when the kth TPT arrives at the ith 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 ith accident to the jth 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.

6. The traffic police force optimization dispatching method according to claim 3 is 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, 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.

7. The traffic police force optimization dispatching method according to claim 3 is 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 ith accident, and A represents the set of traffic accidents.

8. The traffic police force optimization dispatching method according to claim 3 is characterized in that: The specific expression formula of the accident severity constraint is: Among them, s i represents the severity of the ith accident, Indicates whether the kth TPT handles the jth accident immediately after handling the ith accident. M1 and ò1 are constants. s j represents the severity of the jth accident, K represents the available TPT set, and A represents the traffic accident set.

9. The traffic police force optimization dispatching method according to claim 3 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 ith accident. Indicates whether the kth TPT handles the i-th accident first, Indicates whether the kth TPT handles the ith 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 handles the ith accident first and whether the kth TPT handles the ith accident last The following constraints are met: in, represents the time when the kth TPT arrives at the ith accident, M2 and ò2 are constants, G k and H k Represents an intermediate variable, min represents minimization, and max represents maximization.

10. The traffic police force optimization dispatching method according to claim 3, 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, and w i represents the total time to handle the i-th accident, and γ represents the maximum allowed delay time.

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