A global optimization method for traffic control measures without violating the diversity of travel demand

Abstract

This invention discloses a global optimization method for differentiated traffic control measures that does not violate travel demand, relating to the field of intelligent traffic management technology, and includes the following steps: Step 1: Construct a global optimization framework for differentiated traffic control measures; Step 2: Define the urban traffic network and demand flow parameters; Step 3: Establish a mixed-integer linear programming model for optimizing road network flow distribution; Step 4: Consider factors such as flow demand, flow balance, and travel impedance, approximate the impedance function and objective function with secant lines, and construct constraints for the mixed-integer linear programming model; Step 5: Solve the model to obtain the optimal flow distribution result; Step 6: Obtain differentiated traffic control measures from the model based on the flow distribution result. This invention's method can construct a mixed-integer linear programming model that balances individual interests and overall efficiency based on the complex and diverse travel demands in large-scale urban road networks, design hierarchical control measures, and achieve synergistic optimization of control and path guidance, thereby improving the overall traffic efficiency of the road network.

Description

TECHNICAL FIELD

[0001] The present application provides a global optimization MILP method for differential traffic control measures without violating the diversity of travel demand. The present application belongs to the technical field of intelligent traffic management, and specifically relates to a differential traffic control measure design method based on global optimization. The method realizes scientific regulation and control of urban road network traffic by analyzing the topology of the traffic network and travel demand, combining mathematical modeling and optimization algorithms. The technical core includes road network traffic distribution calculation, mixed integer linear programming model construction, and differential control strategy generation. The present application is suitable for urban traffic management systems, navigation software optimization, and traffic planning modules for smart city construction, aiming to solve the low efficiency problem caused by the "one-size-fits-all" strategy in traditional traffic control, and to provide technical support for dynamic and precise traffic management. BACKGROUND

[0002] Traditional traffic control measures (such as specific tail number restrictions, odd-even number restrictions, etc.) usually adopt static rules and do not fully consider the dynamic flow distribution of the road network and the diversity of travel demand, leading to the exacerbation of congestion on some road segments or the waste of resources. Although existing research attempts to improve traffic flow through optimization of path allocation or real-time signal control, there are the following limitations. For example, most methods do not simultaneously consider the "worst-case" (user selfish path selection) and "system optimal" (global time shortest) differences in traffic distribution, making it difficult to balance individual and overall interests. In addition, the solution of the nonlinear optimization problem of large-scale road networks has high complexity, and many existing methods have low computational efficiency, making it difficult to meet real-time requirements. At the same time, existing control measures are relatively single and lack dynamic and differentiated design, which cannot adapt to the temporal and spatial fluctuations of traffic. Furthermore, although navigation software can guide vehicles to detour, it does not optimize with the control strategy, which may cause new congestion points. Therefore, there is an urgent need for a comprehensive method that integrates multi-objective optimization, efficient solution, and differentiated strategy generation to improve the scientificity and flexibility of traffic control. The present method can generate an optimal differential traffic control scheme in a large-scale urban road network, improve road network traffic efficiency, and provide scientific decision support for dynamic and precise traffic management. SUMMARY

[0003] (1) The purpose of the present application is:

[0004] The application aims to provide a global optimization method for differentiated traffic control measures without violating the difference of travel demand. The method identifies key congestion sections by comparing the traffic distribution under the "worst case" and "system optimal", provides data support for differentiated control, avoids the blindness of "one-size-fits-all" strategy, and realizes accurate traffic regulation. The method constructs a mixed integer linear programming model, converts the nonlinear road resistance function into a cutting line approximation constraint, uses a commercial solver (such as CPLEX) to realize efficient solution of large-scale road network, and meets the real-time decision-making demand. Based on the difference of traffic distribution, a hierarchical control measure (such as limiting vehicles entering by proportion) is designed, and the results are embedded into the navigation system to realize the coordinated optimization of control and path induction, and improve the overall traffic efficiency of the road network. The ultimate goal of the application is to realize the scientization, dynamization and individualization of traffic control, to relieve congestion while ensuring travel demand, and to promote the sustainable development of intelligent transportation system.

[0005] (2) Technical scheme: Based on the above theory and idea, the application provides a global optimization method for differentiated traffic control measures without violating the difference of travel demand, i.e. a method based on MILP, the specific implementation steps are as follows:

[0006] Step 1: Construction of global optimization framework for differentiated traffic control measures;

[0007] Specifically: according to the traffic network topology and travel demand, the traffic distribution on the road network under the worst case (assuming that all traffic demand seeks the shortest path to travel) and the traffic distribution under the system optimal (i.e. the total travel time of all traffic demand in the entire road network is the shortest) are calculated respectively, the comprehensive evaluation is carried out for different traffic distribution results, the roads to be implemented traffic control are selected, then the differentiated traffic control measures are formulated for these roads, and the global optimization framework is established. First, the road network traffic distribution under the worst case is calculated by taking formula (1) as the optimization objective, wherein D is the total travel distance of all traffic demand:

[0008]

[0009] Then, according to the road resistance function, formula (2) is taken as the optimization objective to calculate the traffic distribution under the system optimal, wherein T is the total travel time of all traffic demand:

[0010]

[0011] In formula (2), t ij (f ij ) is the road resistance function, i.e. the relationship between the travel time t of the road and the traffic f on the road, a common road resistance function is formula (3), which is taken as an example in the application:

[0012] t=t0[1+α(f / c)β ] (3)

[0013] Then, the traffic control measures of different road segments are obtained by using formula (4) based on the worst-case traffic distribution result (denoted as f1) calculated according to formula (1) and the best-case traffic distribution result (denoted as f2) calculated according to formula (2), which can also be used as a reference for various navigation software when making navigation:

[0014]

[0015] In the above formula represents rounding up, and z takes a value in the range of {1, 2, …, 9, 10}. If z = 8, it means that only 80% of vehicles can enter the road segment, for example, a relatively rough but acceptable way is to limit vehicles with certain two specific license plate numbers from entering the road segment.

[0016] Step 2: Define the parameters of urban traffic road network and demand flow representation;

[0017] Specifically, the traffic road network is mathematically abstracted as a connected graph G = (V, E), where i, j ∈ V are the serial numbers of road nodes, i, j = 1, 2, …, |V| (|*| represents the total number of elements in the set), and the nodes correspond to intersections and key locations in the traffic network with traffic demand, such as schools, factories, hospitals, banks, office buildings, and residential areas, etc. Each edge (i, j) ∈ E in the graph represents a road in the traffic network, d ij represents the length of the edge (i, j) (i.e., the distance from point i to point j on this road); t 0ij represents the free-flow travel time of the edge, i.e., the shortest time to pass through the edge; c ij represents the capacity of the edge (i, j), i.e., the maximum number of vehicles that can pass through the road in a period of time (usually a day). α is a parameter in the road resistance function (3), generally taking a value of 0.15; β is a parameter in the road resistance function (3), generally taking a value of 4; γ ij is a parameter introduced for the piecewise approximation of the impedance function (3), calculated from α, β, and c ij . Parameters and represent the slope and intercept of the introduced piecewise line for the piecewise approximation of the impedance function, specifically, represents the slope of the pth piecewise line for the piecewise approximation of the edge (i, j); represents the intercept of the pth piecewise line for the piecewise approximation of the edge (i, j). K represents a set of travel demands, k ∈ K, k = 1, 2, …, |K|.(s k , t k ) represent the starting point and the ending point of the kth travel demand, respectively, s kt k ∈V. Parameter q k denotes the flow of the kth travel demand.

[0018] Step three: Establish the mixed integer linear programming model of the traffic distribution optimization of the road network, taking the flow on each road section as the decision variable, and taking the minimization of the total travel distance and the minimization of the total travel time for all traffic demands as the optimization objectives respectively.

[0019] Specifically, since people usually choose the shortest path or the second shortest path when traveling, unless the near road is completely blocked, they will not make a detour too far, so taking the minimization of the total travel distance as the optimization objective will obtain a traffic distribution in the worst case, which will cause the flow on some key paths to be large, thereby causing the travel time on these road sections to increase greatly; if the total travel time is taken as the optimization objective, in the same travel demand, part of the vehicles can take the shortest path, while the other part of the vehicles need to detour, which will cause different total travel times, but the necessary detour of part of the vehicles can make the total travel time of the entire network shorter, so it is an ideal case.

[0020] Step 3.1: Define the decision variable of the traffic distribution optimization of the traffic network.

[0021] x ijk : Non-negative continuous variable, representing the flow of the kth pair of travel demands passing through the road section (i, j);

[0022] f ij : Non-negative continuous variable, representing the total flow passing through the road section (i, j);

[0023] t ij : Non-negative continuous variable, representing the travel time of the road section (i, j) when the total flow passing through the road section is f ij ;

[0024] g ij : Non-negative continuous variable introduced when the impedance function is approximated by a secant;

[0025] y ij : Non-negative continuous variable introduced when the impedance function is approximated by a secant;

[0026] Step 3.2: Establish the objective function of the traffic distribution optimization of the traffic network in the worst case.

[0027]

[0028] Step 3.3: Establish the objective function of the traffic distribution optimization of the traffic network in the ideal case.

[0029]

[0030] Step 4: Constrain the model by taking into account factors such as traffic demand, traffic balance, and travel impedance; Steps 2 and 3 determined the model's parameters, variables, and optimization objectives, respectively, and this step imposes multi-dimensional constraints on the model.

[0031] Step 4.1: Establish travel demand constraints;

[0032]

[0033]

[0034] in, For the k-th pair of travel demands starting from origin s k Outflow of traffic Let s be the starting point for the k-th pair of travel demand inflows. k The flow rate, the first expression in constraint (5) represents the flow rate from the starting point s. k The sum of outflows should equal the flow q required for the k-th trip demand. k The second formula represents the inflow starting point s. k The total flow should be 0. Similarly, the first expression in constraint (6) represents the inflow to the endpoint t. k The total flow should equal the flow q required for the k-th trip demand. k The second formula represents the outflow endpoint t. k The total flow rate should be 0.

[0035] Step 4.2: Establish traffic balancing constraints for each node in the network;

[0036]

[0037] This constraint means that for each node in the network and for each travel demand, the flow into that node should equal the flow out of that node. This constraint ensures that the flow in the network will not suddenly disappear.

[0038] Step 4.3: Establish total flow constraints for each edge in the network;

[0039]

[0040] Among them, f ij Let x be the total traffic flow on road segment (i,j). ijk Let be the flow rate of the k-th pair of travel demands on road segment (i,j).

[0041] Step 4.4: Establish constraints on the relationship between the travel time and traffic for each edge in the network;

[0042]

[0043] Among them, t ij Let f be the total traffic flow on road segment (i,j). ij The passage time for this section of road.

[0044] Step 4.5: Perform secant approximation on constraints (9) and objective function (2);

[0045] Specifically: First, substitute constraint (9) into the objective function (2) to obtain equation (10):

[0046]

[0047] in, It is a linear expression. It is nonlinear, and we define equation (11):

[0048]

[0049] Then equation (10) can be written as equation (12):

[0050]

[0051] Next, we define equation (13):

[0052]

[0053] Then equation (11) can be written as equation (14):

[0054]

[0055] Next, we define equation (15):

[0056]

[0057] Then equation (14) can be written as equation (16):

[0058]

[0059] Finally, we approximate equation (16) using a set of secants, so equation (16) can be written as equation (17):

[0060]

[0061] Step 5: Model Solving – The proposed mixed-integer linear programming model is solved to efficiently obtain the optimal flow distribution result that meets the constraints. This step relies on high-performance commercial solvers (such as CPLEX, Gurobi, etc.) to perform global optimization of the model. The linear programming model proposed in this invention also has high solution efficiency for large-scale data.

[0062] Step 5.1: Using equation (1) as the objective function and equations (5)-(8) as constraints, solve for the worst-case flow distribution. The flow distribution on each edge is denoted as f. 1ij ;

[0063] Step 5.2: Using equation (12) as the objective function and equations (5)-(8), (15), and (17) as constraints, solve for the optimal flow distribution. The flow distribution on each edge is denoted as f. 2ij ;

[0064] Step Six: Apply the solution result f obtained from the above model 1ij and f 2ij Substituting the traffic control measure z into the formula (4), the smaller the value obtained, the more priority should be given to implementing traffic control on this road section.

[0065] (3) Advantages and benefits:

[0066] This invention constructs a mixed-integer linear programming (MILP) model that balances individual interests and overall efficiency based on the complex and diverse travel demands in large-scale urban road networks. It designs hierarchical control measures and achieves coordinated optimization of control and route guidance, thereby improving the overall traffic efficiency of the road network. Compared with existing technologies, this invention has the following advantages:

[0067] ① Scientific and precise: By quantitatively analyzing the traffic flow difference between the "worst-case scenario" and the "system optimal scenario", the road sections that need to be controlled are accurately identified, and differentiated traffic restriction ratios are generated to avoid waste of resources.

[0068] ② Efficiency and Scalability: Employing secant approximation and a mixed-integer linear programming model significantly reduces computational complexity and supports rapid solutions for large-scale road networks; the model is compatible with different road resistance functions, adapting to diverse traffic scenarios.

[0069] ③ Collaborative optimization capability: The control measures are linked with the navigation system to dynamically adjust vehicle route allocation, which can alleviate local congestion and reduce the additional time cost caused by detours, thereby improving the overall efficiency of the road network. Attached Figure Description

[0070] Figure 1 This is a flowchart of the global optimization method for differentiated traffic control measures that do not violate travel needs, as described in this invention.

[0071] Figure 2 This is a road network structure diagram used in the specific implementation of this invention. Detailed Implementation

[0072] (1) Project Background

[0073] This study uses a large-scale road network in Beijing's urban area as the research object to simulate travel demand, obtain corresponding parameter values, test the above model and method, and obtain the optimal differentiated traffic control measures.

[0074] This study case study focuses on a densely populated urban traffic network in Beijing, characterized by high population density and various important nodes including hospitals, schools, large shopping malls, banks, office buildings, and residential areas. Traffic demand is complex and diverse, varying across different time periods, making congestion highly likely during peak hours. Therefore, analyzing traffic distribution and implementing traffic control measures in this area is of significant practical importance. The area comprises 4933 nodes, 6632 bidirectional edges, and 7918 pairs of traffic demands. The road network structure of this area is shown in the attached diagram. Figure 2 .

[0075] (2) Basic Information

[0076] The specific data for the network structure is shown in Table 1 below, and the specific data for traffic demand is shown in Table 2 below.

[0077] Table 1. Detailed data on the network structure

[0078]

[0079]

[0080] Table 2 Specific data on traffic demand

[0081] Sequence number Origin Destination Trip scenario Traffic demand / vehicle Occurrence probability / % 1 18 13 Weekday 4021 70 1 18 13 Holiday 2033 30 2 28 125 Weekday 257 70 2 28 125 Holiday 187 30 3 30 116 Weekday 282 70 3 30 116 Holiday 150 30 …… …… …… …… …… …… 7916 3472 191 Weekday 8 70 7916 3472 191 Holiday 200 30 7917 1754 1009 Weekday 25 70 7917 1754 1009 Holiday 370 30 7918 1635 3278 Weekday 25 70 7918 1635 3278 Holiday 400 30

[0082] (3) Optimize calculation results

[0083] The solution results of the model and the top 20 edges that should be subject to traffic control after sorting z from smallest to largest according to the proposed index are shown in Table 3 below:

[0084] Table 3 Results of optimization calculation

[0085]

[0086]

[0087] Table 3 shows the worst-case and best-case traffic flow distributions calculated using the optimization model proposed in this invention. Based on these, differentiated traffic control strategies were calculated, and the 20 most stringent road segments were selected after being ranked by their severity. After implementing traffic control according to this scheme, we found that all travel demands could still be met. Assuming that all demand flow still chooses the shortest path (some vehicles, unable to travel on certain road segments due to traffic control, will choose the shortest available path), the total travel time is reduced to 47.95% compared to the worst-case scenario.

[0088] In summary, this invention proposes a differentiated traffic control measure design method based on global optimization, aiming to solve the problems of single strategy and low efficiency in traditional traffic management. This method analyzes the traffic network topology and travel demand, calculates the flow distribution under worst-case (user selfish path selection) and system-optimal (shortest global time) conditions, respectively, and uses a mixed-integer linear programming model for efficient solution. Furthermore, it incorporates secant approximation techniques to handle nonlinear road resistance functions, significantly improving the computational efficiency for large-scale road networks. Based on the differences in flow distribution, this invention innovatively proposes a hierarchical control strategy and coordinates the results with the navigation system for optimization, achieving dynamic and precise control.

[0089] This invention significantly improves the scientific nature and efficiency of traffic control through the following core innovations:

[0090] ① Dual-objective traffic distribution comparison framework: This invention is the first to propose simultaneously calculating the "shortest path selfish allocation" (worst-case scenario) and the "global time optimal allocation" of traffic distribution. It quantifies road segment control priorities through difference analysis, providing a theoretical basis for strategy formulation. Traditional methods focus only on a single objective, while this invention reveals the root causes of congestion through dual-mode comparison.

[0091] ② Secant approximation and linearization technique: For nonlinear path resistance functions, an innovative secant approximation parameter (γ) is introduced. ij ) and auxiliary variables (y ij g ij This method transforms complex nonlinear problems into mixed-integer linear programming models, significantly improving solution efficiency. It overcomes the bottleneck of traditional nonlinear optimization methods in handling large-scale data.

[0092] ③ Dynamic hierarchical control strategy: A differentiated control scheme based on numerical z (e.g., levels 1-10) is proposed, directly transforming mathematical model results into actionable measures. This strategy can be dynamically adjusted according to real-time traffic flow and collaborate with the navigation system to achieve closed-loop optimization of "control-path," solving the pain point of insufficient flexibility of static strategies.

[0093] Through practical case studies, this invention demonstrates significant advantages on large-scale road networks, enabling effective management of such networks while improving efficiency without compromising individual travel needs. Its core advantages lie in the scientific identification of key congested road sections, efficient solution of complex models, and generation of flexible and operable control schemes. This ensures travel needs are met while improving overall road network efficiency, providing practical technical support for intelligent traffic management.

Claims

1. A global optimization method for differentiated traffic control measures that does not violate travel demand, comprising the following steps: (1) Calculate the traffic flow distribution on the road network in the worst case and the traffic flow distribution in the optimal case for the system based on the traffic network topology and travel demand. Conduct a comprehensive evaluation of the different traffic flow distribution results, select the roads to be subject to traffic control, and then formulate differentiated traffic control measures for these roads to establish a global optimization framework. The worst case refers to all traffic demand seeking the shortest path to travel, while the optimal case refers to all traffic demand seeking the path that minimizes the total travel time. (1.1) First, the worst-case road network traffic distribution is calculated using the following formula as the optimization objective, where D is the total travel distance of all traffic demands: (1.2) Next, based on the road resistance function as the optimization objective, the traffic distribution under the optimal system condition is obtained, where T is the total travel time of all traffic demands: (1.3) In the above formula, t ij (·) is the road resistance function, which is the relationship between the road travel time t and the flow rate f on that road segment. The road resistance function is as follows, where t0 represents the free-flow time of the road and c represents the road capacity. (1.4) Then, based on the worst-case traffic flow distribution result f1 obtained from the shortest total distance and the best-case traffic flow distribution result f2 obtained from the shortest total time, the traffic control measures for different road segments are obtained using the following formula, z; where This indicates rounding up, and the value of z ranges from {1, 2, …, 9, 10}. If z = 8, it means that only 80% of vehicles can enter this section of road. (2) Definition of urban traffic network and demand flow parameters Specifically, the traffic network is mathematically abstracted as a connected graph G = (V, E), where i, j ∈ V, representing the index of a road node, i, j = 1, 2, …, |V|, and |·| represents the total number of elements in the set. Nodes correspond to intersections and key locations in the traffic network with traffic demand, such as schools, factories, hospitals, banks, office buildings, and residential areas. Each edge (i, j) ∈ E in the graph represents a road in the traffic network, d ij t represents the length of edge (i, j); 0ij c represents the free-flow time of edge (i, j), that is, the shortest time to traverse this edge; ij Let represent the capacity of edge (i, j), which is the maximum number of vehicles that can pass through this road in a certain period of time; α is the parameter in the road resistance function (1.3), with a value of 0.15; The parameter in the road resistance function (1.3) takes a value of 4; The parameters introduced when approximating the path resistance function (1.3) by α, and c ij Parameters were calculated together. and Let represent the slope and intercept of the secant introduced when approximating the path resistance function (1.3), respectively. Let represent the slope of the p-th secant when approximating edge (i, j); Let represent the intercept of the p-th secant when approximating edge (i, j); K represents the set of travel demands, k∈K, k = 1, 2, …, |K|; (s k , t k ) represent the origin and destination of the k-th travel request, respectively. k , t k ∈V; parameter q k This represents the traffic volume of the k-th travel demand; (3) Establish a mixed integer linear programming model for optimizing the traffic distribution of the road network, with the traffic flow on each road segment as the decision variable, and the optimization objectives being to minimize the total travel distance and the total travel time to meet all traffic demands, respectively. Since people usually choose the shortest or second shortest path when traveling, they will not take long detours unless all shortcuts are completely blocked. Therefore, optimizing for the minimum total travel distance will result in the worst-case traffic distribution, which will lead to high traffic on some critical paths, resulting in a significant increase in travel time on these road segments. If optimizing for the minimum total travel time, for the same travel demand, some vehicles can take the shortest path while others need to detour, resulting in different total travel times. However, the necessary detours of some vehicles can shorten the total travel time of the entire network, which is the optimal situation for the system. Define the decision variables for optimizing traffic network flow distribution; x ijk : A non-negative continuous variable representing the flow rate of the k-th pair of travel demands on road segment (i, j); f ij : A non-negative continuous variable representing the total traffic flow on road segment (i, j); t ij : A non-negative continuous variable, representing the total traffic flow f on road segment (i, j). ij The travel time for this section of the road; g ij : Non-negative continuous variables, introduced when approximating the road resistance function with a secant line; y ij : Non-negative continuous variables, introduced when approximating the road resistance function with a secant line; (3.1) Establish the objective function for optimizing traffic network flow distribution in the worst-case scenario; (3.2) Establish the objective function for optimizing traffic network flow distribution under the optimal system condition; (4) Constrain the model by taking into account factors such as traffic demand, traffic balance and travel impedance; (4.1) Establish travel demand constraints; where, and These represent the k-th pair of travel demands on road segment (s). k On the road segment (i, s) and on the road segment (j) k Traffic flow on the line; and Let represent the k-th pair of travel demands on road segment (i, t). k On and on the road section (t) k Traffic flow on (j) (4.2) Establish flow balancing constraints for each node in the network; where, This represents the flow rate of the k-th pair of travel demands on road segment (j, i); (4.3) Establish total flow constraints for each edge in the network; (4.4) Establish constraints on the relationship between travel time and traffic for each edge in the network; (4.5) To approximate the nonlinear relationship between time and flow rate, first substitute the flow rate and time relationship of a single edge into the objective function; (4.6) Define a new parameter and two new variables y ij and g ij : (4.7) Therefore, the objective function can be written as: (4.8) According to the definition in (4.6), we can obtain y ij It is g ij of For power functions, since the objective function is to find the minimum value, a set of secant lines is used for y. ij With g ij By approximating the relationship, the following linear constraints can be obtained; (5) Model Solving: The proposed mixed integer linear programming model is solved to efficiently obtain the optimal flow distribution results that meet the constraints; this step relies on the high-performance commercial solver CPLEX to perform global optimization of the model; (5.1) Solve the problem with the objective function of minimizing the total travel distance to obtain the worst-case flow distribution, and obtain the flow f on each edge. 1ij ; (5.2) Solving for the shortest total travel time as the objective function yields the ideal flow distribution, resulting in the flow distribution f on each edge. 2ij ; (6) Generate differentiated traffic control measures solutions: The solution results f obtained from the above model are used to generate solutions. 1ij and f 2ij Substituting the defined traffic control measure z into the value, the smaller the value, the higher the priority should be given to implementing traffic control on that road segment.

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