Differential traffic control measure global optimization method not violating travel demands

Abstract

The invention discloses a differential traffic control measure global optimization method without violating travel demands, and relates to the technical field of intelligent traffic management. The method comprises the following steps: 1, constructing a global optimization framework of differential traffic control measures; 2, defining an urban traffic network and demand flow parameter representation; 3, establishing a mixed integer linear programming model for road network flow distribution optimization; 4, overall planning factors such as flow demand, flow balance and travel impedance, performing secant approximation on an impedance function and a target function, and constructing a mixed integer linear programming model constraint; 5, solving the model to obtain an optimal flow distribution result; and step 6, obtaining different traffic control measures from the model according to a flow distribution result. According to the method, a mixed integer linear programming model considering individual benefits and overall efficiency can be constructed based on complex and diversified travel requirements in a large-scale urban road network, hierarchical control measures are designed, collaborative optimization of control and path induction is realized, and thus the overall traffic efficiency of the road network is improved.

Description

Technical Field

[0001] The present invention provides a MILP method for global optimization of differentiated traffic control measures that do not violate travel demand. The present invention belongs to the field of intelligent traffic management technology, and specifically relates to a method for designing differentiated traffic control measures based on global optimization. This method realizes scientific regulation of urban road network traffic by analyzing the topological structure of the traffic network and travel demand, combining mathematical modeling and optimization algorithms. Its technical core includes road network traffic distribution calculation, mixed integer linear programming model construction, and differentiated control strategy generation. The present invention is suitable for urban traffic management systems, navigation software optimization, and traffic planning modules for smart city construction. It aims to solve the inefficiency problem caused by the "one-size-fits-all" strategy in traditional traffic control, and provide technical support for dynamic and precise traffic management. Background Art

[0002] Traditional traffic control measures (such as specific license plate restrictions and odd-even restrictions) typically employ static rules that fail to fully account for the dynamic distribution of traffic flow and the variability of travel demand across road networks, leading to increased congestion and resource waste on some sections. Existing research has attempted to improve traffic flow through optimized route allocation or real-time signal control, but these approaches suffer from several limitations. For example, most methods fail to simultaneously account for the differences in traffic flow distribution between "worst-case" scenarios (users' selfish path selection) and "system-optimal" scenarios (global time minimization), making it difficult to balance individual and overall interests. Furthermore, the high complexity of solving nonlinear optimization problems in large-scale road networks makes many existing methods computationally inefficient and difficult to meet real-time requirements. Furthermore, existing control measures are relatively simplistic, lacking dynamic, differentiated design, and are unable to adapt to spatiotemporal fluctuations in traffic flow. Furthermore, while navigation software can guide vehicles around, it lacks coordinated optimization with traffic control strategies, potentially leading to new congestion points. Therefore, a comprehensive approach integrating multi-objective optimization, efficient solution, and differentiated strategy generation is urgently needed to enhance the scientific and flexible nature of traffic control. This method can generate optimal differentiated traffic control plans in large-scale urban road networks, improve road network traffic efficiency, and provide scientific decision-making support for dynamic and precise traffic management. Summary of the Invention

[0003] (1) Objects of the present invention:

[0004] The present invention aims to provide a global optimization method for differentiated traffic control measures that does not violate travel demand. This method identifies key congested sections by comparing the traffic distribution under the "worst case" and "system optimal" conditions, provides data support for differentiated control, avoids the blindness of the "one-size-fits-all" strategy, and achieves precise traffic control. This method constructs a mixed integer linear programming model, converts the nonlinear road resistance function into a secant approximation constraint, and uses commercial solvers (such as CPLEX) to achieve efficient solution of large-scale road networks to meet real-time decision-making needs. Based on the differences in traffic distribution, hierarchical control measures are designed (such as restricting vehicle entry in proportion), and the results are embedded in the navigation system to achieve coordinated optimization of control and path induction, thereby improving the overall traffic efficiency of the road network. The ultimate goal of the present invention is to achieve scientific, dynamic and personalized traffic control, alleviate congestion while ensuring travel needs, and promote the sustainable development of smart transportation systems.

[0005] (2) Technical Solution: Based on the above theories and ideas, the present invention provides a global optimization method for differentiated traffic control measures that does not violate travel demand, namely, a MILP-based method. The specific implementation steps are as follows:

[0006] Step 1: Construction of a global optimization framework for differentiated traffic control measures; Specifically, based on the traffic network topology and travel demand, the flow distribution on the road network under the worst-case scenario (assuming all traffic demands seek the shortest path) and the flow distribution under the optimal system (i.e., the shortest total travel time for all traffic demands in the entire road network) are calculated. A comprehensive evaluation is conducted on the different flow distribution results, and roads to be subject to traffic control are selected. Differentiated traffic control measures are then formulated for these roads, and a global optimization framework is established. First, the worst-case road network flow distribution is calculated using Equation (1) as the optimization objective, where D is the total travel distance for all traffic demands:

[0007]

[0008] Then, based on the road resistance function, formula (2) is used as the optimization objective to find the flow distribution under the optimal system condition, where T is the total travel time of all flow demands:

[0009]

[0010] In formula (2), t ij (f ij ) is the road resistance function, that is, the relationship between the travel time t of a road and the flow rate f on the road. A common road resistance function is shown in formula (3). In the present invention, this road resistance function is taken as an example:

[0011] t=t0[1+α(f / c) β] (3)

[0012] Then, based on the traffic distribution results under the worst case (denoted as f1) obtained by formula (1) and the traffic distribution results under the most ideal case (denoted as f2) obtained by formula (2), the traffic control measures for different road sections are obtained using formula (4). This result can also be used as a reference for various navigation software when formulating navigation:

[0013]

[0014] In the above formula The value range of z is {1, 2, ..., 9, 10}. If z = 8, this means that only 80% of vehicles can enter the road section. For example, a relatively crude but acceptable method is to restrict vehicles with two specific license plate numbers from entering the road section.

[0015] Step 2: Define the urban traffic network and demand flow parameter representation;

[0016] Specifically, the traffic network is mathematically abstracted into a connected graph G = (V, E), where i, j ∈ V is the serial number of the road node, i, j = 1, 2, ..., |V| (|*| represents the total number of elements in the set), and the nodes correspond to intersections and key locations with traffic demand in the traffic network, 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 represents the length of edge (i, j) (i.e. the distance from point i to point j on this path); t 0ij represents the free flow travel time of this edge, that is, the shortest time to pass this edge; c ij represents the capacity of edge (i, j), that is, the maximum number of vehicles that can pass through this road within a period of time (usually one day). α is the parameter in the road resistance function (3), which is generally 0.15; β is the parameter in the road resistance function (3), which is generally 4; γ ij The parameters introduced when performing secant approximation on the impedance function (3) are represented by α, β and c. ij Calculated together. Parameters and They represent the slope and intercept of the secant line introduced when the impedance function is approximated by the secant line. Specifically, Represents the slope of the pth secant line when the secant approximation is performed on the edge (i, j); represents the intercept of the pth secant line when the secant line approximates the edge (i, j). K represents the set of travel demands, k∈K, k=1,2,…,|K|. (s k ,t k ) represent the starting point and end point of the k-th travel demand, s k ,tk ∈V. Parameter q k represents the flow of the k-th travel demand.

[0017] Step 3: Establish a mixed integer linear programming model for optimizing road network flow distribution, using the flow on each road segment as the decision variable and minimizing the total travel distance and total travel time to meet all flow demands as the optimization objectives.

[0018] Specifically, people usually choose the shortest or second-shortest route when traveling, and will not take long detours unless the shortcuts are completely blocked. Therefore, minimizing the total travel distance as the optimization goal will result in a worst-case traffic distribution, which will lead to higher traffic on some key paths and a significant increase in travel time on these sections. If minimizing the total travel time is used as the optimization goal, some vehicles can take the shortest route for the same trip, while others need to take a detour, resulting in different total travel times. However, the necessary detours of some vehicles can shorten the total travel time on the entire network, which is an ideal situation.

[0019] Step 3.1: Define the decision variables for optimizing traffic network flow distribution;

[0020] x ijk : a non-negative continuous variable representing the flow of the k-th pair of travel demands on road segment (i, j);

[0021] f ij : a non-negative continuous variable, representing the total traffic flow on the road segment (i, j);

[0022] t ij : Non-negative continuous variable, indicating that the total traffic flow on the road section (i, j) is f ij The travel time of this road;

[0023] g ij : non-negative continuous variable, introduced when performing secant approximation on the impedance function;

[0024] y ij : non-negative continuous variable, introduced when performing secant approximation on the impedance function;

[0025] Step 3.2: Establish the objective function for optimizing the traffic network flow distribution under the worst-case scenario;

[0026]

[0027] Step 3.3: Establish the objective function for optimizing the traffic network flow distribution under the most ideal conditions;

[0028]

[0029] Step 4: Coordinate factors such as flow demand, flow balance, and travel impedance to constrain the model. Steps 2 and 3 determined the model parameters, variables, and optimization objectives, respectively. This step constrains the model in multiple dimensions.

[0030] Step 4.1: Establish travel demand constraints;

[0031]

[0032]

[0033] in, For the kth pair of travel demands from the starting point s k Outflow flow, The kth pair of travel demand flows into the starting point s k The first equation in constraint (5) indicates the flow rate from the starting point s k The sum of the outflows should be equal to the required flow q for the kth travel demand k , the second formula represents the flow into the starting point s k The total flow should be 0. Similarly, the first equation in constraint (6) represents the flow into the terminal t k The sum of the total flows should be equal to the flow q required for the kth travel demand k , the second formula represents the outflow end point t k The total flow should be 0.

[0034] Step 4.2: Establish traffic balance constraints for each node in the network;

[0035]

[0036] This constraint means that for each node in the network and for each travel demand, the flow into the node should be equal to the flow out of the node. This constraint ensures that the flow in the network will not disappear suddenly.

[0037] Step 4.3: Establish the total flow constraint for each edge in the network;

[0038]

[0039] Among them, f ij is the total traffic flow on the road section (i, j), x ijk is the flow of the kth pair of travel demands on road segment (i, j).

[0040] Step 4.4: Establish the relationship constraint between the travel time and flow of each edge in the network;

[0041]

[0042] Among them, t ij The total traffic flow on the road section (i, j) is f ij The travel time of this road.

[0043] Step 4.5: Perform secant approximation for constraint (9) and objective function (2);

[0044] Specifically: First, substitute constraint (9) into objective function (2) to obtain formula (10):

[0045]

[0046] in, is a linear expression, is nonlinear, we define equation (11):

[0047]

[0048] Then formula (10) can be written as formula (12):

[0049]

[0050] Next, we define formula (13):

[0051]

[0052] Then formula (11) can be written as formula (14):

[0053]

[0054] Next, we define formula (15):

[0055]

[0056] Then formula (14) can be written as formula (16):

[0057]

[0058] Finally, we use a set of secants to approximate Equation (16), so Equation (16) can be written as Equation (17):

[0059]

[0060] Step 5: Model Solving - Solve the proposed mixed integer linear programming model to efficiently obtain the optimal flow distribution results that meet the constraints. This step relies on high-performance commercial solvers (such as CPLEX, Gurobi, etc.) to perform global optimization and solve the model. The linear programming model proposed in this invention is also highly efficient for solving large-scale data.

[0061] Step 5.1: Take equation (1) as the objective function and equations (5)-(8) as constraints to solve the worst-case flow distribution result. The flow distribution on each edge is denoted as f 1ij ;

[0062] Step 5.2: Take equation (12) as the objective function and solve equations (5)-(8) and equations (15) and (17) as constraints to obtain the optimal flow distribution result. The flow distribution on each edge is denoted as f 2ij ;

[0063] Step 6: The solution f obtained by the above model 1ij and f 2ij Substituting the traffic control measure z defined in formula (4), the smaller the value obtained, the higher the priority for implementing traffic control on this road section.

[0064] (3) Advantages and effects:

[0065] Based on the complex and diverse travel needs in large-scale urban road networks, this invention constructs a mixed integer linear programming (MILP) model that balances individual interests and overall efficiency. It designs hierarchical control measures and achieves the coordinated optimization of control and path guidance, thereby improving the overall traffic efficiency of the road network. Compared with existing technologies, this invention has the following advantages:

[0066] ① Scientificity and precision: By quantitatively analyzing the traffic flow differences between the "worst case" and "system optimality", the road sections that need to be controlled are accurately identified, and differentiated restriction ratios are generated to avoid waste of resources.

[0067] ② Efficiency and scalability: The use of secant approximation and mixed-integer linear programming models significantly reduces computational complexity and supports rapid solution of large-scale road networks. The model is compatible with different road resistance functions and adapts to diverse traffic scenarios.

[0068] ③ Collaborative optimization capability: Control measures are linked with the navigation system to dynamically adjust vehicle route allocation, which not only alleviates local congestion but also reduces the additional time cost caused by detours, thereby improving the overall efficiency of the road network. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of the global optimization method for differentiated traffic control measures that do not violate travel demand as described in the present invention.

[0070] Figure 2 It is a road network structure diagram used in describing the specific implementation methods of the present invention. DETAILED DESCRIPTION

[0071] (1) Project background

[0072] This implementation takes a large-scale road network in Beijing's urban area as the research object, simulates travel demand, obtains corresponding parameter values, tests the above models and methods, and obtains the optimal differentiated traffic control measures.

[0073] The case study is a densely populated traffic network in Beijing's urban area. It has a high population density and contains a variety of important nodes, including hospitals, schools, large shopping malls, banks, office buildings, and residential areas. Traffic demand is complex and diverse, and varies at different times. Congestion is very likely to occur during peak traffic periods. Therefore, analyzing the traffic distribution in this area and implementing traffic control are of great practical significance. The area has a total of 4,933 nodes, 6,632 bidirectional edges, and 7,918 pairs of traffic demands. The road network structure of the area is shown in the attached diagram. Figure 2 .

[0074] (2) Basic information

[0075] Some specific data of the network structure are shown in Table 1 below, and some specific data of the traffic demand are shown in Table 2 below: Table 1 Specific data of network structure Table 2 Specific data of flow requirements Serial number starting point end Travel scenarios Traffic demand / vehicle Probability of occurrence / % 1 18 13 working day 4021 70 1 18 13 Holidays 2033 30 2 28 125 working day 257 70 2 28 125 Holidays 187 30 3 30 116 working day 282 70 3 30 116 Holidays 150 30 …… …… …… …… …… …… 7916 3472 191 working day 8 70 7916 3472 191 Holidays 200 30 7917 1754 1009 working day 25 70 7917 1754 1009 Holidays 370 30 7918 1635 3278 working day 25 70 7918 1635 3278 Holidays 400 30

[0076] (3) Optimize calculation results

[0077] The solution of the model and the top 20 edges that should be subject to traffic control after calculating z from small to large according to the proposed indicators are shown in Table 3 below: Table 3 Optimization calculation results

[0078] Table 3 shows the worst-case and ideal-case traffic distributions calculated using the optimization model proposed in this paper. Differentiated traffic control strategies were then calculated, with the top 20 most stringent road sections selected after ranking them by degree of strictness. After implementing traffic control based on this strategy, we found that all travel demands could still be met. Assuming that all demand flows still choose the shortest possible route (some vehicles, unable to travel on certain road sections due to traffic control, will choose the shortest available route), the total travel time was reduced by 47.95% compared to the worst-case scenario.

[0079] In summary, the present invention proposes a method for designing differentiated traffic control measures based on global optimization, aiming to solve the problems of single strategy and low efficiency in traditional traffic management. This method analyzes the topological structure of the traffic network and travel demand, calculates the traffic distribution under the worst case (user selfish path selection) and system optimality (global shortest time), uses a mixed integer linear programming model for efficient solution, and combines the secant approximation technology to process nonlinear road resistance functions, significantly improving the computational efficiency of large-scale road networks. Based on the differences in traffic distribution, the present invention innovatively proposes a hierarchical control strategy, and coordinates the optimization of the results with the navigation system to achieve dynamic and precise regulation.

[0080] This invention significantly improves the scientific nature and efficiency of traffic control through the following core innovations:

[0081] ① Dual-Objective Traffic Distribution Comparison Framework: This framework proposes, for the first time, a framework that simultaneously calculates traffic distributions for both "shortest path selfish allocation" (worst-case scenario) and "global time-optimal allocation." This framework uses differential analysis to quantify road section control priorities, providing a theoretical basis for policy formulation. While traditional methods focus solely on a single objective, this new framework reveals the root causes of congestion through dual-mode comparison.

[0082] ②Secant approximation and linearization technology: For nonlinear resistance function, the secant approximation parameter (γ ij ) and auxiliary variables (y ij 、g ij ), transforming complex nonlinear problems into mixed-integer linear programming models, significantly improving solution efficiency. This approach overcomes the bottleneck of traditional nonlinear optimization, which has difficulty handling large-scale data.

[0083] ③ Dynamic hierarchical control strategy: This strategy proposes a differentiated control scheme based on a numerical value z (e.g., levels 1-10), directly translating mathematical model results into actionable measures. This strategy can be dynamically adjusted based on real-time traffic flow and collaborates with the navigation system to achieve closed-loop optimization of the "control-route" process, addressing the inflexibility of static strategies.

[0084] Through practical application, this invention demonstrates significant superiority on large-scale road networks, enabling effective management of these networks, improving efficiency while maintaining individual travel needs. Its core advantages lie in scientifically identifying key congested sections, efficiently solving complex models, and generating flexible and actionable control schemes. This approach improves overall network efficiency while ensuring travel needs, providing practical technical support for intelligent transportation management.

Claims

1. A global optimization method for differentiated traffic control measures that does not violate travel demand, comprising the following steps: (1) Based on the traffic network topology and travel demand, the flow distribution on the road network under the worst-case scenario (assuming that all flow demands seek the shortest path to travel) and the flow distribution under the optimal system (i.e., the total travel time to meet all flow demands in the entire road network is the shortest) are calculated respectively. A comprehensive evaluation is conducted on the different flow distribution results, and the roads to be subject to traffic control are selected. Then, differentiated traffic control measures are formulated for these roads, and a global optimization framework is established. (1.1) First, the worst-case road network flow distribution is calculated using the following equation as the optimization objective, where D is the total travel distance for all flow demands: (1.2) Then, based on the road resistance function, the following formula is used as the optimization objective to find the flow distribution that achieves the optimal system, where T is the total travel time of all flow demands: (1.3) In the above formula, t ij (f ij ) is the road resistance function, that is, the relationship between the travel time t of a road and the flow rate f on the road. A common road resistance function is as follows, which is used as an example in the present invention: t=t0[1+α(f / c) β ] (1.4) Then, based on the worst-case traffic distribution result (denoted as f1) obtained by the shortest total distance and the ideal traffic distribution result (denoted as f2) obtained by the shortest total time, the following formula is used to obtain traffic control measures for different road sections. This result can also be used as a reference for various navigation software when formulating navigation. Indicates rounding up, and the value range of z is {1, 2, ..., 9, 10}. If z = 8, it means that only 80% of vehicles can enter the road section. For example, a relatively crude but acceptable method is to restrict vehicles with two specific license plate numbers from entering the road section: (2) Definition of urban traffic network and demand flow parameters Specifically, the traffic network is mathematically abstracted into a connected graph G = (V, E), where i, j ∈ V is the serial number of the road node, i, j = 1, 2, ..., |V| (|*| represents the total number of elements in the set), and the nodes correspond to intersections and key locations with traffic demand in the traffic network, 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 represents the length of edge (i, j) (i.e. the distance from point i to point j on this path); t 0ij represents the free flow travel time of this edge, that is, the shortest time to pass this edge; c ij represents the capacity of edge (i, j), that is, the maximum number of vehicles that can pass through this road within a period of time (usually one day). α is the parameter in the road resistance function (3), which is generally 0.15; β is the parameter in the road resistance function (3), which is generally 4; γ ij The parameters introduced when performing secant approximation on the impedance function (3) are represented by α, β and c. ij Calculated together. Parameters and They represent the slope and intercept of the secant line introduced when the impedance function is approximated by the secant line. Specifically, Represents the slope of the pth secant line when the secant approximation is performed on the edge (i, j); represents the intercept of the pth secant line when the secant line approximates the edge (i, j). K represents the set of travel demands, k∈K, k=1,2,…,|K|. (s k ,t k ) represent the starting point and end point of the k-th travel demand, s k ,t k ∈V. Parameter q k represents the flow of the kth travel demand. (3) A mixed integer linear programming model for optimizing road network flow distribution is established, with the flow on each road segment as the decision variable and the optimization objectives of minimizing the total travel distance and the total travel time to meet all flow demands; Since people usually choose the shortest or second-shortest route when traveling, they will not take long detours unless the shortcuts are completely blocked. Therefore, minimizing the total travel distance as the optimization goal will result in a worst-case traffic distribution, which will cause heavy traffic on some key paths, resulting in a significant increase in travel time on these sections. If minimizing the total travel time is used as the optimization goal, some vehicles can take the shortest route for the same trip demand, while others need to take a detour, resulting in different total travel times. However, the necessary detours of some vehicles can shorten the total travel time on the entire network, which is an ideal situation. Define decision variables for optimizing traffic network flow distribution; x ijk : a non-negative continuous variable representing the flow 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 the road segment (i, j); t ij : Non-negative continuous variable, indicating that the total traffic flow on the road section (i, j) is f ij The travel time of this road; g ij : non-negative continuous variable, introduced when performing secant approximation on the impedance function; y ij : non-negative continuous variable, introduced when performing secant approximation on the impedance function; (3.1) Establish the objective function for optimizing the traffic network flow distribution under the worst-case scenario; (3.2) Establish the objective function for optimizing the traffic network flow distribution under the most ideal conditions; (4) Coordinate factors such as flow demand, flow balance, and travel impedance to constrain the model; (4.1) Establish travel demand constraints; (4.2) Establish traffic balance constraints for each node in the network; (4.3) Establish the total flow constraint for each edge in the network; (4.4) Establish the relationship constraints between the travel time and flow of each edge in the network; (4.5) For the nonlinear relationship between time and flow, the secant approximation is performed. First, the flow and time relationship of a single edge is substituted into the objective function; (4.6) Define a new parameter γ ij and two new variables y ij and g ij : (4.7) Thus, the objective function can be written as: (4.8) Using a set of secant lines for y ij With g ij By approximating the relationship between , we can get the following linear constraints (5) Model Solving: Solve the proposed mixed-integer linear programming model to efficiently obtain the optimal flow distribution that meets the constraints. This step relies on high-performance commercial solvers (such as CPLEX and Gurobi) to perform global optimization on the model. The proposed linear programming model is also highly efficient for solving large-scale data. (5.1) Taking the shortest total travel distance as the objective function, we solve the worst-case flow distribution result, and the flow distribution on each edge is denoted as f 1ij ; (5.2) Taking the shortest total travel time as the objective function, we solve the optimal flow distribution result. The flow distribution on each edge is denoted as f 2ij . (6) Generate differential traffic control solution: The solution f obtained by the above model 1ij and f 2ij Substituting the defined traffic control measure z, the smaller the value obtained, the higher the priority for implementing traffic control on this road section.

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