A multi-path coordinated control method and system for urban roads based on an improved AM-Band model

Abstract

This invention discloses a method and system for coordinated multipath control of urban roads based on an improved AM-Band model. The method comprises the following steps: improving the original AM-Band model based on path flow and turning requirements to obtain a multipath-oriented green wave bandwidth maximization model; determining the speed guidance range based on the indicator light signal devices between upstream and downstream intersections, and establishing a delay minimization model based on optimal speed guidance; and solving the green wave bandwidth maximization model and the delay minimization model using a multi-objective locust optimization algorithm to obtain a signal timing solution. This invention addresses the problems of insufficient green wave bandwidth and path competition at continuous intersections by implementing a two-stage optimization model that combines signal timing and vehicle speed guidance to achieve comprehensive optimization of urban traffic.

Description

Technical Field

[0001] The present invention belongs to the field of urban traffic technology, and in particular relates to an urban road multi-path coordinated control method and system based on an improved AM-Band model. Background Art

[0002] With the acceleration of urbanization, urban road networks are becoming increasingly complex. This is particularly true during peak weekday commuting times, when residents from multiple regions migrate toward the city center or other work destinations, creating a complex network of multiple origin-destination (OD) paths. The competitive and intertwined nature of these paths not only increases the difficulty of traffic management but also poses new challenges to traditional traffic signal coordination and control strategies. Against this backdrop, research on coordinated urban traffic signal control has gradually shifted from green wave coordination on single arterial roads to the more complex coordinated optimization of multiple commuting paths.

[0003] Traditional green wave coordinated control originated with the MAXBAND model proposed by Little. This model, which optimized signal period, phase difference, and travel speed through linear programming, laid the foundation for subsequent research. However, the MAXBAND model did not fully account for the differences in traffic flow directions. To address this issue, Gartner introduced bandwidth variation into the MULTIBAND model, providing a more flexible green wave solution for different traffic flows. Building on this, Zhang proposed the MULTIBAND model by relaxing the symmetric bandwidth restriction, enabling better green wave coordinated control for varying traffic flows and road conditions.

[0004] However, existing research has mostly focused on speed guidance on trunk roads or under specific conditions. For complex trunk networks with multi-path integration, how to further optimize the speed guidance strategy and make it more closely integrated with green wave coordinated control is an issue worthy of in-depth exploration. Summary of the Invention

[0005] The present invention aims to solve the deficiencies of the prior art and provides the following solutions:

[0006] A multi-path coordinated control method for urban roads based on an improved AM-Band model includes the following steps:

[0007] Based on the path flow and steering requirements, the original AM-Band model is improved to obtain a multi-path oriented green wave bandwidth maximum model.

[0008] Based on the indicator light signal devices between upstream and downstream intersections, the speed guidance range is determined and a delay minimization model based on optimal speed guidance is established;

[0009] The green wave bandwidth maximization model and the delay minimization model are solved by using a multi-objective locust optimization algorithm to obtain a signal timing solution.

[0010] Preferably, the method for constructing the maximum green wave bandwidth model includes:

[0011] The original AM-Band model is improved to obtain the multipath green wave objective function:

[0012]

[0013] Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N j represents the number of critical paths on intersection j;

[0014] Several constraints are imposed on the multipath green wave objective function to obtain the maximum green wave bandwidth model.

[0015] Preferably, the method for constructing the delay minimization model includes:

[0016] Determine the speed guidance range:

[0017]

[0018] Among them, L c Indicates the speed guidance area control range, V max Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time;

[0019] When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy:

[0020]

[0021] Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d (j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j,k) represents the average speed of vehicles in the coordination phase j of intersection;

[0022] A vehicle cannot accelerate through the current signal cycle, but can decelerate through the next cycle, thus achieving non-stop passage. A green light guidance model is generated based on the deceleration guidance strategy:

[0023]

[0024] Where t(j,x+1) represents the green light on time of intersection j in the coordination phase of x+1 cycle, t n Indicates the current moment;

[0025] When a vehicle reaches the end of the queue and the startup fluctuation is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, a red light guidance model is generated based on the deceleration guidance strategy:

[0026]

[0027] in, represents the speed of the saturated traffic flow at intersection j passing through the intersection;

[0028] The delay minimization model is constructed based on the speed guidance range, the green light guidance model, and the red light guidance model:

[0029]

[0030] Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

[0031] Preferably, the method of solving the green wave bandwidth maximum model and the delay minimization model using the locust optimization algorithm includes:

[0032] Randomly generate a group of m locust individuals, each locust represents a potential traffic signal adjustment solution, and initialize the algorithm parameters;

[0033] Constraint checks are performed on each locust individual in the swarm. If a locust individual's signal plan is judged to not comply with traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the swarm.

[0034] For each locust individual, the fitness is calculated based on the green wave bandwidth maximization model and the delay minimization model, and a non-inferior solution set is identified according to the Pareto dominance principle, and the non-inferior solution set is evaluated and ranked;

[0035] The locust individual with the best distribution density in the non-inferior solution set is selected as the global optimal solution Gbest of this iteration, and the current position of the individual is determined as the historical optimal position of the individual;

[0036] According to the global optimal solution Gbest and the historical optimal position of each locust individual, the weight coefficient of the algorithm is adjusted to update the position and speed of each locust individual;

[0037] If the current position of the locust individual is better than the historical optimal position, the historical optimal position is replaced by the current position, the global optimal solution is selected according to the optimal density distance, and the global optimal solution Gbest is updated. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, Gbest is added to the new non-inferior solution set and the dominated individuals in the solution set are removed;

[0038] Detect whether the preset maximum number of iterations is reached, or whether the accuracy of the locust individuals meets the set requirements. If any condition is met, output the maximum dominance Pareto solution corresponding to the fitness value and the corresponding signal timing scheme.

[0039] The present invention also provides an urban road multi-path coordination control system based on an improved AM-Band model, wherein the system applies any of the above-mentioned methods and comprises: a first model construction module, a second model construction module and a solution solving module;

[0040] The first model building module improves the original AM-Band model based on path traffic and turning requirements to obtain a multi-path oriented green wave bandwidth maximum model;

[0041] The second model building module determines the speed guidance range based on the indicator light signal device between the upstream and downstream intersections, and establishes a delay minimization model based on the optimal speed guidance;

[0042] The solution solving module uses a multi-objective locust optimization algorithm to solve the green wave bandwidth maximization model and the delay minimization model to obtain a signal timing solution.

[0043] Preferably, the workflow of the first model building module includes:

[0044] The original AM-Band model is improved to obtain the multipath green wave objective function:

[0045]

[0046] Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N j represents the number of critical paths on intersection j;

[0047] Several constraints are imposed on the multipath green wave objective function to obtain the maximum green wave bandwidth model.

[0048] Preferably, the workflow of the second model building module includes:

[0049] Determine the speed guidance range:

[0050]

[0051] Among them, L c Indicates the speed guidance area control range, V max Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time;

[0052] When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy:

[0053]

[0054] Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d(j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j,k) represents the average speed of vehicles in the coordination phase j of intersection;

[0055] A vehicle cannot accelerate through the current signal cycle, but can decelerate through the next cycle, thus achieving non-stop passage. A green light guidance model is generated based on the deceleration guidance strategy:

[0056]

[0057] Where t(j,x+1) represents the green light on time of intersection j in the coordination phase of x+1 cycle, t n Indicates the current moment;

[0058] When a vehicle reaches the end of the queue and the startup fluctuation is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, a red light guidance model is generated based on the deceleration guidance strategy:

[0059]

[0060] in, represents the speed of the saturated traffic flow at intersection j passing through the intersection;

[0061] The delay minimization model is constructed based on the speed guidance range, the green light guidance model, and the red light guidance model:

[0062]

[0063] Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

[0064] Preferably, the workflow of the solution-solving module includes:

[0065] Randomly generate a group of m locust individuals, each locust represents a potential traffic signal adjustment solution, and initialize the algorithm parameters;

[0066] Constraint checks are performed on each locust individual in the swarm. If a locust individual's signal plan is judged to not comply with traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the swarm.

[0067] For each locust individual, the fitness is calculated based on the green wave bandwidth maximization model and the delay minimization model, and a non-inferior solution set is identified according to the Pareto dominance principle, and the non-inferior solution set is evaluated and ranked;

[0068] The locust individual with the best distribution density in the non-inferior solution set is selected as the global optimal solution Gbest of this iteration, and the current position of the individual is determined as the historical optimal position of the individual;

[0069] According to the global optimal solution Gbest and the historical optimal position of each locust individual, the weight coefficient of the algorithm is adjusted to update the position and speed of each locust individual;

[0070] If the current position of the locust individual is better than the historical optimal position, the historical optimal position is replaced by the current position, the global optimal solution is selected according to the optimal density distance, and the global optimal solution Gbest is updated. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, Gbest is added to the new non-inferior solution set and the dominated individuals in the solution set are removed;

[0071] Detect whether the preset maximum number of iterations is reached, or whether the accuracy of the locust individuals meets the set requirements. If any condition is met, the maximum dominance Pareto solution corresponding to the fitness value and its corresponding signal timing scheme are output.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] This invention significantly reduced average vehicle delays on high-traffic routes, with a maximum reduction of approximately 12.5%, and also reduced the average number of stops by approximately 0.21, demonstrating that the solution is particularly effective on high-traffic routes. Overall, the invention excels in increasing green wave bandwidth, reducing average vehicle delays, and reducing average vehicle stops. The signal timing adjustment effect is particularly prominent on high-traffic routes. To address the issues of insufficient green wave bandwidth and route competition at continuous intersections, this two-stage optimization model, combined with signal timing and vehicle speed guidance, achieves comprehensive optimization of urban traffic. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0075] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention;

[0076] Figure 2 This is the coordinated intersection multipath according to an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0078] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] Example 1

[0080] In path coordination control, there is a close relationship between the Green Wave Maximization Bandwidth model and the Delay Model. The Green Wave Maximization Bandwidth model primarily focuses on improving vehicle traffic efficiency by optimizing traffic signal timing, achieving higher throughput rates and smoother traffic flow. In contrast, the Delay Model focuses on the time loss caused by traffic signal control, quantifying the waiting time of vehicles at red lights and the parking time caused by traffic signal changes. The two complement each other, and the Green Wave Maximization Bandwidth Model can provide a basis for optimizing the Delay Model. By evaluating the delays of different signal timing schemes, the settings of traffic signals can be further improved, so that the overall traffic system can achieve both efficient passage and effectively reduce delays. Therefore, combining the advantages of these two models can more comprehensively improve the efficiency and operational quality of the traffic system.

[0081] In this embodiment, if Figure 1 As shown, a multi-path coordinated control method for urban roads based on an improved AM-Band model includes the following steps:

[0082] S1. Based on the path traffic and steering requirements, the original AM-Band model is improved to obtain a multi-path oriented green wave bandwidth maximum model.

[0083] The method for constructing the maximum green wave bandwidth model includes: improving the original AM-Band model to obtain the multipath green wave objective function:

[0084]

[0085] Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N j Represents the number of critical paths on intersection j.

[0086] Several constraints are imposed on the multipath green wave objective function, and a green wave bandwidth maximization model is obtained.

[0087] In this embodiment, it is ensured that paths with heavy traffic volume can obtain wider green wave belts, thereby improving the efficiency and smoothness of the entire traffic network. By constructing the following constraint conditions, traffic congestion can be reduced and the road capacity can be improved:

[0088]

[0089] Among them, k j Indicates the target ratio of upstream and downstream bandwidths at intersection j.

[0090] The upper and lower limits of each intersection cycle are shown in the following formula:

[0091]

[0092] Among them, C1 represents the lower limit of the cycle, and C2 represents the upper limit of the cycle.

[0093] In order to ensure that the green wave bandwidth in the up and down directions of each path i at each intersection k does not overlap with the red light signal time, the following constraints are constructed to ensure that vehicles can pass smoothly within the green wave bandwidth and avoid stops and delays caused by red lights:

[0094]

[0095]

[0096] Among them, w i,j represents the green light duration portion before the green wave band of the uplink path i at intersection j, w i,j+1 Indicates the green light duration portion after the green wave band of the uplink path i at intersection j+1, represents the green light duration portion after the green wave band of downlink path i at intersection j, The green light duration portion before the green wave band of downlink path i at intersection j+1, r i,jrepresents the total duration of the red light on the left side of the green wave band of path i at intersection j, r i,j+1 represents the total duration of the red light on the left side of the green wave band of path i at intersection j+1, represents the total duration of the red light on the left side of the green wave band of path i at intersection j, represents the total duration of the red light on the left side of the green wave band of path i at intersection j+1, τ i,j+1 represents the up-queue release time of path i at intersection j+1, It represents the down-line queue release time of exit path i at intersection j.

[0097] To ensure efficient allocation of green bandwidth and avoid allocating resources to paths that do not actually receive green bandwidth, the following constraint is proposed to help the model select paths during the decision-making process, ensuring that only those paths that actually need and should receive green bandwidth are considered in signal timing optimization:

[0098]

[0099] in, is a binary decision variable, indicating the bandwidth of the incorrect green wave, z indicates the periodic derivative, b e Indicates the effective green light time, and L is a large constant.

[0100] In order to ensure that vehicles can continuously pass through the intersection on the entry and exit paths and form an effective green wave belt, the following cycle constraint formula is constructed:

[0101]

[0102] Among them, θ j represents the phase difference at intersection j, n i,j represents the number of uplink signal cycles of exit path i at intersection j, represents the number of downlink signal cycles of exit path i at intersection j, t j represents the travel time of the upward path i from intersection j to j+1, represents the travel time of downstream path i from intersection j to j+1; these constraints account for vehicle waiting time at intersections, green wave bandwidth, and time synchronization between adjacent intersections. For outbound paths that do not participate in the green wave, the constraints are adjusted to avoid allocating invalid green wave bandwidth to these paths, thus ensuring that the solution of the entire optimization model is feasible.

[0103] Setting upper and lower speed limits for each road segment helps improve road safety, reduce accident risks, and maintain smooth and efficient traffic flow. The constraints are as follows:

[0104]

[0105] Among them, f j represents the upper limit of driving speed at intersection j, represents the upper limit of the downhill speed at intersection j, e j represents the lower limit of driving speed at intersection j, represents the lower limit of the downhill speed at intersection j, d j represents the distance from the upstream path at intersection j to j+1, It represents the distance of the downlink path from intersection j to j+1.

[0106] Setting upper and lower limits on speed changes between consecutive road sections. This means that when a vehicle transitions from one road section to the next, its speed change (acceleration or deceleration) must remain within a certain range. This helps avoid traffic safety issues caused by sudden acceleration or deceleration, and also helps reduce fuel consumption and emissions. The constraints are as follows:

[0107]

[0108] Among them, h j Indicates the lower limit of the speed change at intersection j, g j represents the upper limit of the speed change at intersection j, represents the lower limit of the speed change of the downlink path at intersection j, Indicates the upper limit of the speed change of the downlink path at intersection j.

[0109] To ensure that all relevant time and bandwidth parameters are reasonable and in line with the actual situation when optimizing traffic signals, the following constraints are constructed:

[0110]

[0111] S2. Determine the speed guidance range based on the indicator light signal devices between upstream and downstream intersections, and establish a delay minimization model based on optimal speed guidance.

[0112] Methods for building delay minimization models include:

[0113] When determining the shortest control range of the speed guidance zone, it is necessary to consider that the vehicle has sufficient time to adjust the speed at any speed. When determining the longest control range, it is necessary to consider the driver's reaction time while ensuring that the vehicle can pass through the intersection within one signal cycle. Therefore, the speed guidance range is determined as follows:

[0114]

[0115] Among them, L c Indicates the speed guidance area control range, Vmax Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time;

[0116] When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy:

[0117]

[0118] Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d (j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j,k) represents the average speed of vehicles in the coordination phase j of intersection;

[0119] A vehicle cannot accelerate through the current signal cycle, but can decelerate through the next cycle, thus achieving non-stop passage. A green light guidance model is generated based on the deceleration guidance strategy:

[0120]

[0121] Where t(j,x+1) represents the green light on time of intersection j in the coordination phase of x+1 cycle, t n Indicates the current moment;

[0122] When a vehicle reaches the end of the queue and the startup fluctuation is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, a red light guidance model is generated based on the deceleration guidance strategy:

[0123]

[0124] in, represents the speed of the saturated traffic flow at intersection j passing through the intersection;

[0125] In speed guidance, vehicle travel delay refers to the difference between the time a vehicle actually travels a specific road section and the time it would take to travel the same section at free-flow speed. In this embodiment, delay is defined as the difference between the time required to pass through the delay detection zone (which is longer than the guidance zone) at the target speed and the time required to pass through the intersection at free-flow speed within a certain time. Therefore, a delay minimization model is constructed based on the speed guidance range, green light guidance model, and red light guidance model:

[0126]

[0127] Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

[0128] S3. Using the multi-objective locust optimization algorithm, the green wave bandwidth maximization model and delay minimization model are solved to obtain the signal timing plan.

[0129] Because decision variables are multidimensional, their dimensionality increases with the number of coordinated intersections and paths. This makes traditional analytical and graphical methods computationally complex and cumbersome, resulting in poor performance and failure to achieve the desired optimization goal. The Multi-Objective Locust Optimization Algorithm (MOGOA) is an intelligent optimization algorithm for solving multi-objective problems. It offers efficient global search capabilities, ease of implementation, and high solution quality. The algorithm draws on the feeding habits of locusts, where the position of each searching individual (i.e., locust) represents a possible solution to the problem. Its mathematical model is as follows:

[0130] X l =S l +G l +A l

[0131] Among them, X l represents the position of the lth locust in the population, S l Indicates that it is affected by social forces, G l Indicates the influence of gravity, A l Indicates that it is affected by wind.

[0132] The social interaction between populations is the most important factor affecting locust movement, which can be described by the following formula:

[0133]

[0134]

[0135] Among them, d ml represents the distance between the mth and lth locusts, represents the unit vector between the mth and lth locusts, and s(r) represents the social force between locusts.

[0136] The influence of locust gravity and wind force can be expressed as follows:

[0137]

[0138] Where g is the gravitational constant, represents the unit vector of gravity, t represents the drift constant in the wind direction, Represents the wind direction unit vector.

[0139] The update model of locust position can be expressed as the following formula:

[0140]

[0141] Among them, ub d Indicates the upper bound of the position in the d dimension, lb d Represents the lower bound of the position in the d dimension, It represents the position of the dominant guiding individual in the current population, and c represents the linear reduction coefficient.

[0142] The multi-objective locust algorithm searches for a Pareto-optimal set of solutions that achieves a balance across all objectives by evaluating and updating the positions of individuals in each generation. The algorithm uses an external archive to record the optimal individuals (solutions) found during the optimization process and maintains and updates this archive using dominance relationships—that is, determining whether a solution is no worse than another solution across all objectives.

[0143] In this embodiment, the method of solving the green wave bandwidth maximization model and the delay minimization model using the locust optimization algorithm includes:

[0144] A swarm of m locusts is randomly generated, each representing a potential traffic signal adjustment scheme, including a multi-dimensional parameter vector such as the traffic signal cycle, the green light duration at each intersection and each phase, and the phase difference. Algorithm parameters are also initialized, such as the maximum speed, learning factor, and inertia weight of the locust.

[0145] Constraint checks are performed on each locust individual in the swarm. If a locust individual's signal plan is judged to not comply with traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the swarm.

[0146] Starting with the iteration counter t set to 1, for each locust individual, the fitness is calculated based on the green wave bandwidth maximization model and the delay minimization model, and the non-inferior solution set is identified according to the Pareto dominance principle, and the non-inferior solution set is evaluated and ranked;

[0147] The locust individual with the best distribution density in the non-inferior solution set is selected as the global optimal solution Gbest of this iteration, and the current position of the individual is determined as the historical optimal position of the individual;

[0148] The iteration counter is incremented by one (i.e., n=n+1). In the new iteration, the weight coefficient of the algorithm is adjusted according to the global optimal solution Gbest and the historical optimal position p of each locust individual, and the position and speed of each locust individual are updated.

[0149] If the current position of the locust individual is better than the historical optimal position p, the historical optimal position is replaced by the current position, the global optimal solution is selected according to the optimal density distance, and the global optimal solution Gbest is updated. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, Gbest is added to the new non-inferior solution set and the dominated individuals in the solution set are removed;

[0150] Check whether the preset maximum number of iterations has been reached, or whether the accuracy of the locust individuals meets the set requirements. If any of the conditions are met, the maximum dominance Pareto solution of the corresponding fitness value and the corresponding signal timing plan are output.

[0151] Example 2

[0152] In this embodiment, if Figure 1 As shown, an urban road multi-path coordinated control system based on an improved AM-Band model includes: a first model building module, a second model building module and a solution solving module;

[0153] The first model building module improves the original AM-Band model based on path traffic and turning requirements to obtain a multi-path oriented green wave bandwidth maximum model.

[0154] The workflow of the first model building module includes:

[0155] The original AM-Band model is improved to obtain the multipath green wave objective function:

[0156]

[0157] Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N jrepresents the number of critical paths at intersection j; several constraints are imposed on the multi-path green wave objective function to obtain the maximum green wave bandwidth model.

[0158] The second model building module determines the speed guidance range based on the indicator light signal devices between the upstream and downstream intersections and establishes a delay minimization model based on optimal speed guidance.

[0159] The workflow of the second model building module includes: Determine the speed guidance range:

[0160]

[0161] Among them, L c Indicates the speed guidance area control range, V max Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time. When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy:

[0162]

[0163] Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d (j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j, k) represents the average speed of vehicles in the jth coordinated phase of the intersection. When a vehicle cannot accelerate through the current signal cycle but can decelerate through the next cycle, thus achieving non-stop passage, a green light guidance model is generated based on the deceleration guidance strategy:

[0164]

[0165] Where t(j,x+1) represents the green light on time of intersection j in the coordination phase of x+1 cycle, t n Represents the current moment; when the vehicle reaches the end of the queue and the startup wave is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, the red light guidance model is generated based on the deceleration guidance strategy:

[0166]

[0167] in, represents the speed of the saturated traffic flow at intersection j passing through the intersection; a delay minimization model is constructed based on the speed guidance range, green light guidance model, and red light guidance model:

[0168]

[0169] Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

[0170] The solution solving module uses the multi-objective locust optimization algorithm to solve the green wave bandwidth maximization model and delay minimization model to obtain the signal timing solution.

[0171] The workflow of the solution solving module includes: randomly generating a group of m locust individuals, each locust represents a potential traffic signal adjustment plan, and initializing the algorithm parameters at the same time; performing constraint condition checks on each locust individual in the group, and if it is determined that the signal plan of a locust individual does not meet the traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the group; for each locust individual, based on the green wave bandwidth maximum model and the delay minimization model, calculate the fitness, and identify the non-inferior solution set according to the Pareto dominance principle, and evaluate and sort the non-inferior solution set; select the locust individual with the best distribution density in the non-inferior solution set as the global optimal solution Gbest of this iteration, and determine the current position of the individual as the individual's historical best. optimal position; according to the global optimal solution Gbest and the historical optimal position of each locust individual, adjust the weight coefficient of the algorithm and update the position and speed of each locust individual; if the current position of the locust individual is better than the historical optimal position, replace the historical optimal position with the current position, select the global optimal solution according to the optimal density distance, and update the global optimal solution Gbest. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, add the Gbest to the new non-inferior solution set and remove the dominated individuals in the solution set; detect whether the preset maximum number of iterations is reached, or whether the accuracy of the locust individual meets the set requirements. If any condition is met, output the maximum dominance Pareto solution corresponding to the fitness value and its corresponding signal timing scheme.

[0172] Example 3

[0173] In this embodiment, the effectiveness of the present invention is verified through case analysis.

[0174] To validate the model's effectiveness, we selected four consecutive intersections in Tianjin: Xingguang Road, Haitai North Road, Ziyang Road, Huikang Road, and Zhongbei Avenue. This section of road is densely populated with residential communities and numerous office buildings, making it a key intersection for commuters. The main road in this section is a four-lane, two-way road, with spacing between adjacent intersections of 628, 580, and 862 meters.

[0175] The peak hour traffic flow at each intersection along the line was collected. The survey period was the morning peak hour of September 5, 2024: 7:00-8:00. The flow direction of each intersection is shown in Table 1.

[0176] Table 1

[0177]

[0178] Using the Webster formula to calculate the optimal cycle for each intersection, we determined that intersection ③ was a critical intersection with an optimal cycle of 150 seconds. The cycles for intersections ① and ④ were also adjusted to 150 seconds, and the cycle for intersection ② was adjusted to 75 seconds. The green light display times for each intersection are shown in Table 2.

[0179] Table 2

[0180]

[0181] According to the relevant literature and the flow data of the field survey, the following four key paths are determined. The path information is as follows: Figure 2 As shown in Table 3, based on traffic volume, Paths 1 and 3 can be considered high-traffic paths, while Paths 2 and 4 are low-traffic paths. High-traffic paths are more important, bearing greater traffic pressure and playing a key role in the smooth operation of the entire transportation network. Low-traffic paths can serve as auxiliary routes when necessary, sharing some of the traffic pressure on high-traffic paths.

[0182] Table 3

[0183]

[0184] This embodiment optimizes the signal timing scheme, setting the upper limit of the cycle length to 180 seconds, the lower limit to 60 seconds, the shortest green light time to 10 seconds, and the green light interval to 3 seconds. Based on the multi-objective locust optimization algorithm, the maximum number of iterations t is set to 100 times, the population size m is set to 200, and the population random variable rand is initialized to a value between (0, 1). l Set to 0.8, G l 、A lare all set to 0.1. The increasing coefficient is 1, and the decreasing coefficient is 0.00001. The gravitational constant and wind direction constant are 1. To fully demonstrate the superiority of the model proposed in this paper in the field of multipath trunk signal coordination control, this example selects the multipath model proposed by Yang et al. (abbreviated as Yang-M2) for comparative analysis.

[0185] It can be seen from the coordination scheme of the Yang-M2 model that the cumulative green wave bandwidth of each path is 107 seconds. It can be seen from the coordination scheme of the present invention that the cumulative green wave bandwidth is increased to 110 seconds. Compared with the Yang-M2 model, due to bandwidth redistribution, although the green wave bandwidth of sections ①-② and ②-③ is reduced, the overall cumulative green wave bandwidth is increased by 3 seconds. This is mainly due to the prioritization of high-traffic intersections, which significantly improves the bandwidth of each path in section ③-④ (increase of 8 seconds, 6 seconds, and 6 seconds).

[0186] Simulation verification result analysis:

[0187] First, a simulation scenario is established using Vissim. In order to verify the effectiveness of the model proposed in this invention, the Webster timing scheme, the Yang-M2 scheme, and the optimization model scheme of this invention are simulated respectively, and a comparative analysis is performed based on the simulation results.

[0188] In the research optimization model, according to the traffic flow, the length of the speed guidance area is determined to be 180m, the length of the queuing area is 60m, the maximum speed of vehicle guidance is 17m / s, the transmission speed of the starting wave is 4.5m / s, and the maximum acceleration is 2m / s. 2 , the maximum deceleration is -2m / s 2 The saturated flow rate of the through lane is 1650 pcu / h, and the saturated flow rate of other entrance lanes is 1550 pcu / h. The standard headway is 2 seconds, and the driver reaction time is 1.5 seconds. The load threshold δ is set to 0.7.

[0189] Simulation parameters were set: a 4500-second simulation period was used. Considering the instability of the initial simulation phase, the first 900 seconds were set as a simulation warm-up period, and the remaining 3600 seconds were used for experimental analysis. Table 4 shows the comparison of various indicators before and after optimization for the critical path along the line.

[0190] Table 4

[0191]

[0192] As can be seen, the proposed scheme demonstrates significant advantages over the Yang-M2 scheme on multiple routes. For example, the average delay per vehicle on route 1 was reduced by 4.82 seconds (approximately 4%), by 14.89 seconds (approximately 12.5%) on route 3, and by 7.2 seconds (approximately 7%) on route 4, demonstrating a particularly significant optimization effect on high-traffic routes. The average number of stops per vehicle decreased by 0.09 on route 1, 0.21 on route 3, and 0.12 on route 4, further improving traffic efficiency. However, on route 2, while the average delay per vehicle on the proposed scheme was lower than that of the Webster scheme, it was still 8.39 seconds higher than that of the Yang-M2 scheme. This is due to the reduction in the green wave band caused by route competition, which prevented adequate coordination of signal timing. Furthermore, while the average number of stops per vehicle on route 2 was reduced, it was still higher than that of the Yang-M2 scheme, indicating that there is room for improvement in green wave optimization on low-traffic routes.

[0193] To further consider the impact of the proposed model on vehicles outside the four critical paths, a comprehensive analysis of vehicles at all intersections on the main road was conducted. To verify the overall effectiveness of the optimization scheme, average vehicle delay and average number of vehicle stops were used as evaluation indicators for the simulation results. The simulation results are shown in Table 5.

[0194] Table 5

[0195]

[0196] As can be seen, compared to the classic Webster model, the optimized model in this study reduces average vehicle delay by approximately 10.75%, reduces the average number of stops by approximately 43.26%, and increases the average travel time by approximately 10.84%. Compared to the Yang-M2 model, the optimized model in this study reduces average vehicle delay by approximately 6.53%, increases the average number of stops by approximately 16.44%, and increases the average travel time by approximately 3.69%. This demonstrates that the proposed method has significant advantages in improving commuting efficiency.

[0197] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A multi-path coordinated control method for urban roads based on an improved AM-Band model, characterized in that: The following steps are involved: Based on the path flow and steering requirements, the original AM-Band model is improved to obtain a multi-path oriented green wave bandwidth maximum model. Based on the indicator light signal devices between upstream and downstream intersections, the speed guidance range is determined and a delay minimization model based on optimal speed guidance is established; The green wave bandwidth maximization model and the delay minimization model are solved by using a multi-objective locust optimization algorithm to obtain a signal timing plan; The method for constructing the maximum green wave bandwidth model includes: The original AM-Band model is improved to obtain the multipath green wave objective function: Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N j represents the number of critical paths on intersection j; Applying several constraints to the multipath green wave objective function to obtain the maximum green wave bandwidth model; The method of constructing the delay minimization model includes: Determine the speed guidance range: Among them, L c Indicates the speed guidance area control range, V max Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time; When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy: Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d (j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j,k) represents the average speed of vehicles in the coordination phase j of intersection; A vehicle cannot accelerate through the current signal cycle, but can decelerate through the next cycle, thus achieving non-stop passage. A green light guidance model is generated based on the deceleration guidance strategy: Where t(j, x+1) represents the green light on time of intersection j in the coordination phase x+1 cycle, t n Indicates the current moment; When a vehicle reaches the end of the queue and the startup fluctuation is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, a red light guidance model is generated based on the deceleration guidance strategy: in, represents the speed of the saturated traffic flow at intersection j passing through the intersection; The delay minimization model is constructed based on the speed guidance range, the green light guidance model, and the red light guidance model: Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

2. The urban road multi-path coordinated control method based on the improved AM-Band model according to claim 1 is characterized in that: The method for solving the green wave bandwidth maximum model and the delay minimization model using the locust optimization algorithm includes: Randomly generate a group of m locust individuals, each locust represents a potential traffic signal adjustment solution, and initialize the algorithm parameters; Constraint checks are performed on each locust individual in the swarm. If a locust individual's signal plan is judged to not comply with traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the swarm. For each locust individual, the fitness is calculated based on the green wave bandwidth maximization model and the delay minimization model, and a non-inferior solution set is identified according to the Pareto dominance principle, and the non-inferior solution set is evaluated and ranked; The locust individual with the best distribution density in the non-inferior solution set is selected as the global optimal solution Gbest of this iteration, and the current position of the individual is determined as the historical optimal position of the individual; According to the global optimal solution Gbest and the historical optimal position of each locust individual, the weight coefficient of the algorithm is adjusted to update the position and speed of each locust individual; If the current position of the locust individual is better than the historical optimal position, the historical optimal position is replaced by the current position, the global optimal solution is selected according to the optimal density distance, and the global optimal solution Gbest is updated. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, Gbest is added to the new non-inferior solution set and the dominated individuals in the solution set are removed; Detect whether the preset maximum number of iterations is reached, or whether the accuracy of the locust individuals meets the set requirements. If any condition is met, output the maximum dominance Pareto solution corresponding to the fitness value and the corresponding signal timing scheme.

3. An urban road multi-path coordinated control system based on an improved AM-Band model, characterized in that: include: a first model building module, a second model building module and a solution solving module; The first model building module improves the original AM-Band model based on path traffic and turning requirements to obtain a multi-path oriented green wave bandwidth maximum model; The second model building module determines the speed guidance range based on the indicator light signal device between the upstream and downstream intersections, and establishes a delay minimization model based on the optimal speed guidance; The solution solving module uses a multi-objective locust optimization algorithm to solve the green wave bandwidth maximization model and the delay minimization model to obtain a signal timing solution; The workflow of the first model building module includes: The original AM-Band model is improved to obtain the multipath green wave objective function: Where Z represents the sum of the weighted green wave bandwidths of the uplink and downlink key paths of all intersections on the entire road section of the optimization target. represents the weight of the upward direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the uplink direction, represents the green wave bandwidth of the right half of path i in the uplink direction at intersection j, represents the weight of the downlink direction of path i at intersection j, represents the left half of the green wave bandwidth of path i on intersection j in the downlink direction, represents the right half of the green wave bandwidth of path i on intersection j in the downlink direction, M represents the total number of intersections, N j represents the number of critical paths on intersection j; Applying several constraints to the multipath green wave objective function to obtain the maximum green wave bandwidth model; The workflow of the second model building module includes: Determine the speed guidance range: Among them, L c Indicates the speed guidance area control range, V max Indicates the maximum speed of the road section, V min Indicates the minimum speed of the road section, a sp Indicates the acceleration that the driver feels comfortable with, a sd Indicates the deceleration that the driver feels comfortable with, t rt Indicates the driver's reaction time; When a vehicle cannot pass through the intersection at its original speed during the current signal cycle but can pass through the intersection through acceleration guidance, a green light guidance model is generated based on the acceleration guidance strategy: Among them, V t (j,k) represents the theoretical optimal speed of vehicle k in the coordinated phase of intersection j, L d (j,k) represents the distance between vehicle k in the coordinated phase j and the intersection, L s (j,k) The length of vehicle k in the coordinated phase queue at intersection j, V a (j,k) represents the average speed of vehicles in the coordination phase j of intersection; A vehicle cannot accelerate through the current signal cycle, but can decelerate through the next cycle, thus achieving non-stop passage. A green light guidance model is generated based on the deceleration guidance strategy: Where t(j, x+1) represents the green light on time of intersection j in the coordination phase x+1 cycle, t n Indicates the current moment; When a vehicle reaches the end of the queue and the startup fluctuation is transmitted to the end of the queue, but the vehicle cannot pass through the intersection, a red light guidance model is generated based on the deceleration guidance strategy: in, represents the speed of the saturated traffic flow at intersection j passing through the intersection; The delay minimization model is constructed based on the speed guidance range, the green light guidance model, and the red light guidance model: Where D(j) represents the total delay at intersection j on the path, L(j) represents the delay detection area at intersection j, represents the average speed of the remaining sections of the delay detection area at intersection j except the guidance area, U(j) represents the number of vehicles passing through, and v f Indicates free flow speed.

4. The urban road multi-path coordinated control system based on the improved AM-Band model according to claim 3 is characterized in that: The workflow of the solution-solving module includes: Randomly generate a group of m locust individuals, each locust represents a potential traffic signal adjustment solution, and initialize the algorithm parameters; Constraint checks are performed on each locust individual in the swarm. If a locust individual's signal plan is judged to not comply with traffic rules or safety requirements, the individual that does not meet the requirements will be removed from the swarm. For each locust individual, the fitness is calculated based on the green wave bandwidth maximization model and the delay minimization model, and a non-inferior solution set is identified according to the Pareto dominance principle, and the non-inferior solution set is evaluated and ranked; The locust individual with the best distribution density in the non-inferior solution set is selected as the global optimal solution Gbest of this iteration, and the current position of the individual is determined as the historical optimal position of the individual; According to the global optimal solution Gbest and the historical optimal position of each locust individual, the weight coefficient of the algorithm is adjusted to update the position and speed of each locust individual; If the current position of the locust individual is better than the historical optimal position, the historical optimal position is replaced by the current position, the global optimal solution is selected according to the optimal density distance, and the global optimal solution Gbest is updated. If the fitness of the global optimal solution Gbest is higher than the previous optimal fitness, Gbest is added to the new non-inferior solution set and the dominated individuals in the solution set are removed; Detect whether the preset maximum number of iterations is reached, or whether the accuracy of the locust individuals meets the set requirements. If any condition is met, the maximum dominance Pareto solution corresponding to the fitness value and its corresponding signal timing scheme are output.

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