A double-layer optimization design method for a CAV special lane deployment strategy

Abstract

The application discloses a CAV special lane deployment strategy double-layer optimization design method, relates to the field of traffic network computer technologies under an intelligent network connection environment, and constructs an intelligent network connection expansion network; constructs a road section impedance function considering CAV proportion and headway parameters, constructs a travel cost function of CAV users and HV users; constructs a double-layer optimization model of the traffic bearing capacity of the intelligent network connection expansion network; forms a double-layer optimization model of the CAV special lane deployment strategy; converts a nonlinear user equilibrium UE traffic distribution model into a linearized user equilibrium UE traffic distribution model; linearly processes the nonlinear road section impedance function to obtain a CAV special lane deployment strategy double-layer optimization model in a mixed integer linear programming form; solves the CAV special lane deployment strategy double-layer optimization model in the mixed integer linear programming form, and obtains the design result of the CAV special lane deployment strategy of the urban road network. The method can find an optimal deployment scheme.

Description

Technical Field

[0001] The present invention relates to the field of traffic network computer technology in an intelligent network environment, and in particular to a double-layer optimization design method for CAV dedicated lane deployment strategy. Background Art

[0002] With the emergence of intelligent, connected autonomous vehicles (CAVs), future transportation systems are expected to undergo significant transformation. Compared to human-driven vehicles (HVs), CAVs can achieve shorter vehicle-to-vehicle distances due to their collaborative driving capabilities using advanced sensors and communication systems. Furthermore, CAVs can mitigate some of the errors and delays associated with human driving through their autonomous driving technology. Consequently, CAVs are expected to bring numerous benefits to transportation network performance, such as increased road capacity, lower fuel consumption, and reduced traffic congestion.

[0003] Considering the multiple benefits of intelligent connected technologies, numerous studies have optimized CAV driving trajectories through simulation-based experiments. With the advancement of emerging technologies and policy support, CAVs are likely to become increasingly popular. However, before fully connected and autonomous vehicles are achieved, the road traffic system will experience a long transition period in which HVs and CAVs will coexist—optimistic estimates suggest at least three decades. It is important to note that many of the aforementioned CAV-related advantages depend on a 100% or very high market share of CAVs. Therefore, in a mixed traffic environment of CAVs and HVs, exploiting the potential advantages of CAVs in increasing network capacity and optimizing network efficiency presents a significant challenge. To address these challenges during this transition period, it is of practical significance to study the characteristics of mixed traffic flows under varying CAV market shares and develop corresponding traffic network management strategies. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a two-layer optimization design method for CAV dedicated lane deployment strategy. This method constructs a two-layer optimization model to evaluate network performance in a mixed traffic flow environment and integrates the deployment decision variables of intelligent connected dedicated lanes to find the optimal deployment plan.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A two-tier optimization design method for CAV dedicated lane deployment strategy proposed in the present invention includes:

[0007] Build an intelligent connected expansion network including conventional lanes and alternative arc sections of CAV-dedicated lanes;

[0008] Construct a road impedance function that takes into account the CAV ratio and headway parameters. The headway parameters include HV-HV, HV-CAV, CAV-CAV, and CAV-HV. HV-HV means that both the front and rear vehicles are HVs, HV-CAV means that the rear vehicle is an HV and the front vehicle is a CAV, CAV-CAV means that both the front and rear vehicles are CAVs, and CAV-HV means that the rear vehicle is a CAV and the front vehicle is an HV.

[0009] Considering the time value cost and fuel cost, the travel cost function of CAV users and HV users is constructed;

[0010] Construct a two-layer optimization model for the traffic carrying capacity of the intelligent connected network. The two-layer optimization model includes an upper optimization model and a lower optimization model. The upper optimization model aims to maximize the travel demand carried by the road network, while the lower optimization model is a user equilibrium UE traffic allocation model that aims to minimize the cumulative value of the integral of the travel cost function.

[0011] The two-tier optimization model for road network carrying capacity was constructed by introducing CAV lane deployment constraints. These constraints included CAV market share, potential unfairness factors for HV users, and CAV lane construction costs, forming a two-tier optimization model for CAV lane deployment strategies.

[0012] By introducing sufficiently large values ​​and binary 0-1 variables, the nonlinear user equilibrium UE traffic assignment model is transformed into a linear user equilibrium UE traffic assignment model;

[0013] The nonlinear road impedance function is linearized to obtain a two-level optimization model for CAV lane deployment strategy in the form of mixed integer linear programming.

[0014] A standard mathematical optimization solver is used to solve the bi-level optimization model of CAV dedicated lane deployment strategy in the form of mixed integer linear programming, and the design results of the CAV dedicated lane deployment strategy in the urban road network are obtained.

[0015] As a further optimization scheme of the dual-layer optimization design method for CAV dedicated lane deployment strategy described in the present invention, an intelligent connected extended network including conventional lanes and alternative arc sections of CAV dedicated lanes is constructed; the details are as follows:

[0016] Step S1.1: Define the arc element a in the basic road network 0 ∈A 0 , A 0 is a set of arc elements, and the number of lanes in each arc is The basic traffic capacity is The free flow travel time is The mixed traffic includes both CAV and HV, and the mixed traffic is expressed as M={CAV, HV}, m e M, M is a set of travel modes, and m is an element included in M;

[0017] Step S1.2, arc segment element a 0 e A 0 An extension of a CAV exclusive lane alternative arc segment Forming an alternative arc segment set

[0018] Step S1.3, for each a 0 e A 0 Introducing 0-1 variable If The CAV exclusive lane alternative arc segment is set as a CAV exclusive lane, otherwise the arc segment is not set as a CAV exclusive lane.

[0019] Step S1.4, forming an intelligent network extension network through steps S1.1-S1.3, all arc segments belong to the intelligent network extension network arc segment set A, expressed as:

[0020]

[0021] Wherein, a is all arc segments in the intelligent network extension network.

[0022] As a further optimization scheme of the double-layer optimization design method of the CAV exclusive lane deployment strategy, a road section impedance function considering the CAV proportion and the headway parameter is constructed, and the specific steps are as follows:

[0023] Step S2.1, introducing parameter p a represents the CAV proportion of the traffic flow of arc segment a e A, p a is expressed as:

[0024]

[0025] Wherein, is the CAV traffic flow of arc segment a e A, is the traffic flow of travel mode m of arc segment a e A;

[0026] Step S2.2, introducing the correction coefficient e of the road section impedance function, expressed as:

[0027]

[0028] Wherein, γ, γ1, γ2 are respectively the headway coefficient of CAV-CAV, CAV-HV, HV-CAV driving mode relative to HV-HV driving mode, and k2 is the CAV fleet size;

[0029] Step S2.3, combined with the correction coefficient of step S2.2, the mixed traffic flow impedance function of the road section in the form of the BPR function of the US Federal Highway Administration is:

[0030]

[0031] Wherein, is a 0 free-flow travel time, is the basic capacity of arc segment a 0 , and are respectively the CAV and HV traffic flow of arc segment a 0 , and are the CAV and HV traffic flow of arc segment , is the number of lanes of arc segment a 0 , and α and β are the parameters of the BPR function, and are respectively the impedance functions of arc segment a 0 and arc segment .

[0032] As a further optimization scheme of the double-layer optimization design method of the CAV special lane deployment strategy, the travel cost functions of CAV users and HV users are constructed by considering the time value cost and fuel cost, and the specific steps are as follows:

[0033] Step S3.1, the travel cost function includes travel time cost and fuel cost;

[0034]

[0035] Wherein, represents the travel cost of travel mode m through arc segment a, VOT m is the resident travel time value, t a is the travel time of arc segment a, χ m is the fuel cost of m travel mode per unit distance, and L a is the length of arc segment a;

[0036] Step S3.2, according to the travel cost function of each arc segment, the travel cost function of each path is constructed;

[0037]

[0038] wherein, is the cost required for trip mode m through traffic origin-destination pair (r,s) by path k, K rs is the set of paths for (r,s), is a binary 0-1 variable representing the relationship between arc segment and path, denotes that path k goes through arc segment a, denotes that path k does not go through arc segment a, r is the origin traffic zone, R is the set of origin traffic zones, s is the origin traffic zone, and S is the set of destination traffic zones.

[0039] As a further optimization scheme of the CAV special lane deployment strategy double-layer optimization design method described in the application, a double-layer optimization model for building intelligent network expansion network traffic carrying capacity is constructed, the double-layer optimization model includes an upper-layer optimization model and a lower-layer optimization model, the upper-layer optimization model takes maximizing the travel demand carried by the road network as the target, and the lower-layer optimization model is a user equilibrium UE traffic distribution model taking minimizing the cumulative value of the integral of the travel cost function as the target; the specific implementation is as follows:

[0040] Step S4.1, constructing the upper-layer optimization model of the double-layer optimization model for traffic road network carrying capacity, taking maximizing the travel demand carried by the road network as the target under the constraint that the flow on each road section does not exceed the traffic capacity;

[0041]

[0042] subject to

[0043]

[0044] wherein, denotes the maximum traffic volume accommodated by O-D pair (r,s), denotes all a vector matrix composed of, denotes the element sum of vector matrix is the traffic flow of arc segment a at the scale, C a is the traffic capacity of arc segment a;

[0045] Step S4.2, constructing the lower-layer optimization model of the double-layer optimization model for traffic road network carrying capacity based on the user equilibrium UE traffic distribution model, the objective function of which is minimizing the cumulative value of the integral of the travel cost function;

[0046]

[0047] subject to

[0048] ​

[0049]

[0050] in, is the traffic flow of mode m on OD pair (r, s) through path k, is the travel volume of mode m in the OD pair (r,s), is the traffic flow of mode m in arc a, v a is the traffic flow of arc segment a, Z is the objective function value, is the travel cost of travel mode m through arc segment a, ω is the traffic flow variable of the travel cost function of arc segment a;

[0051] Step S4.3: Based on the UE conditions, when the urban traffic system reaches a stable state, the path flows of HVs and CAVs meet the following constraints:

[0052]

[0053] in, represents the traffic flow of travel mode m on path k between OD pair (r, s), represents the travel cost of travel mode m on path k between OD pair (r, s), u rs,m It represents the minimum travel cost of travel mode m between the OD pair (r, s).

[0054] As a further optimization scheme for the dual-layer optimization design method for CAV lane deployment strategy described in the present invention, CAV lane deployment constraints are introduced into the constructed dual-layer optimization model for traffic network carrying capacity. The CAV lane deployment constraints include CAV market share, potential unfairness factors for HV users, and CAV lane construction costs, forming a dual-layer optimization model for CAV lane deployment strategy. The details are as follows:

[0055] Step S5.1: Construct the constraints for CAV market share:

[0056]

[0057] in, and denote the CAV and HV travel volumes of the OD pair (r, s), respectively, and ρ denotes the market share of CAV;

[0058] Step S5.2: Construct constraints for potential unfairness factors for HV users:

[0059]

[0060] in, represents the travel cost of HV users passing the OD pair (r, s) after deploying CAV dedicated lanes, represents the travel cost of HV users passing the OD pair (r, s) when CAV dedicated lanes are not deployed, and λ represents the degree of unfair impact of deploying CAV dedicated lanes on HV users;

[0061] Step S5.3: Constructing the cost constraints for CAV lane construction

[0062]

[0063] Among them, y a is a binary 0-1 variable, indicating the deployment of CAV dedicated lanes in arc a, y a =1 means that arc a is deployed with a CAV dedicated lane, otherwise y a =0,L a represents the length of arc segment a, d represents the unit mileage construction cost of the CAV dedicated lane, represents the total budgeted cost of CAV dedicated lane deployment.

[0064] As a further optimization scheme of the dual-layer optimization design method for CAV dedicated lane deployment strategy described in the present invention, the nonlinear user equilibrium UE traffic assignment model is transformed into a linear user equilibrium UE traffic assignment model by introducing sufficiently large values ​​and binary 0-1 variables; the details are as follows:

[0065]

[0066] Among them, U is a sufficiently large value, is a binary 0-1 variable representing the relationship between path and travel mode, Indicates that the traffic flow of travel mode m on path k between OD pair (r, s) is non-zero, otherwise

[0067] As a further optimization scheme of the dual-level optimization design method for CAV dedicated lane deployment strategy described in the present invention, the nonlinear road section impedance function is linearized to obtain a dual-level optimization model for CAV dedicated lane deployment strategy in the form of mixed integer linear programming. Specifically, the method includes:

[0068] Step S7.1: Introduce auxiliary variable w a and l a :

[0069]

[0070] Among them, w a The lower bound of the value range w a and upper bound wa =0 and is the basic traffic capacity of arc segment a∈A, is the HV traffic flow of arc segment a∈A;

[0071] Step S7.2: Using auxiliary variables and Convert the link impedance function into a univariate polynomial:

[0072]

[0073] Step S7.3, in the auxiliary variable w a The value range of Set N+1 breakpoints in the

[0074] The pth breakpoint is p∈P={1,2,...,N,N+1},

[0075] p is an integer, P is a set of integers, and N is any positive integer;

[0076] Step S7.4: Introduce variables Indicates a breakpoint The weight coefficient of The variable w in a Expressed as is the p+1th breakpoint, For breakpoints The weight coefficient of , according to the partition linear approximation method, obtains the following linear constraints:

[0077]

[0078] in, Indicates l a The piecewise linear approximation of ;

[0079] Step S7.5: According to the special order set second type SOS2 constraint, there are at most two adjacent is an integer, and its constraints are expressed as:

[0080]

[0081] in, is a binary 0-1 variable, express otherwise All are parameters;

[0082] Step S7.6: Introduce auxiliary variable ω a =l a ya , its value range is:

[0083]

[0084] Linearize the product formula of continuous variables and binary variables to obtain the linear expression formula of the road section impedance function:

[0085]

[0086] At this point, the two-level optimization model of the CAV dedicated lane deployment strategy is reconstructed into a mixed integer linear programming.

[0087] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0088] (1) The method of the present invention can provide a mathematical optimization model for the deployment strategy of CAV dedicated lanes, thereby serving all stages of intelligent connected vehicle development and avoiding the over-deployment of CAV dedicated lanes;

[0089] (2) This method constructs a two-layer optimization model to evaluate network performance in a mixed traffic flow environment and integrates the deployment decision variables of intelligent connected dedicated lanes to find the optimal deployment solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flowchart of the overall implementation of the present invention;

[0091] Figure 2 A road network diagram according to an embodiment of the present invention;

[0092] Figure 3 Schematic diagram of headway under different driving modes;

[0093] Figure 4 Schematic diagram of the partitioned linear approximation method;

[0094] Figure 5 This is a diagram showing the design results of a dedicated lane deployment strategy according to an embodiment of the present invention. DETAILED DESCRIPTION

[0095] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0096] To minimize the negative impact of CAVs and HVs traveling together while maximizing the advantages of CAV fleets, the deployment of dedicated CAV lanes has proven to be one of the most effective future solutions. Its goal is to separate CAV and HV traffic flows, thereby creating a local ideal area with 100% CAV traffic flow. However, the deployment of CAV lanes may reduce the number of feasible routes for HV users and increase their travel time, thereby creating social inequities. Therefore, the deployment strategy of CAV lanes should be based on a mathematical and rational design method that fully considers the various factors that affect CAV and HV users.

[0097] This paper proposes a two-level optimization design method for CAV dedicated lane deployment strategy based on mixed traffic network carrying capacity assessment. Taking the Sioux-Falls urban road network as an example, the CAV dedicated lane deployment strategy is designed. Figure 1 As shown, the following steps are included:

[0098] S1: Build an intelligent connected extended network that includes conventional lanes and alternative arc sections of CAV-dedicated lanes;

[0099] Step S1.1: Define the arc element a in the basic road network 0 ∈A 0 , A 0 is a set of arc elements, and the number of lanes in each arc is The basic traffic capacity is The free flow travel time is Mixed traffic includes two travel modes, CAV and HV. Mixed traffic is expressed as M = {CAV, HV}, m∈M, where M is the set of travel modes and m is the element contained in M;

[0100] S1.2: Each arc element a 0 ∈A 0 Expand an alternative arc section of the CAV dedicated lane Forming a collection

[0101] S1.3: For each a 0 ∈A 0 Introducing 0-1 variables like Then the alternative arc section of the CAV dedicated lane Set as a CAV dedicated lane, otherwise the arc Not set up as a CAV-only lane;

[0102] S1.4: Through steps S1.1 to 1.3, an intelligent connected extended network is formed, such as Figure 2As shown in Figure 2, all arcs belong to the intelligent connected extended network arc set A, which can be expressed as:

[0103]

[0104] Where a represents all arcs in the intelligent connected extended network.

[0105] S2: Construct a road section impedance function that takes into account the CAV ratio and headway parameters. The headway parameters include four cases: HV-HV, HV-CAV, CAV-CAV, and CAV-HV.

[0106] S2.1: Introducing parameter ρ a As the CAV ratio of the traffic flow of arc segment a∈A, it is expressed as:

[0107]

[0108] in, is the CAV traffic flow of arc segment a∈A, is the traffic flow of travel mode m in arc segment a∈A;

[0109] S2.2: Introduce ε as the correction coefficient of the link impedance function, expressed as:

[0110]

[0111] Among them, γ, γ1, and γ2 are the headway coefficients of CAV-CAV, CAV-HV, and HV-CAV driving modes relative to HV-HV driving mode, respectively, and k2 is the size of the CAV fleet, as shown in Figure 3 As shown, in this example, γ=0.6, γ1=0.9, γ2=1.4, k2=4;

[0112] S2.3: Combined with the correction coefficient in step S2.2, the impedance function of the mixed traffic flow section in the BPR function form can be expressed as:

[0113]

[0114] in, Arc segment a 0 Free circulation time, Arc segment a 0 basic traffic capacity, and Arc segment a 0 CAV and HV traffic flows, and For arc segments CAV and HV traffic flows, Arc segment a 0the number of lanes, and α and β are parameters of the BPR function, and are impedance functions of arc segment a 0 and arc segment , respectively, and the present example is set as α = 0.15 and β = 4;

[0115] S3: Construct a travel cost function of CAV users and HV users, comprehensively considering the time value cost and fuel cost;

[0116] S3.1: The travel cost function includes the travel time cost and the fuel cost;

[0117]

[0118] wherein, Cm(a) represents the travel cost (unit: yuan) of travel mode m through arc segment a, VOT m is the time value of resident travel (unit: yuan / hour), t a is the travel time (unit: hour) of arc segment a, χ m is the fuel cost of travel mode m per unit distance (unit: yuan / km), L a is the length (unit: km) of arc segment a, and the present example is set as χ HV = 0.40 (yuan / km) and χ CAV = 0.35 (yuan / km);

[0119] S3.2: According to the travel cost function of each arc segment, the travel cost function of each path can be constructed;

[0120]

[0121] wherein, Cm(k) represents the cost required by travel mode m through path k of traffic origin-destination pair (r, s), K rs is the path set of (r, s), is a binary 0-1 variable representing the relationship between arc segment and path, represents that path k passes through arc segment a, represents that path k does not pass through arc segment a, r is the origin traffic zone, R is the set of origin traffic zones, s is the origin traffic zone, and S is the set of destination traffic zones.

[0122] S4: Construct a double-layer optimization model of intelligent network expansion network traffic carrying capacity, which includes an upper-layer optimization model and a lower-layer optimization model. The upper-layer optimization model aims to maximize the travel demand carried by the road network, and the lower-layer optimization model is a user equilibrium (UE) traffic distribution model aiming to minimize the cumulative value of the travel cost function integral; specifically as follows:

[0123] S4.1: Construct an upper-level optimization model for the two-level optimization model of the road network carrying capacity, with the goal of maximizing the travel demand that the road network can carry, under the constraint that the flow rate of each road section does not exceed the traffic capacity;

[0124]

[0125] Limited by

[0126]

[0127] in, represents the maximum traffic volume accommodated by the OD pair (r,s), Indicates all The vector matrix composed of Represents a vector matrix The elements and for Traffic flow of arc segment a under the scale, C a is the traffic capacity of arc segment a;

[0128] S4.2: Based on the User Equilibrium (UE) traffic assignment model, a lower-level optimization model of the two-level optimization model for the road network carrying capacity is constructed, whose objective function is to minimize the cumulative value of the integral of the travel cost function;

[0129]

[0130] Limited by

[0131]

[0132] in, is the traffic flow of travel mode m on OD pair (r, s) through path k, is the travel volume of mode m in the OD pair (r,s), is the traffic flow of mode m in arc a, v a is the traffic flow of arc segment a, Z is the objective function value, is the travel cost of travel mode m through arc segment a, ω is the traffic flow variable of the travel cost function of arc segment a;

[0133] S4.3: According to the UE conditions, when the urban traffic system reaches a steady state, the path flows of HVs and CAVs should meet the following constraints:

[0134]

[0135]

[0136] wherein, denotes the traffic flow of travel mode m on path k between O-D pair (r, s), denotes the travel cost of travel mode m on path k between O-D pair (r, s), u rs,m denotes the minimum travel cost of travel mode m between O-D pair (r, s);

[0137] S5: introducing the CAV special lane deployment constraint condition in the constructed double-layer optimization model of the traffic network carrying capacity, the CAV special lane deployment constraint condition including the CAV market share, the HV user potential unfair factor and the CAV special lane construction cost, forming the double-layer optimization model of the CAV special lane deployment strategy; the specific content is as follows:

[0138] S5.1: constructing the constraint condition of the CAV market share:

[0139]

[0140] wherein, and denote the CAV and HV traffic volume of O-D pair (r, s) respectively, and p denotes the market share of CAV;

[0141] S5.2: constructing the constraint condition of the HV user potential unfair factor

[0142]

[0143] wherein, denotes the travel cost of HV user through O-D pair (r, s) after deploying the CAV special lane, denotes the travel cost of HV user through O-D pair (r, s) without deploying the CAV special lane, and λ denotes the unfair influence degree of deploying the CAV special lane on the HV user, which is set as λ = 1.6 in the present example;

[0144] S5.3: constructing the constraint condition of the CAV special lane construction cost

[0145]

[0146] wherein, y a is a binary 0-1 variable indicating the condition of deploying the CAV special lane on arc segment a, y a = 1 indicates that the CAV special lane is deployed on the arc segment a, otherwise y a = 0, L a denotes the length (unit: km) of the arc segment a, and d denotes the unit mileage construction cost (unit: yuan / km) of the CAV special lane, represents the total budget cost of deploying CAV dedicated lanes (unit: yuan). In this example, d is set to 8.5×10 5 (Yuan / km), (Yuan),;

[0147] S6: By introducing sufficiently large values ​​and binary 0-1 variables, the nonlinear user equilibrium UE traffic assignment model is transformed into a linear user equilibrium UE traffic assignment model:

[0148]

[0149]

[0150] Among them, U is a sufficiently large value, is a binary 0-1 variable representing the relationship between path and travel mode, Indicates that the traffic flow of travel mode m on path k between OD pair (r, s) is non-zero, otherwise

[0151] S7: Linearize the nonlinear road impedance function to obtain a two-level optimization model for CAV lane deployment strategy in the form of mixed integer linear programming. This includes:

[0152] S7.1: Introducing the auxiliary variable w a and l a :

[0153]

[0154] Among them, w a The lower and upper bounds of the value range are w a =0 and is the basic traffic capacity of arc segment a∈A, is the HV traffic flow of arc segment a∈A;

[0155] S7.2: Using auxiliary variables and Convert the link impedance function into a univariate polynomial:

[0156]

[0157] S7.3: In the auxiliary variable w a The value range of Set N+1 breakpoints in the

[0158] Among them, the pth breakpoint is p∈P={1,2,...,N,N+1},

[0159] p is an integer, P is a set of integers, and N is any positive integer;

[0160] S7.4: Introducing variables Indicates a breakpoint The weight coefficient of The variable w in a Expressed as is the p+1th breakpoint, For breakpoints The weight coefficient of Figure 4 As shown, according to the partition linear approximation method, the following linearization constraints can be obtained:

[0161]

[0162]

[0163] in, Indicates l a The piecewise linear approximation of ;

[0164] S7.5: According to the SOS2 constraint (Special Order Set Type 2), there are at most two adjacent is an integer, and its constraints are expressed as:

[0165]

[0166] in, is a binary 0-1 variable, express otherwise

[0167] S7.6: Introducing the auxiliary variable ω a =l a y a , its value range is

[0168]

[0169] Linearize the product formula of continuous variables and binary variables to obtain the linear expression formula of the road section impedance function:

[0170]

[0171] At this point, the two-level optimization model of the CAV dedicated lane deployment strategy is reconstructed into a mixed integer linear programming.

[0172] S8: The CPLEX standard mathematical optimization solver is used to solve the mixed integer linear programming form of the CAV dedicated lane deployment strategy bi-level optimization model, and the design results of the CAV dedicated lane deployment strategy for the urban road network are obtained, such as Figure 5 shown.

[0173] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A two-layer optimization design method for CAV dedicated lane deployment strategy, characterized by: include: Build an intelligent connected expansion network including conventional lanes and alternative arc sections of CAV-dedicated lanes; Construct a road impedance function that takes into account the CAV ratio and headway parameters. The headway parameters include HV-HV, HV-CAV, CAV-CAV, and CAV-HV. HV-HV means that both the front and rear vehicles are HVs, HV-CAV means that the rear vehicle is an HV and the front vehicle is a CAV, CAV-CAV means that both the front and rear vehicles are CAVs, and CAV-HV means that the rear vehicle is a CAV and the front vehicle is an HV. Considering the time value cost and fuel cost, the travel cost function of CAV users and HV users is constructed; Construct a two-layer optimization model for the traffic carrying capacity of the intelligent connected network. The two-layer optimization model includes an upper optimization model and a lower optimization model. The upper optimization model aims to maximize the travel demand carried by the road network, while the lower optimization model is a user equilibrium UE traffic allocation model that aims to minimize the cumulative value of the integral of the travel cost function. The two-tier optimization model for road network carrying capacity was constructed by introducing CAV lane deployment constraints. These constraints included CAV market share, potential unfairness factors for HV users, and CAV lane construction costs, forming a two-tier optimization model for CAV lane deployment strategies. By introducing sufficiently large values ​​and binary 0-1 variables, the nonlinear user equilibrium UE traffic assignment model is transformed into a linear user equilibrium UE traffic assignment model; The nonlinear road impedance function is linearized to obtain a two-level optimization model for CAV lane deployment strategy in the form of mixed integer linear programming. A standard mathematical optimization solver was used to solve a two-level optimization model for CAV lane deployment strategy in the form of a mixed integer linear programming, and the design results of the CAV lane deployment strategy for the urban road network were obtained. Construct an intelligent connected extended network including conventional lanes and alternative arc sections of CAV-dedicated lanes; the details are as follows: Step S1.1: Define arc elements in the basic road network , is a set of arc elements, and the number of lanes in each arc is , the basic traffic capacity is , the free flow travel time is , mixed traffic includes two travel modes, CAV and HV, and mixed traffic is expressed as , M is the set of travel modes, and m is the element contained in M; Step S1.2: Arc element Expand an alternative arc section of the CAV dedicated lane , forming a set of candidate arc segments ; Step S1.3: For each Introducing 0-1 variables ,like Then the alternative arc section of the CAV dedicated lane Set as a CAV dedicated lane, otherwise the arc Not set up as a CAV-only lane; Step S1.4: A smart connected extended network is formed through steps S1.1 to S1.

3. All arcs belong to the smart connected extended network arc set A, which is expressed as: ； Where a represents all arcs in the intelligent connected extended network; Construct a road impedance function that takes into account the CAV ratio and headway parameters. The specific steps are as follows: Step S2.1: Introduce parameters Represents an arc segment CAV ratio of traffic flow, Expressed as: ； in, For arc segments CAV traffic flow, For arc segments Traffic flow of travel mode m; Step S2.2: Introduce the correction coefficient of the road section impedance function , expressed as: ； in, 、 、 are the headway coefficients of CAV-CAV, CAV-HV, and HV-CAV driving modes relative to HV-HV driving mode, is the size of the CAV fleet; Step S2.3: Combined with the correction coefficient in step S2.2, the impedance function of the mixed traffic flow section in the form of the Federal Highway Administration BPR function is: ； in, for Free circulation time, For arc segments basic traffic capacity, and Arc segments CAV and HV traffic flow, and For arc segments CAV and HV traffic flow, For arc segments The number of lanes, and is the parameter of the BPR function, and Arc segments and arc segments The impedance function.

2. A dual-layer optimization design method for CAV dedicated lane deployment strategy according to claim 1, characterized in that: Considering the time value cost and fuel cost, the travel cost functions of CAV users and HV users are constructed as follows: Step S3.1, the travel cost function includes travel time cost and fuel cost; ； in, represents the travel cost of travel mode m through arc a, is the value of residents’ travel time, is the travel time of arc segment a, is the fuel cost per unit distance traveled by mode m, is the length of arc segment a; Step S3.2: construct a travel cost function for each path based on the travel cost function of each arc segment; ； ； in, is the cost required for travel mode m to travel through path k of the origin and destination OD pair (r, s), is the path set of (r,s), It is a binary 0-1 variable representing the relationship between arc segments and paths. Indicates that path k passes through arc segment a, Indicates that path k does not pass through arc a, Starting point traffic area Gather at the starting point traffic area, For the starting point of the traffic zone, Gather at the terminal traffic area.

3. The dual-layer optimization design method for CAV dedicated lane deployment strategy according to claim 2 is characterized in that: A two-layer optimization model for the traffic carrying capacity of the intelligent connected network is constructed. The two-layer optimization model includes an upper optimization model and a lower optimization model. The upper optimization model aims to maximize the travel demand carried by the road network, while the lower optimization model is a user equilibrium UE traffic allocation model with the goal of minimizing the cumulative value of the integral of the travel cost function. The details are as follows: Step S4.1: Construct an upper-level optimization model of the two-level optimization model for the carrying capacity of the road network, with the goal of maximizing the travel demand carried by the road network under the constraint that the flow rate of each road section does not exceed the traffic capacity; ； Limited by ； in, represents the maximum traffic volume that the OD pair (r, s) can accommodate, Indicates all The vector matrix composed of Represents a vector matrix The elements and for Traffic flow of arc segment a under the scale, is the traffic capacity of arc segment a; Step S4.2: Based on the user equilibrium UE traffic assignment model, construct a lower-level optimization model of the two-level optimization model for the traffic network carrying capacity, whose objective function is to minimize the cumulative value of the integral of the travel cost function; ； Limited by ； ； ； ； ； in, is the traffic flow of mode m through path k on the OD pair (r, s), is the travel volume of mode m in the OD pair (r, s), is the traffic flow of mode m in arc a, is the traffic flow of arc a, is the objective function value, is the travel cost of travel mode m through arc a, is the traffic flow variable of the travel cost function of arc segment a; Step S4.3: Based on the UE conditions, when the urban traffic system reaches a stable state, the path flows of HVs and CAVs meet the following constraints: ； ； in, represents the traffic flow of travel mode m on path k between OD pair (r, s), represents the travel cost of travel mode m on path k between OD pair (r, s), It represents the minimum travel cost of travel mode m between the OD pair (r, s).

4. A dual-layer optimization design method for CAV dedicated lane deployment strategy according to claim 3, characterized in that: The two-tier optimization model for road network carrying capacity was constructed by introducing CAV lane deployment constraints. These constraints include CAV market share, potential unfairness factors for HV users, and CAV lane construction costs, forming a two-tier optimization model for CAV lane deployment strategies. The details are as follows: Step S5.1: Construct the constraints for CAV market share: ； in, and denote the CAV and HV travel volumes of the OD pair (r, s), Indicates the market share of CAV; Step S5.2: Construct constraints for potential unfairness factors for HV users: ； in, represents the travel cost of HV users passing the OD pair (r, s) after deploying CAV dedicated lanes, represents the travel cost of HV users passing the OD pair (r, s) when no CAV dedicated lane is deployed, Indicates the degree of unfair impact of deploying CAV-only lanes on HV users; Step S5.3: Constructing the cost constraints for CAV lane construction ； in, is a binary 0-1 variable, indicating the deployment of CAV dedicated lanes in arc a. Indicates that arc a is deployed with a CAV dedicated lane, otherwise , represents the length of arc segment a, represents the unit mileage construction cost of CAV dedicated lanes, represents the total budgeted cost of CAV dedicated lane deployment.

5. A dual-layer optimization design method for CAV dedicated lane deployment strategy according to claim 4, characterized in that: By introducing sufficiently large values ​​and binary 0-1 variables, the nonlinear user equilibrium UE traffic assignment model is transformed into a linear user equilibrium UE traffic assignment model; the details are as follows: ； ； ； ； ； in, is a sufficiently large value. is a binary 0-1 variable representing the relationship between path and travel mode, Indicates that the traffic flow of travel mode m on path k between OD pair (r, s) is non-zero, otherwise .

6. A dual-layer optimization design method for CAV dedicated lane deployment strategy according to claim 5, characterized in that: The nonlinear road impedance function is linearized to obtain a two-level optimization model for CAV lane deployment strategy in the form of mixed integer linear programming. The model includes: Step S7.1: Introduce auxiliary variables and : ； ； in, Lower bound of the value range and upper bound They are and , For arc segments basic traffic capacity, For arc segments HV traffic flow; Step S7.2: Using auxiliary variables and , convert the link impedance function into a univariate polynomial: ； Step S7.3, in the auxiliary variable The value range of Set N+1 breakpoints in the The pth breakpoint is , , , is an integer, is a set of integers, is any positive integer; Step S7.4: Introduce variables Indicates a breakpoint The weight coefficient of Variables within Expressed as , is the p+1th breakpoint, For breakpoints The weight coefficient of , according to the partition linear approximation method, obtains the following linear constraints: ； ； ； ； ； in, express The piecewise linear approximation of ; Step S7.5: According to the special order set second type SOS2 constraint, there are at most two adjacent is an integer, and its constraints are expressed as: ； ； ； ； in, is a binary 0-1 variable, express ,otherwise , 、 、 All are parameters; Step S7.6: Introduce auxiliary variables , its value range is: ； Linearize the product formula of continuous variables and binary variables to obtain the linear expression formula of the road section impedance function: ； At this point, the two-level optimization model of the CAV dedicated lane deployment strategy is reconstructed into a mixed integer linear programming.

Images