A path traffic flow induction method considering herding effect of travelers

Abstract

The application provides a path traffic flow induction method considering the herding effect of travelers. By selecting a plurality of paths as induction paths and providing path subsidy information to part of the travelers, the part of the travelers is attracted to select the induction paths for traveling, and the rest of the travelers are guided to select the induction paths under the influence of the herding effect. Therefore, the application constructs a bi-level programming model as a traffic flow regulation model, the upper model of which takes the minimum system total travel time cost and path subsidy cost as an objective function, and the lower model of which is a dynamic evolution model considering the herding effect under the given induction paths. The model is solved by a genetic algorithm, and example analysis shows that the model can effectively reduce the system total travel time cost of the whole network and relieve traffic congestion to a certain extent. Meanwhile, the existence of the herding effect can reduce the subsidy cost while reducing the system total travel time cost of the road network, and further improve the effect of the traffic flow regulation strategy based on the path subsidy.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of traffic flow induction methods, and particularly relates to a path traffic flow induction method considering the herding effect of travelers. BACKGROUND

[0002] In the past decade, the number of motor vehicles in China has been steadily increasing, and the huge number of motor vehicles has put great pressure on urban traffic in China. Urban traffic congestion has become a major problem that needs to be solved urgently. Traffic flow regulation strategies aim to optimize the spatio-temporal distribution of traffic flow on the road network, and through scientific and reasonable adjustment of traffic flow state, effectively alleviate traffic congestion, and thus become an important means to improve traffic conditions. In order to better develop traffic flow regulation strategies, residents can be induced to choose appropriate paths for travel, and the government can provide appropriate traffic subsidies. Traffic subsidies refer to any assistance or benefit subsidies provided by the government to certain enterprises, industries or individuals. Appropriate traffic subsidies can attract people to choose paths that are more beneficial to the entire traffic system, thereby alleviating traffic congestion problems. However, excessive traffic subsidies will put pressure on government finances, so the application considers further enhancing the effect of subsidies through the herding effect. The herding effect refers to the psychological change process in which people consciously or unconsciously take the opinions of the majority as the criterion for making judgments and forming impressions. In the field of transportation, the travel behavior of travelers is also influenced by the herding effect. Therefore, the government only needs to provide traffic subsidies to some travelers, and other travelers will choose paths that are more beneficial to the entire traffic system due to the herding effect, thereby reducing the total travel time cost of the road network system, alleviating traffic congestion, and reducing the cost of traffic subsidies.

[0003] For the field studied by the application, the problems and defects of the prior art are: at present, in the field of traffic science, the related research on the herding effect is mainly concentrated in the aspects of "dense crowd evacuation" and "pedestrian illegal crossing", and the influence of the herding effect on the path selection of travelers has not been systematically studied. In the aspect of traffic congestion charging and subsidy strategies, most researches are directed to traffic congestion charging, and there are few researches on subsidy strategies, and there are few researches on path subsidy mechanisms. Based on the above shortcomings, the application first studies to establish a traffic flow dynamic evolution model considering the herding effect, and on this basis, studies a traffic flow regulation strategy based on path subsidies, aiming to optimize the path flow distribution, realize the effective use of road resources in the traffic network, and alleviate traffic congestion. The application helps to provide important reference and guidance value for the government departments to scientifically and reasonably develop traffic flow regulation strategies. SUMMARY

[0004] To overcome the problems in the related art, the application provides a path traffic flow induction method considering the herding effect of travelers.

[0005] Technical scheme: the path traffic flow induction method of the application considering the herding effect of travelers includes the following steps:

[0006] The application assumes that the government provides path subsidy information for only part of the travelers in the traffic network. The government first selects several paths with potential to achieve system optimization as induction paths, and then publishes path subsidy information to part of the travelers through an information platform or the like. Under the incentive of the path subsidy information, a considerable part of the travelers will choose the induction paths. Under the influence of the herding effect, the remaining travelers will follow suit and choose the induction paths, so as to achieve the purpose of optimizing the flow distribution on the traffic network. It is worth pointing out that only the travelers who receive the path subsidy information will obtain the corresponding subsidies when they choose the induction paths to travel; the travelers who do not receive the path subsidy information will not obtain the subsidies even if they choose the induction paths. In this case, the government does not need to provide subsidies to all the travelers who choose the induction paths, and can achieve a good traffic flow regulation effect, thereby effectively reducing the path subsidy cost of the government.

[0007] Under the above assumption, step 1, according to the related theory of the Logit-type random user equilibrium model, the generalized travel impedance function considering the herding effect under the induction paths is defined under the condition that the travelers are simultaneously influenced by the herding effect and the path subsidy information; step 2, the traffic flow dynamic evolution model considering the herding effect under the induction paths is determined on the basis of the travel impedance function; step 3, the dynamic evolution model is taken as a lower model, and a traffic flow regulation bi-level programming model is established by taking the minimization of the total travel time cost and the path subsidy cost of the system as an objective function as an upper model; step 4, a genetic algorithm for solving the bi-level programming model is designed, and the above problem is quickly and accurately solved.

[0008] In step 1, according to the related theory of the Logit-type random user equilibrium model, the generalized travel impedance function considering the herding effect under the induction paths is defined under the condition that the travelers are simultaneously influenced by the herding effect and the path subsidy information.

[0009]

[0010] The generalized travel impedance function of the travelers who do not receive the path subsidy information is:

[0011]

[0012] wherein is the actual path travel time of the k+1 stage path r, r∈R w ,w∈W, is defined as the "attractiveness" of path r to travelers in the k+1th stage. β is an important parameter that relates the "attractiveness" of a path to the travel time. θ is a parameter greater than 0 that describes the familiarity of travelers with the road network and is inversely proportional to their familiarity with the road network. φ is an important parameter that converts the path subsidy into the generalized travel impedance of the path. ρ rw is a relation variable. If the path r between OD pairs w∈W is an induced path, then ρ rw is 1, otherwise it is 0, χ is the unit subsidy standard of the induced path, L rw is the path length of the path r between the OD pair w∈W, ε rw is a random term in the utility function;

[0013] It is easy to know that this problem is a convex programming problem. According to the relevant theory of the Logit model, the optimal solution of the problem (f 1,rw ,f 2,rw ) is unique; therefore, if the travelers in stage k+1 choose the path with the minimum generalized travel impedance according to the travel impedance function defined above, the traffic flow solution when the system reaches a stable state at the end of this stage is the minimum point of the model.

[0014] In step 2, specifically: determine the traffic flow dynamic evolution model considering the herd effect under the induced path;

[0015] According to the travel impedance function determined in claim 2, the dynamic evolution process and dynamic evolution model of traffic flow can be further derived.

[0016] The specific expression for the dynamic evolution process framework of traffic flow considering the herd effect under the induced path can be simplified as follows:

[0017]

[0018] Where Ω is:

[0019]

[0020] in, and They represent the path flow of travelers who receive path subsidy information and travelers who do not receive path subsidy information when the system reaches a steady state at the end of the k+1th stage, f is the path flow, f∈Ω, f 1,rw and f 2,rw They represent the path flows of travelers who receive and do not receive path subsidy information when the system reaches a steady state at the end of the k+1th stage, A is the set of road segments, a∈A, W is the set of OD pairs generated by travel demand between OD pairs, w∈W, R w is the set of feasible paths between OD pairs w, r∈Rw , x a is the traffic flow on link a, t a is the travel impedance of link a, δ arw is the relationship variable, if link a is on path r between OD pair w, then δ arw is 1, otherwise 0, ψ is the proportion of travelers who receive path subsidy information, q w is the travel demand between OD pair w e W.

[0021] Step 3 is specifically: constructing a traffic flow regulation bi-level programming model considering herding effect under induced route;

[0022] The traffic flow regulation bi-level programming model considering herding effect under induced route is constructed, and the proportion of travelers who receive path subsidy information (referred to as subsidy proportion) and path subsidy standard are optimized, so as to achieve better traffic flow regulation effect and smaller path subsidy cost;

[0023] The lower model of the traffic flow regulation bi-level programming model is the evolution model of traffic flow following the dynamic evolution law of traffic flow under herding effect (i.e. the model constructed in step 2); the upper model of the traffic flow regulation bi-level programming model takes the minimization of the total travel time cost and path subsidy cost of the system as the objective function, and the cost is calculated based on the dynamic evolution result of the traffic flow of the lower model, and the path subsidy cost budget constraint of the government is considered to ensure that the path subsidy cost is lower than the path subsidy cost budget of the government;

[0024] The upper model is:

[0025] The objective function of the upper model is composed of two parts, the first part is the total travel time cost of the system, which is defined as the sum of the path flow of all paths multiplied by the path impedance; the second part is the path subsidy cost, and the path subsidy cost budget constraint of the government is considered to ensure that the path subsidy cost is lower than the path subsidy cost budget of the government; in summary, the upper model of the traffic flow regulation bi-level programming model can be represented by the following formula:

[0026]

[0027] The constraint conditions are:

[0028]

[0029] Where f 1,rw and f 2,rw are the path flows of travelers who receive path subsidy information and travelers who do not receive path subsidy information respectively under the traffic flow regulation strategy of the upper model, when the lower model, i.e. the dynamic evolution model of traffic flow considering herding effect under induced route, finally reaches a steady state, λ is an important parameter for converting path subsidy cost into time cost, and ρrw is a relation variable. If the path r between OD pairs w∈W is an induced path, then ρ rw =1, otherwise 0, χ is the path unit subsidy standard, its unit is χ yuan / km, D is the upper limit of the path subsidy cost; Formula (6) represents the constraint of the path subsidy cost, ensuring that the path subsidy cost is lower than the government's path subsidy cost budget; Formula (7) indicates that the time equivalent cost of the path subsidy on any path is not greater than the travel time of the path;

[0030] Lower model:

[0031] The lower model is a traffic flow dynamic evolution model that considers the herd effect under a given induced path; where (f1, f2) is the path flow obtained after the following traffic flow dynamic evolution model evolves over a period of time:

[0032]

[0033] in

[0034]

[0035] Where ψ is the proportion of travelers who receive path subsidy information, that is, the subsidy ratio, q w is the traffic demand between OD pairs w∈W;

[0036] In summary, the traffic flow control strategy considering the herd effect under the inductive path in the present invention is to solve a two-level programming problem in which the upper-level objective is Equation (6) and the lower-level model is a traffic flow dynamic evolution model considering the herd effect under the inductive path.

[0037] Step 4 is specifically as follows: solving the bi-level programming model of traffic flow control considering the herd effect under the induced path;

[0038] A genetic algorithm is used to solve the bi-level programming model for traffic flow control under induced paths (i.e., the model constructed in step 2) with the herd effect. This algorithm can improve the convergence efficiency of the algorithm iteration and solve the above problem quickly and accurately. The specific steps are as follows:

[0039] Step 4-1: Perform double-layer coding on the traffic flow control problem considering the herd effect under the induced path and generate an initial population to form an initial traffic flow induction scheme candidate set;

[0040] The genetic algorithm maps the solution of the optimization problem to the individual of the iterative search by the gene coding; the chromosome is double coded according to the specific conditions of the constructed traffic flow regulation bi-level programming model, each layer respectively represents the path unit subsidy standard and the proportion of travelers receiving path subsidy information; in order to facilitate the design of genetic operations such as crossover and mutation, the relevant real numbers are represented by binary sequence, and all genotypes are composed of binary symbol set {0, 1}; taking the path unit subsidy standard as an example, the solution space of the actual problem is denoted as [a, b], the chromosome length is set as N, and the search space is {0, 1, 2 N -1}; if the binary gene sequence is converted into a decimal number n, then the path unit subsidy standard represented by the decoded n is The proportion of travelers receiving path subsidy information is the same;

[0041] Taking the population size as g, the initial population is generated according to the value range of the path unit subsidy standard and the proportion of travelers receiving path subsidy information (i.e. the subsidy proportion), the selection crossover probability P c and the genetic mutation probability P m of the genetic algorithm are set, and the maximum iteration number Maxgen is set;

[0042] Step 4-2: the chromosome is passed to the lower model;

[0043] The path unit subsidy standard and the proportion of travelers receiving path subsidy information (i.e. the subsidy proportion) represented by the chromosome in the population are extracted, and the solution of the traffic flow dynamic evolution model considering the herding effect under the current path unit subsidy standard and the subsidy proportion is solved, i.e. the path flow solution of the two types of travelers;

[0044] Step 4-3: the traffic flow evolution result of the lower model is fed back to the upper model;

[0045] Step 4-4: the fitness function value is calculated according to the traffic flow dynamic evolution result of the lower model;

[0046] The objective function of the upper model of the traffic flow regulation bi-level programming model considering the herding effect under the induced path is to minimize the sum of the total travel time cost and the total path subsidy cost; it is easy to know that the value of the objective function is always positive, so the reciprocal of the value of the objective function can be mapped to the fitness value, the smaller the value of the objective function, the greater the fitness value; at the same time, in order to ensure that the path subsidy cost is lower than a certain value, when the path subsidy cost is higher than a certain value, the penalty function is added to make the fitness value smaller; according to the principle of genetic algorithm, the individual with greater fitness value is more likely to be selected as the parent to be inherited to the next generation, and vice versa, the individual with smaller fitness value will be gradually eliminated with the continuous evolution and development of the population; the fitness function Fit is shown in formula (10):

[0047]

[0048] wherein F is a penalty function, flag is a relationship variable, if the path subsidy cost is greater than D, then flag is 1, otherwise flag is 0;

[0049] Step 4-5: Roulette wheel selection strategy;

[0050] The roulette wheel selection strategy is used to screen the relatively excellent individuals in the population to form a new population;

[0051] According to the individual fitness value calculated in the above formula, the selection probability of the individual in the population with a size of g is further determined, and the calculation formula is:

[0052]

[0053] wherein P i is the selection probability of the individual in the population, and Fit i is the fitness value of the individual in the population;

[0054] The cumulative probability Q i of the individual in the population is calculated, and the calculation formula is:

[0055]

[0056] g uniform distribution random numbers ζ in [0,1] are generated, if Q i ≤ζ≤Q i+1 , then the individual i is selected;

[0057] Step 4-6: crossover operation;

[0058] The two-point crossover method is used, and two crossover points are randomly set in the two chromosome coding strings of the parent population matched with each other with a certain crossover probability P c , and the parts of the two chromosomes between the two set crossover points are exchanged;

[0059] Step 4-7: genetic mutation operation;

[0060] The basic bit mutation method is used, and a random number r∈[0,1] is generated in the chromosome of each offspring in the crossover offspring set with a certain mutation probability P m , if r≤P m , then the value of the first or several bits on the chromosome is randomly mutated, for the individual represented by the binary coded symbol string in this chapter, if the gene value to be mutated is 0, the mutation operation changes it to 1; otherwise, if the original gene value is 1, the mutation operation changes it to 0;

[0061] Repeat steps 4-2 to 4-7 until the genetic algorithm runs the number of iterations reaches the maximum number of iterations Maxgen set, stop running and output the optimal path unit subsidy standard and the optimal subsidy ratio.

[0062] In summary, the present application proposes a path traffic flow induction method considering the herding effect of travelers, and constructs a traffic flow regulation bi-level programming model. The model selects several paths as induction paths, and attracts a part of travelers to select the induction paths by providing path subsidy information to them, and guides the remaining travelers to select the induction paths under the influence of the herding effect. The bi-level programming model has an upper model taking the minimization of the system total travel time cost and the path subsidy cost as the objective function, and a lower model being a dynamic evolution model considering the herding effect under the given induction paths. The genetic algorithm is used to solve the model, and the result shows that the traffic flow regulation model considering the herding effect can effectively reduce the system total travel time cost of the whole network, and relieve traffic congestion to a certain extent. Meanwhile, the existence of the herding effect can reduce the subsidy cost while reducing the system total travel time cost of the road network, and further improve the effect of the traffic flow regulation strategy based on path subsidy.

[0063] Advantages: Compared with the prior art, the present application has the following remarkable advantages:

[0064] (1) The present application points out that the herding psychology of travelers in the traffic network can guide the travelers to tend to select the paths selected by the majority of people by studying the influence of the herding effect on the path selection of travelers, and finds that the existence of the herding effect can further improve the effect of path subsidy.

[0065] (2) The traditional traffic charging / subsidy strategy is usually a path charging / subsidy strategy, and the present application proposes a traffic flow regulation strategy based on path subsidy under the herding effect by using the finding that the herding effect can further enhance the effect of path subsidy, and discusses the rationality and feasibility of the strategy.

[0066] (3) The present application establishes a traffic flow regulation bi-level programming model considering the herding effect under the induction paths. The model attracts a part of travelers to select the induction paths by providing path subsidy information to them, and guides the remaining travelers to select the induction paths under the influence of the herding effect, so as to realize the traffic flow regulation effect while reducing the path subsidy cost. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 A flow chart of the path traffic flow induction method considering the herding effect of travelers provided by the present application is shown in the figure;

[0068] Figure 2The genetic algorithm solving flow chart of the traffic flow regulation double-layer planning model of the path under the influence of the herding effect provided by the application is shown in the figure;

[0069] Figure 3 The 9-node road network model schematic diagram in the embodiment 1 of the application is shown in the figure;

[0070] Figure 4 The genetic algorithm optimal objective function value iteration process schematic diagram is shown in the figure;

[0071] Figure 5 The relationship between the system total travel time cost, the path subsidy cost and λ is shown in the figure. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the application. Obviously, the described embodiments are only used as examples, and are not used to limit the application.

[0073] The path traffic flow induction method provided by the application considering the herding effect of travelers is shown in the figure, and includes the following steps: Figure 1

[0074] The application assumes that the government only provides path subsidy information for part of the travelers in the traffic network. The government first selects several paths with potential to achieve system optimization as induction paths, and then publishes path subsidy information to part of the travelers through an information platform or the like. Under the incentive of the path subsidy information, a considerable part of the part of the travelers will choose the induction paths. Under the influence of the herding effect, the remaining travelers will follow suit and choose the induction paths, so as to achieve the purpose of optimizing the flow distribution on the traffic network. It is worth pointing out that only the travelers receiving the path subsidy information choose the induction paths to travel, and can obtain the corresponding subsidies; the travelers not receiving the path subsidy information will not obtain the subsidies even if they choose the induction paths. In this case, the government does not need to provide subsidies to all the travelers choosing the induction paths, and can achieve a good traffic flow regulation effect, thereby effectively reducing the path subsidy cost of the government.

[0075] Given a traffic network G(N,A), wherein N is defined as the set of nodes in the network, A is defined as the set of directed arcs (i.e. road segments) in the network, and W represents the set of OD pairs (Origin and Destination, OD points for short) generated by travel demand between OD pairs.

[0076] Step 1: define the generalized travel impedance function under the influence of the herding effect.

[0077] ​According to the related theory of classical Logit-type random user equilibrium model, the generalized travel impedance function of the traveler under the double influence of conformity effect and path subsidy information is defined as:

[0078]

[0079] The generalized travel impedance function of the traveler without receiving path subsidy information is:

[0080]

[0081] Wherein is the actual path travel time of the k+1 stage path r (r∈R w ,w∈W), is defined as the “attractiveness” of the k+1 stage path r to the traveler, β is an important parameter relating the path “attractiveness” and path travel time, θ is a parameter greater than 0, which is used to describe the familiarity of the traveler to the road network, and is inversely proportional to the familiarity of the traveler to the road network, φ is an important parameter of converting path subsidy into path generalized travel impedance, ρ rw is a relational variable, if the path r between OD pair w∈W is an induced path, then ρ rw is 1, otherwise 0, χ is the unit subsidy standard of the induced path, L rw is the path length of the path r between OD pair w∈W, and ε rw is a random term in the utility function.

[0082] It is known that the problem is a convex programming problem, and according to the related theory of Logit model, the optimal solution (f 1,rw ,f 2,rw ) is unique. Therefore, if the k+1 stage traveler selects the path with the minimum generalized travel impedance according to the travel impedance function defined above, the traffic flow solution when the system reaches a stable state at the end of the stage is the minimum point of the model.

[0083] Step 2: Determine the traffic flow dynamic evolution model considering conformity effect under induced path.

[0084] According to the travel impedance function determined in step 1, the traffic flow dynamic evolution process and dynamic evolution model can be further derived. The specific expression of the traffic flow dynamic evolution process framework considering conformity effect under induced path defined by the application can be simplified as:

[0085]

[0086] Wherein Ω is:

[0087]

[0088] where, and respectively represent the path flow of the traveler who receives the path subsidy information and the path flow of the traveler who does not receive the path subsidy information at the end of the k+1 stage when the system reaches steady state, f is the path flow, f [Omega], f 1,rw and f 2,rw respectively represent the path flow of the traveler who receives the path subsidy information and the path flow of the traveler who does not receive the path subsidy information at the end of the k+1 stage when the system reaches steady state, A is the link set, a [A], W is the OD pair set generated by the travel demand between the OD pairs, w [W], R w is the feasible path set between the OD pair w, r [R w , x a is the traffic flow on the link a, t a is the travel impedance of the link a, [delta] arw is the relationship variable, if the link a is in the path r between the OD pair w, [delta] arw is 1, otherwise 0, [psi] is the proportion of the traveler who receives the path subsidy information, q w is the travel demand between the OD pairs w [W].

[0089] Step 3: Construct the traffic flow regulation bi-level programming model considering the conformity effect under the induced path.

[0090] The application constructs the traffic flow regulation bi-level programming model considering the conformity effect under the induced path, and optimizes the proportion of the traveler who receives the path subsidy information (referred to as the subsidy proportion) and the path subsidy standard, so as to achieve better traffic flow regulation effect and smaller path subsidy cost.

[0091] The lower model of the traffic flow regulation bi-level programming model is the evolution model of the traffic flow following the dynamic evolution law of the traffic flow under the conformity effect (i.e. the model constructed in step 2). The upper model of the traffic flow regulation bi-level programming model takes the minimization of the total travel time cost and the path subsidy cost of the system as the objective function, and the cost is calculated based on the dynamic evolution result of the traffic flow of the lower model, and the path subsidy cost budget constraint of the government is considered, so as to ensure that the path subsidy cost is lower than the path subsidy cost budget of the government.

[0092] The upper model:

[0093] The objective function of the upper model is composed of two parts, the first part is the total travel time cost of the system, which is defined as the sum of the path impedance of all the path flows here, and the second part is the path subsidy cost, and the path subsidy cost budget constraint of the government is considered, so as to ensure that the path subsidy cost is lower than the path subsidy cost budget of the government. In summary, the upper model of the traffic flow regulation bi-level programming model can be represented by the following formula:

[0094]

[0095] The constraint condition is:

[0096]

[0097] Wherein f 1,rw And f 2,rw Respectively, under the traffic flow regulation strategy of the upper model, the path flow of the traveler receiving path subsidy information and the traveler not receiving path subsidy information when the lower model, i.e. the traffic flow dynamic evolution model considering the conformity effect under induced path, finally reaches a steady state, λ is an important parameter for converting path subsidy cost into time cost, ρ rw Is a relational variable, if the path r between OD pair w is an induced path, then ρ rw Is 1, otherwise 0, χ is the path unit subsidy standard, the unit is χ yuan / km, D is the upper limit of path subsidy cost. Equation (6) represents the constraint of path subsidy cost, which ensures that the path subsidy cost is lower than the path subsidy cost budget of the government; equation (7) represents that the time equivalent cost of path subsidy on any path is not greater than the travel time of the path.

[0098] Lower model:

[0099] The lower model is a traffic flow dynamic evolution model considering the conformity effect under induced path. Wherein (f1, f2) is the path flow obtained after a period of evolution of the following traffic flow dynamic evolution model:

[0100]

[0101] Wherein

[0102]

[0103] Wherein ψ is the proportion of travelers receiving path subsidy information, i.e. the subsidy proportion, q w Is the traffic demand between OD pair w.

[0104] In summary, the traffic flow regulation strategy considering the conformity effect under induced path in the application is to solve the bi-level programming problem meeting the upper target of equation (6) and the lower model of the traffic flow dynamic evolution model considering the conformity effect under induced path.

[0105] Step 4: realize the solution of the traffic flow regulation bi-level programming model considering the conformity effect under induced path.

[0106] The application proposes a genetic algorithm for solving the traffic flow regulation bi-level programming model considering the conformity effect under induced path. The algorithm can improve the convergence efficiency of algorithm iteration, and quickly and accurately solve the above problem.

[0107] The genetic algorithm used in the present application solves the flowchart as shown in the figure, and the specific steps are as follows: Figure 2

[0108] Step 4-1: Double-layer coding is performed on the traffic flow regulation problem considering the herding effect under the induced path, and an initial population is generated to form an initial traffic flow induced scheme candidate set;

[0109] The genetic algorithm maps the solution of the optimization problem to the individual of iterative search through gene coding. In combination with the specific circumstances of the constructed double-layer planning model of traffic flow regulation (i.e. the model constructed in step 2), the chromosome is double-layer coded, and each layer represents the path unit subsidy standard and the proportion of travelers receiving path subsidy information. In order to facilitate the design of genetic operations such as crossover and mutation, a binary sequence is used to represent the relevant real numbers, and all genotypes are composed of a binary symbol set {0, 1}. Taking the path unit subsidy standard as an example, the solution space of the actual problem is denoted as [a, b], the chromosome length is set to N, and the search space is {0, 1, 2 N -1}. If the binary gene sequence is converted to a decimal number n, then the path unit subsidy standard represented by its decoding is The proportion of travelers receiving path subsidy information is the same.

[0110] Taking the population size as g, the initial population is generated according to the value range of the path unit subsidy standard and the proportion of travelers receiving path subsidy information (i.e. the subsidy ratio), the selection crossover probability P c and the genetic mutation probability P m of the genetic algorithm are set, and the maximum iteration number Maxgen is set.

[0111] Step 4-2: The chromosome is passed to the lower model;

[0112] The path unit subsidy standard and the proportion of travelers receiving path subsidy information (i.e. the subsidy ratio) represented by the chromosome in the population are extracted, and the solution of the traffic flow dynamic evolution model considering the herding effect under the current path unit subsidy standard and the subsidy ratio is solved, i.e. the path flow solution of the two types of travelers when the final steady state is reached.

[0113] Step 4-3: The traffic flow evolution result of the lower model is fed back to the upper model;

[0114] Step 4-4: Calculate the fitness function value according to the traffic flow dynamic evolution result of the lower model;

[0115] ​The objective function of the upper model of the traffic flow regulation bi-level programming model considering the herding effect in the induced route is to minimize the sum of the total travel time cost and the total route subsidy cost of the system. It is easy to know that the value of the objective function is always positive, so the reciprocal of the value of the objective function can be mapped as the fitness value, and the smaller the value of the objective function is, the greater the fitness value is. At the same time, in order to ensure that the route subsidy cost is lower than a certain value, when the route subsidy cost is higher than a certain value, a penalty function is added to make the fitness value smaller. According to the principle of genetic algorithm, the individual with greater fitness value is selected as the parent to be inherited to the next generation, and vice versa, the individual with smaller fitness value will be gradually eliminated with the continuous evolution and development of the population. The fitness function Fit is shown in formula (10):

[0116]

[0117] Wherein, F is a penalty function, flag is a relationship variable, if the route subsidy cost is greater than D, then flag is 1, otherwise flag is 0.

[0118] Step 4-5: roulette wheel selection strategy.

[0119] The roulette wheel selection strategy is adopted to screen the relatively excellent individuals in the population to form a new population.

[0120] According to the fitness value of the individual calculated in the above formula, the selection probability of the individual in the population with a size of g is further determined, and the calculation formula is:

[0121]

[0122] Wherein, P i is the selection probability of the individual in the population, and Fit i is the fitness value of the individual in the population.

[0123] The cumulative probability Q i of the individual in the population is calculated, and the calculation formula is:

[0124]

[0125] g uniform distribution random numbers ζ in [0, 1] are generated, if Q i ≤ζ≤Q i+1 , then the individual i is selected.

[0126] Step 4-6: crossover operation.

[0127] The two-point crossover method is adopted, and two crossover points are randomly set in the two chromosome coding strings of the parent population with a certain crossover probability P c , and the parts of the two chromosomes between the two set crossover points are exchanged.

[0128] Steps 4-7: Genetic variation operation.

[0129] Using the basic bit mutation method, with a certain mutation probability P m , generate a random number r∈[0,1] in the chromosome of each offspring in the crossover offspring set, if r≤P m , then randomly mutate the value of the number or some bits on the chromosome. For the individuals represented by binary coded symbol strings in this chapter, if the value of a gene to be mutated is 0, the mutation operation will change it to 1; conversely, if the original gene value is 1, the mutation operation will change it to 0.

[0130] Repeat steps 4-2 to 4-7 until the number of iterations of the genetic algorithm reaches the set maximum number of iterations Maxgen, then stop running and output the optimal path unit subsidy standard and optimal subsidy ratio.

[0131] Example 1:

[0132] The present invention adopts Figure 3 A 9-node road network is given as the research object to verify the traffic flow control double-level programming model considering the herd effect under a given induction path constructed by the present invention and the designed genetic algorithm. Figure 3 This is a small transportation network consisting of 9 nodes, 18 road sections and 96 paths. The traffic capacity between each road section is shown in the figure.

[0133] In a 9-node traffic network, there are four OD pairs: (1,3), (1,4), (2,3), and (2,4). The traffic demands for each OD pair are 10, 30, 20, and 40, respectively. There are 96 valid paths in the network, 24 of which are valid for each OD pair. The segment travel time function follows the BPR form.

[0134] The present invention runs a genetic algorithm solution code written in Matlab on a personal computer with an Intel Core i5 CPU @ 3.6GHz and 16GB of RAM to obtain the optimal path unit subsidy standard and the proportion of travelers who receive path subsidy information (i.e., subsidy ratio) corresponding to the optimal solution. The number of categories is set to 20 and the maximum number of iterations is set to 200. The penalty coefficient F is set to 10 -10 , the crossover probability is 0.8, and the mutation probability is 0.05. Take λ = 0.001 and φ = 0.1 as an example to solve the solution of the bilevel programming model.

[0135] The relationship between the objective function value and the number of iterations is as follows: Figure 4The target function value is constantly reduced with the increase of iteration number, and converges to the optimal solution at about 65 generations. In general, the genetic algorithm converges faster and the optimization effect is better. The optimal path unit subsidy standard is 2.252 yuan / km, and the subsidy ratio is 81.89%. The subsidy costs of the induced paths are shown in Table 1. The relationship between the total travel time cost, the path subsidy cost and lambda is shown in Figure 2. Figure 5

[0136] Table 1 Subsidy costs of induced paths

[0137]

[0138]

[0139] The results of Example 1 show that when the traffic network reaches a steady state, the system total travel time cost under the traffic flow regulation model considering the herding effect under the given induced path is reduced by 15.18% compared with the system total travel time cost under the random user equilibrium state under the same conditions, which shows that the model can effectively reduce the system total travel time cost of the entire traffic network and alleviate traffic congestion to a certain extent. Compared with the traffic flow regulation model not considering the herding effect under the given induced path, the system total travel time cost under the traffic flow regulation model considering the herding effect under the given induced path is reduced by 0.79% when the traffic network reaches a steady state, and the path subsidy cost is reduced by 5.22%. This shows that the existence of the herding effect can reduce the path subsidy cost while reducing the system total travel time cost of the road network, and further improve the effect of the traffic flow regulation strategy based on path subsidy.

[0140] In summary, the traffic flow regulation method considering the herding effect under the given induced path proposed by the present application is verified to be feasible and operable through example verification analysis, and has important significance.

[0141] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or replacements within the technical range disclosed by the present application can be easily thought by those skilled in the art, and should be covered within the protection scope of the present application.​

Claims

1.A path traffic flow induction method considering a herding effect of travelers, characterized by, Comprising the following steps: Assuming that the government only provides path subsidy information for part of the travelers in the traffic network; the government first selects several paths with potential to achieve system optimization as induced paths, and then publishes path subsidy information to part of the travelers through an information platform or the like; under the incentive of the path subsidy information, a considerable part of the travelers will choose the induced paths; under the influence of the herding effect, the remaining travelers will follow suit and choose the induced paths, so as to achieve the purpose of optimizing the traffic flow distribution on the traffic network; Under the above assumption, step 1, according to the related theory of the Logit-type random user equilibrium model, the generalized travel impedance function considering the herding effect under the induced path is defined under the condition that the travelers are simultaneously affected by the herding effect and the path subsidy information; step 2, on the basis of the travel impedance function, the traffic flow dynamic evolution model considering the herding effect under the induced path is determined; step 3, the dynamic evolution model is taken as the lower model, and a traffic flow regulation bi-level programming model is established by taking the minimization of the system total travel time cost and the path subsidy cost as the objective function of the upper model; step 4, a genetic algorithm for solving the bi-level programming model is designed, and the above problem is quickly and accurately solved; In step 1, according to the related theory of the Logit-type random user equilibrium model, the generalized travel impedance function considering the herding effect under the induced path is defined under the condition that the travelers are simultaneously affected by the herding effect and the path subsidy information: The generalized travel impedance function of the travelers who do not receive the path subsidy information is: wherein is the actual path travel time of the k+1th stage path r, r e R w , w e W, is defined as the "attractiveness" of the k+1th stage path r to the traveler, β is an important parameter relating the path "attractiveness" to the path travel time, θ is a parameter greater than 0, which is used to describe the familiarity of the traveler to the road network, and is inversely proportional to the familiarity of the traveler to the road network, φ is an important parameter for converting the path subsidy into the path generalized travel impedance, ρ rw is a relationship variable, if the path r between the OD pair w e W is an induced path, then ρ rw is 1, otherwise it is 0, χ is the unit subsidy standard of the induced path, L rw is the path length of the path r between the OD pair w e W, ε rw is the random term in the utility function; It is easy to know that this problem is a convex programming problem, and according to the relevant theory of Logit model, the optimal solution (f 1,rw ,f 2,rw ) is unique; therefore, if the traveler in the k+1 stage selects the path with the minimum generalized travel impedance according to the travel impedance function defined above, the traffic flow solution at the stable state of the system at the end of the stage is the minimum point of the model. In step 2, the traffic flow dynamic evolution model considering the herding effect under the induced path is determined. The travel impedance function can further deduce the traffic flow dynamic evolution process and the dynamic evolution model; The specific expression of the traffic flow dynamic evolution process framework considering the herding effect under the induced path can be simplified as: Wherein Ω is: where, and respectively represent the path flow of travelers who received path subsidy information and the path flow of travelers who did not receive path subsidy information at the end of the k+1th stage when the system reaches steady state, f is the path flow, f ∈ Ω, f 1,rw and f 2,rw respectively represent the path flow of travelers who received path subsidy information and the path flow of travelers who did not receive path subsidy information at the end of the k+1th stage when the system reaches steady state, A is the link set, a ∈ A, W is the OD pair set generated by travel demand between OD pairs, w ∈ W, R w is the feasible path set between OD pairs w, r ∈ R w , x a is the traffic flow on link a, t a is the travel impedance of link a, δ arw is a relational variable, if link a is in path r between OD pair w, then δ arw is 1, otherwise 0, ψ is the proportion of travelers who received path subsidy information, q w is the travel demand between OD pairs w ∈ W. 2.The route traffic flow induction method considering the herding effect of travelers according to claim 1, wherein, In step 3, the traffic flow regulation bi-level programming model considering the herding effect under the induced path is constructed. The traffic flow regulation bi-level programming model considering the herding effect under the induced path is constructed, and the proportion of the travelers who receive the path subsidy information and the path subsidy standard are optimized, so as to achieve better traffic flow regulation effect while the path subsidy cost is smaller; The lower model of the traffic flow regulation bi-level programming model is the evolution model of the traffic flow following the traffic flow dynamic evolution law under the herding effect; the upper model of the traffic flow regulation bi-level programming model takes the minimization of the system total travel time cost and the path subsidy cost as the objective function, and the cost is calculated based on the traffic flow dynamic evolution result of the lower model, and the path subsidy cost budget of the government is considered, so as to ensure that the path subsidy cost is lower than the path subsidy cost budget of the government; The upper model is: The objective function of the upper model is composed of two terms, the first term is the total travel time cost of the system, which is defined as the sum of all path flows multiplied by path impedance here, and the second term is the path subsidy cost, which needs to consider the government's path subsidy cost budget constraint to ensure that the path subsidy cost is lower than the government's path subsidy cost budget; in summary, the upper model of the traffic flow regulation bi-level programming model can be expressed as follows: The constraint condition is: where f 1,rw and f 2,rw They are the path flows of travelers who receive and do not receive path subsidy information under the traffic flow control strategy of the upper model and the dynamic evolution model of traffic flow considering the herd effect under the induced path when the lower model finally reaches a steady state. λ is an important parameter for converting path subsidy cost into time cost, and ρ rw is a relation variable. If the path r between OD pairs w∈W is an induced path, then ρ rw =1, otherwise 0, χ is the path unit subsidy standard, its unit is χ yuan / km, D is the upper limit of the path subsidy cost; Formula (6) represents the constraint of the path subsidy cost, ensuring that the path subsidy cost is lower than the government's path subsidy cost budget; Formula (7) indicates that the time equivalent cost of the path subsidy on any path is not greater than the travel time of the path; The lower model is: The lower model is a traffic flow dynamic evolution model considering conformity effect under given induced path; wherein (f1, f2) is the path flow obtained after a period of evolution of the following traffic flow dynamic evolution model: Wherein where ψ is the proportion of travelers receiving the path subsidy information, i.e., the subsidy proportion, q w is the traffic demand between OD pairs w e W; In summary, the traffic flow regulation strategy considering conformity effect under induced path in the application is to solve the bi-level programming problem that the upper objective is formula (6) and the lower model is the traffic flow dynamic evolution model considering conformity effect under induced path. 3.The route traffic flow induction method considering the herding effect of travelers according to claim 2, wherein, Step 4 is specifically: realizing the solution of the traffic flow regulation bi-level programming model considering conformity effect under induced path; The genetic algorithm for solving the traffic flow regulation bi-level programming model considering conformity effect under induced path; the algorithm can improve the convergence efficiency of algorithm iteration, and quickly and accurately solve the above problem, and the specific steps are as follows: Step 4-1: double-layer coding is performed on the traffic flow regulation problem considering conformity effect under induced path, and an initial population is generated to form an initial traffic flow induction scheme candidate set; Genetic algorithm maps the solution of optimization problem to the individual of iterative search by gene coding. According to the specific situation of the constructed traffic flow regulation bi-level programming model, double coding is used for chromosome, each layer represents path unit subsidy standard and the proportion of travelers receiving path subsidy information respectively. In order to facilitate the design of genetic operations such as crossover and mutation, binary sequence is used to represent the related real number, and all genotypes are composed of binary symbol set {0, 1}. Taking path unit subsidy standard as an example, the solution space of actual problem is denoted as [a, b], the chromosome length is set as N, and the search space is {0, 1, 2…, 2 N -1}. If the binary gene sequence is converted into a decimal number n, then the path unit subsidy standard represented after decoding is The proportion of travelers receiving path subsidy information is also the same. Taking the population size as g, generating the initial population according to the value range of the path unit subsidy standard and the proportion of the travelers receiving the path subsidy information, setting the selection crossover probability P of the genetic algorithm c and the genetic mutation probability P m , and setting the maximum iteration number Maxgen; Step 4-2: the chromosome is transmitted to the lower model; The path unit subsidy standard and the proportion of travelers receiving path subsidy information represented by the chromosome in the population are extracted, and the solution of the traffic flow dynamic evolution model considering conformity effect under the current path unit subsidy standard and subsidy ratio is solved, that is, the path flow solution of the two types of travelers when finally reaching the steady state; Step 4-3: the traffic flow evolution result of the lower model is fed back to the upper model; Step 4-4: the fitness function value is calculated according to the traffic flow dynamic evolution result of the lower model; The objective function of the upper model of the traffic flow regulation bi-level programming model considering conformity effect under induced path is to minimize the sum of the total travel time cost of the system and the total path subsidy cost; it is easy to know that the value of the objective function is always positive, so the reciprocal of the value of the objective function can be mapped as the fitness value, that is, the smaller the value of the objective function, the greater the fitness value; at the same time, in order to ensure that the path subsidy cost is lower than a certain value, when the path subsidy cost is higher than a certain value, a penalty function is added to make the fitness value smaller; according to the principle of genetic algorithm, the individual with greater fitness value is selected as the parent to be inherited to the next generation with a greater probability, and vice versa, the individual with smaller fitness value will be gradually eliminated with the continuous evolution and development of the population; the fitness function Fit is shown in formula (10): Wherein, F is a penalty function, and flag is a relationship variable; if the path subsidy cost is greater than D, then flag is 1, otherwise flag is 0; Step 4-5: roulette selection strategy; The roulette selection strategy is used to select the better individuals in the population to form a new population; The genetic algorithm for solving the traffic flow regulation bi-level programming model considering conformity effect under induced path; the algorithm can improve the convergence efficiency of algorithm iteration, and quickly and accurately solve the above problem, and the specific steps are as follows: Step 4-1: double-layer coding is performed on the traffic flow regulation problem considering conformity effect under induced path, and an initial population is generated to form an initial traffic flow induction scheme candidate set; Step 4-2: the chromosome is transmitted to the lower model; The path unit subsidy standard and the proportion of travelers receiving path subsidy information represented by the chromosome in the population are extracted, and the solution of the traffic flow dynamic evolution model considering conformity effect under the current path unit subsidy standard and subsidy ratio is solved, that is, the path flow solution of the two types of travelers when finally reaching the steady state; Step 4-3: the traffic flow evolution result of the lower model is fed back to the upper model; Step 4-4: the fitness function value is calculated according to the traffic flow dynamic evolution result of the lower model; The genetic algorithm for solving the traffic flow regulation bi-level programming model considering conformity effect under induced path; the algorithm can improve the convergence efficiency of algorithm iteration, and quickly and accurately solve the above problem, and the specific steps are as follows: According to the individual fitness value calculated in the above formula, the selection probability of the individual in the population with the size of g is further determined, and the calculation formula is: where P i is the selection probability of an individual in the population, Fit i is the fitness value of an individual in the population; Cumulative probability Q of individuals in the population i The formula is: Generate g random numbers ζ of uniform distribution [0,1], if Q i ≤ζ≤Q i+1 Select individual i; Step 4-6: crossover operation; Two-point crossover method is adopted, with a certain crossover probability P c Two crossover points are randomly set in two chromosome encoding strings paired with each other in the parent population, and the parts of the two chromosomes between the two set crossover points are exchanged; Step 4-7: genetic mutation operation; The basic bit mutation method is used to mutate a bit at a certain mutation probability P m A random number r e [0, 1] is generated in the chromosome of each offspring in the cross offspring set, and if r ≤ P m The value of the bit or bits on the chromosome is randomly mutated. For the individual represented by the binary coded symbol string in this chapter, if the gene value to be mutated is 0, the mutation operation changes it to 1; otherwise, if the original gene value is 1, the mutation operation changes it to 0. Steps 4-2 to 4-7 are repeatedly executed until the genetic algorithm running iteration reaches the set maximum iteration number Maxgen, and the optimal path unit subsidy standard and the optimal subsidy ratio are output.

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