CN110837686A

CN110837686A - Traffic network design method based on subjective welfare maximization

Info

Publication number: CN110837686A
Application number: CN201910771337.5A
Authority: CN
Inventors: 林宏志; 尹璐
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2019-08-20
Filing date: 2019-08-20
Publication date: 2020-02-25

Abstract

The invention aims to provide a traffic network design method based on the maximization of subjective welfare of travelers. The invention establishes a new double-layer model system, the upper layer of the double-layer model system is used for realizing the maximization of subjective welfare of a traveler under given investment budget, and the lower layer of the double-layer model system is a feedback process between a Nested Loit model and a user equilibrium model. It is noted here that the invention uses the Nested Logit model to describe travel selection and destination selection, so it is a flexible travel demand, while the user balance model is applied to traffic distribution of the road network. Because the trip demand prediction adopts a discrete selection model, the subjective welfare of travelers can be measured. However, it is well known that the solution of the two-layer model is very challenging. Therefore, the invention designs a simulated annealing algorithm to find the optimal solution. The results of simulation studies show that the invention can effectively find the traffic network design with the largest subjective welfare of the travelers under the given investment budget.

Description

Traffic network design method based on subjective welfare maximization

The technical field is as follows:

the invention provides a traffic network design method based on subjective welfare maximization, and belongs to the technical field of traffic engineering.

Background art:

user-centric mobile services are one of the mobile services that will emerge in the future. Unlike traditional vehicle-centric mobile services, it claims mobile solutions that are centered on improving user experience. While there are many ways to measure user experience, subjective welfare or social welfare are the most common indicators. High welfare means that the experience of an individual or population is positive, while low welfare is associated with a negative experience. The welfare study is divided into subjective welfare study and objective welfare study. Objective welfare generally refers to the remaining of the consumer on a general level. It is defined as the difference between the total amount a consumer is willing or able to pay for a certain product or service and the total amount they actually pay. Subjective welfare refers to social welfare based on the personal utility of the consumer. It is the sum of all personal utilities obtained by the consumer from the product or service.

Objective welfare is widely applied to traffic network design of elastic travel demands. It is often manifested as a consumer's surplus, even sometimes referred to as social welfare. It should be noted that although consumer surplus and social welfare are two different concepts in economics, these two concepts are interchangeable in past traffic network analysis. They all refer to the difference between the total travel fare that the consumer is willing or able to pay and the total travel fare they actually pay. Yang and Bell^[1]And taking the consumer surplus as an objective function of the road network design. Since then, this measurement method has been widely used. Yang and Meng^[2]A two-level planning model is proposed to determine the best capacity and toll for the newly-built roads, thereby maximizing consumer surplus and producer surplus. Szeto and Lo^[3，4]Three different government road network design strategies were compared, where network benefits were measured in terms of the total amount of discount remaining for the consumer. Chen et al^[5]A genetic algorithm is proposed to solve the problem of building-operation-handover (BOT) network design when demand is uncertain, where the government's goal is to maximize the expected consumer residuals and minimize their variance. Ukkusuri and Patil^[6]And in consideration of uncertainty and elasticity of the demand, establishing a consumer residual maximization model of the network design problem. Jiang and Szeto^[7]Decision makers are believed to aim at increasing consumer residuals and reducing health costs when time-varying traffic network designs. Zhang et al^[8]A double-layer planning model is provided for the road network design problem, the upper layer is used for realizing the consumer residual maximization, and the lower layer adopts the elastic demand random user balance.

Subjective well-being is based on the perception of a product or service by an individual. Rather, it is used by economistsTo represent personal utility derived from travel selection. In addition, social welfare is a collection of individual utilities in welfare economics. It must be noted that the definition of the remaining or objective welfare of the consumer corresponds to the case with an aggregated demand function. It is widely adopted by traffic network modelers. However, this definition does not apply to the case where a user consumes discrete products or services, which is a difficult problem for travel behavior researchers. In this discrete case, subjective well-being is defined as the maximum utility that an individual obtains from travel selection. Generally, the expected maximum utility (logsum) is an indicator that measures the well-being/welfare of the consumer in the Logit selection model. Although discrete selection models are often used in transportation, logsum is rarely used in project evaluation^[9]. Dong et al^[10]Consumer benefits based on utility are suggested to replace traditional benefits. Bhandari et al^[11]Logsum is used to estimate the benefit of a rider when introducing a subway system in germany. Geurs et al^[12]Maximum utility will be expected as an accurate measure of the benefit of the traffic user. Tillema et al^[13]It is proposed to evaluate the impact of city congestion charging from a logsum-based consumer welfare perspective. NaHmias-Biran and Shiftan^[14]The recommendation can take logsum as a measurement index of subjective welfare in traffic project evaluation. In addition, fairness should be considered to more reasonably allocate resources. Van Wee^[15]The advantages and disadvantages of the logsum method are discussed and it is desirable to have more research work on this problem, especially on fairness and social rejection problems. Javanmardi et al^[16]The problem of service network design is studied in which utility functions are introduced into objective functions.

Reference documents:

[1]Yang，H.，Bell，M.G.H.(1998)Models and algorithms for road networkdesign：a review and some new developments[J].Transport Reviews 18，257-278.

[2]Yang，H.，Meng，Q.(2000)Highway pricing and capacity choice in a roadnetwork under a build-operate-transfer scheme[J].Transp.Res.Pt.A-PolicyPract.34，207-222.

[3]Szeto，W.Y.，Lo，H.K.(2005)Strategies for road network design overtime：Robustness under uncertainty[J].Transportmetrica 1，47-63.

[4]Szeto，W.Y.，Lo，H.K.(2008)Time-dependent transport networkimprovement and tolling strategies[J].Transp.Res.Pt.A-Policy Pract.42，376-391.

[5]Chen，A.，Subprasom，K.，Ji，Z.W.(2006)A simulation-based multi-objective genetic algorithm(SMOGA)procedure for BOT network design problem[J].Optim.Eng.7，225-247.

[6]Ukkusuri，S.V.，Patil，G.(2009)Multi-period transportation networkdesign under demand uncertainty[J].Transp.Res.Pt.B-Methodol.43，625-642.

[7]Jiang，Y.，Szeto，W.Y.(2015)Time-dependent transportation networkdesign that considers health cost[J].Transportmetrica A 11，74-101.

[8]Zhang，X.，Wang，H.，Wang，W.(2015)Bi-level programming and algorithmsfor stochastic network with elastic demand[J].Transport 30，117-128.

[9]de Jong，G.，Daly，A.，Pieters，M.，van der Hoorn，T.(2007)The logsum asan evaluation measure：Review of the literature and new results[J].Transp.Res.Pt.A-Policy Pract.41，874-889.

[10]Dong，X.J.，Ben-Akiva，M.E.，Bowman，J.L.，Walker，J.L.(2006)Moving fromtrip-based to activity-based measures of accessibility[J].Transp.Res.Pt.A-Policy Pract.40，163-180.

[11]Bhandari，K.，Kato，H.，Hayashi，Y.(2009)Economic and EquityEvaluation of Delhi Metro[J].International Journal of Urban Sciences 13，187-203.

[12]Geurs，K.，Zondag，B.，de Jong，G.，de Bok，M.(2010)Accessibilityappraisal of land-use/transport policy strategies：More than just adding uptravel-time savings[J].Transport.Res.Part D-Transport.Environ.15，382-393.

[13]Tillema，T.，Verhoef，E.，van Wee，B.，van Amelsfort，D.(2011)Evaluatingthe effects of urban congestion pricing：geographical accessibility versussocial surplus[J].Transp.Plan.Technol.34，669-689.

[14]Nahmias-Biran，B.H.，Shiftan，Y.(2016)Towards a more equitabledistribution of resources：Using activity-based models and subjective well-being measures in transport project evaluation[J].Transp.Res.Pt.A-PolicyPract.94，672-684.

[15]Van Wee，B.(2016)Accessible accessibility research challenges[J].Journal of Transport Geography 51，9-16.

[16]Javanmardi，S.，Hosseini-Nasab，H.，Mostafaeipour，A.，Fakhrzad，M.，Khademizare，H.(2017)Developing a New Algorithm for a Utility-based NetworkDesign Problem with Elastic Demand[J].Int.J.Eng.30，758-767.

the invention content is as follows:

the technical problem is as follows: in past traffic network design methods, consumer surplus and social welfare were interchangeable. However, they are different concepts in economics and should not be considered equivalents. In fact, consumer remains an objective welfare analyzed on an overall level, while social welfare is a subjective welfare consisting of personal utility. Policy makers and researchers have generally desired an analysis technique that is less dependent on aggregate analysis, but has more behavioral mechanisms. Therefore, the invention takes the social welfare maximization centered on the user as an evaluation index of the traffic network design and provides a new traffic network design method.

The technical scheme is as follows: the invention provides a traffic network design method based on subjective welfare maximization, which is a double-layer model and specifically comprises the following steps:

concrete method for establishing upper layer model

According to the random utility theory, the Nested Logit model probability can be written as the product of two Logit probabilities. The first layer is a binary choice of whether to go or not. The second level is to make multiple selections among destinations of the trip. The utility that a decision-maker n residing at the origin r derives from the destination selection s is:

wherein

Depending on the variable describing whether to go or not,

depending on the variable describing the destination s,

is an independent and identically distributed distribution of extrema. In general,

and

are specified as linear parameters. There may be many interpretation variables depending on the availability of data. However, OD travel time is recognized as the most basic one. Therefore, can be used to

The expression is as follows:

β therein₀Is a term of constant amount and is used as a constant value,

is of coefficient β₁The shortest travel time between OD of (1) to rs,

is a vector of other observable variables with coefficients β.

The probability of selecting the destination s is the product of two probabilities, namely the probability of traveling and the probability of determining that the post-travel destination s is selected:

wherein

Is the marginal probability of travel,

is the conditional probability of selecting the destination s after the line is determined. The marginal conditional probability and the conditional probability respectively adopt a binomial Logit form and a polynomial Logit form, and the binomial Logit form and the polynomial Logit form can be expressed as follows:

wherein

And S_rIs a destination set of origin r.

Is the desired maximum utility that decision n derives from the destination selection.

Because its expression is also called logsum term. λ is commonly referred to as logsum coefficient. λ reflects the degree of independence between destinations, with larger λ showing greater independence and smaller correlation. λ is in the range of [0, 1%]. When λ is 1, it means that the selection between destinations is completely independent. In this case, the Nested Logit model can be reduced to a standard Logit model.

It is noted that the subscript n may be omitted if an individual n is considered to be a representative n. Potential travel demand O given origin r_rThen the travel demand of origin r can be expressed as:

Q_r＝O_rp_rT， (7)

wherein p is_rTObtained from equation (4). The travel demand between OD and rs can be defined as:

wherein p is_rsObtained from equation (3). Note that the OD trip distribution matrix at this timeThe matrix is measured by human, and usually cannot be directly assigned to the road network, and needs to be converted into units of passenger cars (pcu) using the vehicle loading factor μ. Thus, the travel distribution matrix in passenger cars can be expressed as:

q_rs＝O_rp_rs/μ. (9)

where μ can be determined by investigation.

Since the purpose of a transportation system is to provide as many services as possible to users, the policy goal is to maximize the subjective well-being of the outgoing trip. Equation (4) is selected according to a binomial representing whether to travel or not, and the expected travel utility of the individual n residing at the departure point r can be expressed as:

since the absolute level of utility is not measurable, it can be divided by the marginal utility of revenue θ_nThereby obtaining the outgoing welfare of the user n living at the departure place r:

this division converts the units of utility into currency. The subscript n is omitted assuming that the individual residing in the traffic analysis region r has the same utility as the representative individual n. Total amount CW of welfare of residents in residential area r_rIs equal to

And the total travel demand Q of the area_rThe product of:

whereas the subjective welfare of the system is the set of all origin areas, expressed as

Combined solution of trip demand Q_rEquations (7) and (4) of (a), the mathematical programming of the upper layer can be written as:

wherein B is the investment budget, g_aIs a function of the cost of the road segment a,

is the maximum increment allowed on segment a. Other symbols are consistent with the previous definition. The OD travel time is implicitly determined by the underlying model.

(II) concrete method for establishing lower layer model

The loop feedback process of the underlying model is shown in fig. 2. In the Nested Logit model, a travel distribution matrix can be generated from an initial solution of OD travel time. The travel demand between the ODs is then assigned to the road network using a user balance model. Thereby, the road trip time can be obtained. According to the Wardrop principle, a shortest path algorithm (typically Dijkstra's algorithm) can be used to calculate the new OD travel time. For the running average, the new OD trip time is the weighted sum of the first two OD trip times. The latest OD travel time is then input into the Nested Logit model. The iterative process will continue until the OD travel times for successive iterations are substantially equal. In other words, the OD travel time is internally determined and consistent.

The detailed procedure for the continuous averaging Method (MSA) is as follows:

step 1 is initialized. The feasible solution of OD travel time is expressed as

In addition, let i equal to 1, which indicates the number of iterations.

Step 2 combines travel-destination selection modes. Travel distribution matrix

Generated by a Nested Logit model, and the parameters of the model can be obtained in advance through empirical research.

And 3, carrying out traffic distribution by using a user balance model. Given a traffic network, calculating the travel time of the road section by adopting a Frank-Wolfe algorithm

a∈A。

And 4, solving the shortest path travel time by using a Dijkstra algorithm. According to the Wardrop principle, the shortest path travel time can be used as a new travel time

And 5, updating the OD travel time. MSA method averaging with decreasing weight (i.e. inverse of the number of iterations i)

And

step 6 checks the convergence of the OD travel time using the predetermined relative square root error (RRSE) epsilon:

if the convergence condition is satisfied, go to step 7. Otherwise, let i equal to i +1 and

and then go to step 2.

Step 7 ends the feedback process. Output consistent OD trip time

Travel distribution matrix

(III) specific steps of simulated annealing algorithm

For complex bilayer problems, traditional methods are difficult to work with due to their non-linearity, non-differentiability, non-convexity, etc. In this case, the heuristic approach, although computationally demanding, may be an alternative tool to solve some of the difficulties described above and to obtain an approximately optimal solution. The present invention employs a Simulated Annealing (SA) algorithm that is particularly well suited for two-layer models. The algorithm flow chart is shown in fig. 3. The specific steps of the algorithm are as follows:

step 0 initialization: given a feasible solution set omega, a parameter 0 < delta < 1.0 and an integer L₀，M₀And T_s(stop temperature). In addition, let k equal to 0 as the outer loop control parameter, k₁And 0 is an inner ring control parameter.

Step 1, searching an initial temperature and an initial point: uniformly randomly generating M over a feasible solution set omega₀Points of interest, using z⁽ⁱ⁾(i＝1，2，...，M₀) To indicate. For each z⁽ⁱ⁾Using the underlying model to obtain z⁽ⁱ⁾Relative OD travel time, then calculating the corresponding upper layer performance

I.e., subjective well being. Then calculate

The variance of (A) is the initial temperature T⁽⁰⁾And the initial point y⁽⁰⁾E.g. omega is optimal

The point to which the value corresponds.

Step 2 check the stop conditions of the external cycle: if T is^(k)＜T_sThen it stops. Otherwise, go to step 3.

Step 3 check the stop conditions of the internal loop: if k is₁＞L₀N (where N is the number of decision variables in the upper model), go to step 6. Otherwise, go to step 4.

Step 4, generating feasible points: in that

Generates a small random perturbation, thereby generating a feasible point x.

Step 5Metropolis criteria: the upper model is subjective welfare maximization, which is different from the minimization problem of the standard. If it is notThen order

Let k₁：＝k₁+1 and then go to step 3. Otherwise, ifGreater than [0, 1 ]]An inner random value, then order

Let k₁：＝k₁+1, then go to step 3; otherwise, it orders

Let k₁：＝k₁+1 and then go to step 3.

Step 6, cooling schedule: calculating a target value

Standard deviation of (2) by σ (T)^(k)) And (4) showing. The cooling temperature is set as follows:

and k is set as follows: at least one of the two groups k +1,

k₁go to step 2 when 0.

Has the advantages that: the invention provides a novel double-layer model for traffic network design, wherein the upper layer of the double-layer model aims to realize the maximization of subjective welfare, the lower layer of the double-layer model is an iterative feedback process between a Nested Logit model and a user equilibrium model, and the OD travel time is determined endogenously. Conventional optimization algorithms are computationally difficult to implement since the two-layer model is generally considered a strong NP-complete problem. Therefore, the invention provides a meta-heuristic simulated annealing algorithm to solve the problem. Research shows that the method can be used for designing the traffic network with the maximized subjective welfare.

Description of the drawings:

FIG. 1 is a diagram of a two-layer model structure

FIG. 2 is a loop feedback process for the underlying model

FIG. 3 is a flow chart of a simulated annealing algorithm

FIG. 4 is a Nguyen-Dupuis network for simulation studies

The specific implementation mode is as follows:

the Nguyen-Dupis network shown in fig. 4 is widely used for method validation in various traffic studies. Table 1 shows the road section parameters including free-run time, road section traffic capacity and road section lengthAnd (4) degree. In the Nguyen-Dupis network, there are two

origin areas

1 and 4 and two

destination areas

2 and 3. Assume that during peak hours, the potential travel needs for

departure areas

1 and 4 are 2000pcu/h and 3000pcu/h, respectively. That is, O₁2000pcu/h and O₄＝3000pcu/h。

TABLE 1 road section parameters of Nguyen-Dupuis network

There are many interpretation variables in the Nested Logit model for travel-destination combination selection. However, as a simulation study, we only consider the most important variable, namely the OD trip time t_rsAnd an employee number em of the destination s_s. For example, the system utility Y of a representative individual residing at the origin 1₁₂And Y₁₃Is assumed to be:

the parameters may be given by empirical calculations. Generally, the coefficient of OD travel time is negative as it has a negative effect. Assuming that the number of workers is em₂Em 5 ten thousand₃5 ten thousand. The expected travel utility can be reduced to:

V₁＝-1+λln(exp(Y₁₂/λ)+exp(Y₁₃/λ)) (19)

here, the effect of staying at home (not traveling) is 0, that is, the reference value is 0. W₁Is expressed by a constant of-1, i.e., the intrinsic utility of egress is negative. Assume a lambda value of 0.8.

In trip allocation, the research adopts a classical user balancing method, which combines a road section performance function with a balancing state. One commonly used road segment performance function given by the U.S. highway administration (BPR) is as follows:

wherein, t_a(v_a，c_a) Given a traffic volume v_aThe road section passing capacity is c_aThe impedance function on the road section a of (a),

is the free flow impedance of segment a. α and β are flow/delay coefficients that can be calibrated by empirical means BPR gives empirical values of α and β of 0.15 and 4.0, respectively, which are also used in the simulation studies herein.

The convergence criterion of MSA is 0.01, i.e., ∈ 0.01. For a given road network design, it is possible to converge to a single stable solution, and the OD travel time matrix of this solution is consistent. The parameters used in the simulated annealing algorithm generally affect the computation time and the computation results. They are set to δ 0.5, L₀＝20，M₀100 and T _s1. Assuming a road segment investment function of

g_a(Δc_a)＝0.3×Δc_a×l_a，a∈A (21)

Wherein l_aIs the length (in kilometers) of the segment a. Further, the investment budget is determined to be B2000. The program is written in an open source language R. The final OD distribution matrix is shown in table 2. The results show that only 50.55% and 49.13% of travel needs of origin 1 and origin 4, respectively, are met. That is, almost half of the potential travel needs are limited. Therefore, we need more investment to enhance the user experience. Note that the vehicle loading factor μ is set to 1 in the routine, and the marginal utility of the income θ is also set to 1. The optimal network design and segment operating conditions are shown in table 3. This means that in order to maximize subjective well-being, road maintenance is required for the

road segments

3, 9, 16, while road traffic needs to be increased for the

road segments

4, 5, 13.

TABLE 2. travel distribution matrix

TABLE 3 optimal traffic network design and road segment operating conditions

Claims

1. The invention provides a traffic network design method based on subjective welfare maximization, which is a double-layer model and specifically comprises the following characteristics:

(1) the upper layer model maximizes the subjective welfare of the travelers by adjusting the traffic network design, the measurement of the subjective welfare is based on a non-ensemble discrete selection model, and particularly, a Nestedlogit model is adopted for trip generation and destination selection, so that the subjective welfare of the travelers can be measured;

(2) the lower layer model is traffic system balance, which is a feedback iterative process between a Nested logic model for trip-destination selection and a user balance model for traffic distribution, and is a series of behavior reactions of a traveler on the upper layer traffic network design, each upper layer traffic network design corresponds to one lower layer traffic system balance, the subjective welfare of the traveler is measured on the basis, and the result is fed back to the upper layer model;

(3) the two-layer model is solved using a simulated annealing algorithm.