CN109325757A - Alleviate the optimal charge collection pricing method of transportation network risk - Google Patents
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Abstract
Research now about Congestion Toll and tail gas pollution charge is very extensive, but the secure charge to reduce transportation network risk is but seldom concerned.For this purpose, the present invention establishes a kind of completely new bilayer model system.In upper layer model, manager minimizes the security performance function of the network of communication lines, and designs charging mode with this.In underlying model, traveler will embody the behavior reaction of upper layer charge collection pricing by a four stage progressive die types with feedback mechanism.In order to solve above-mentioned bilayer model, the present invention is based on Monte Carlo simulation, feasible direction method, iteration weighting method (MSA), Frank-Wolfe algorithm and dijkstra's algorithms, have devised a kind of random feasible direction method.Finally, the present invention is verified using Nguyen-Dupuis network, the results showed that mentioned method and derivation algorithm have operability and validity.For traffic safety to be considered as to the policy maker of major policies target and evaluation index, method of the invention can become a kind of tool of preciousness.
Description
Technical field:
The present invention establishes a kind of optimal charge collection pricing method based on transportation network security performance, belong to traffic programme with
Administrative skill field.
Background technique:
Security performance is still a relatively vague concept in traffic programme and management, definition, measurement, especially
Its practice, there are still a series of problems.Using government as the transportation network manager of representative, usually pass through network design
With the policy instruments such as charge collection pricing, optimize the performance of traffic system.Currently, for congestion and discharge charge offering question
It is widely studied, i.e. congestion-pricing and tail gas pollution charge.But it is fixed about the optimal pass cost for alleviating transportation network risk
The research of valence is relatively fewer.
In general, there are two kinds of risks of shipping and passenger traffic in transportation network: one is harmful substance (dangerous material) leakage,
It is another then be common traffic injury accident.In the people of hazardous materials transportation near roads life and work, it is generally faced with fortune
Defeated accident bring risk.Because this is to the public, there are potential threats, in recent years, for the Optimization Work land of hazardous materials transportation
Extension is opened.Marcotte etc.[1]Charge collection pricing is proposed with as policy instrument, to prevent carrier from using certain sections.
They propose a kind of Bi-level Programming Models, in upper layer model, government by certain sections to the vehicle for being loaded with dangerous substances
Charge, to reduce risk in transit；In underlying model, carrier independently selects route.They show that " fees policy is than existing
Network design policy it is more effective " conclusion.Wang etc.[2]With Esfandeh etc.[3]Double Dipping pricing model is expressed as
One Bi-level Programming Models, by controlling conventional vehicles and HAZMAT vehicle simultaneously, to achieve the purpose that reduce risk.
Assadipour etc.[4]The Bi-objective bilayer model based on charge is proposed to manage hazardous materials transportation, it is intended to drop to the maximum extent
Low transport network risk and charge.Charge collection pricing policy is compared by they with network design policy, research shows that the former is more
It is practical, more effectively.They suggest this two policy mixs being two stages strategy, and are applied to long-term hazardous materials transportation
In control.Bianco etc.[5]Charge collection pricing policy is studied with specification hazardous materials transportation, manager (such as government organs) is intended to most
Reduce to limits transportation network overall risk and maximum section risk (solve risk justice).
Academia possesses some special knowledge to the pass cost pricing problem for reducing hazardous materials transportation risk, but for reducing passenger traffic risk
The research of pass cost be not yet unfolded.Haas and Bekhor[6]Bi-objective Bi-level Programming Models have been formulated, have been set by transportation network
Meter, reduces the travel time, and reach the maximized effect of road safety to the maximum extent.Security performance function is one minus two
Item formula model, lays particular emphasis on the estimation to section accident.Zhong etc.[7]It is excellent using Bi-objective bilayer under random trip requirements
Change model to determine best charge setting, to reduce the negative external effect of congestion and accident to the maximum extent.Usually, traffic
The ratio between flow-traffic capacity (v/c) and traffic accident rate meet U-shaped relationship, and therefore, security performance can pass through quadratic function
To measure.Their conclusion is, traditional take efficiency as the congestion pricing scheme of guiding, it is not intended that the influence to safety, no
Conducive to the reduction of accident.Possel etc.[8]Multiple target bi-level optimal model is then defined, makes every effort to reduce exhaust gas discharge, traffic thing
Therefore sum and system total travel time.For traffic safety, all there is certain accident rate in each type of section, the accident
Rate is multiplied by the truck kilometer number in one day, and then, the sum of the accident rate in all sections can be used for determining the safety of transportation network
Energy.
Bibliography:
[1] Marcotte, P., Mercier, A., Savard, G., Verter, V. (2009) Toll Policies for
Mitigating Hazardous Materials Transport Risk.Transp.Sci.43,228-243.
[2] Wang, J., Kang, Y., Kwon, C., Batta, R. (2012) Dual Toll Pricing for
Hazardous Materials Transport with Linear Delay.Netw Spat.Econ.12,147-165.
[3] Esfandeh, T., Kwon, C., Batta, R. (2016) Regulating hazardous materials
transportation by dual toll pricing.Transportation Research Part B-
Methodological 83,20-35
[4] Assadipour, G., Ke, G.Y., Verma, M. (2016) A toll-based bi-level
programming approach to managing hazardous materials shipments over an
intermodal transportation network.Transportation Research Part D-Transport
And Environment 47,208-221.
[5] Bianeo, L., Caramia, M., Giordani, S., Piccialli, V. (2016) A Game-
Theoretic Approach for Regulating Hazmat Transportation.Transp.Sci.50,424-
438.
[6] Haas, I., Bekhor, S. (2017) Network design problem considering system
Time minimization and road safety maximization:formulation and solution
Approaches.Transportmetrica A 13,829-851.
[7] Zhong, S.P., Xiao, X.T., Bushell, M., Sun, H. (2017) Optimal Road
Congestion Pricing for Both Traffic Efficiency and Safety under Demand
Uncertainty.J.Transp.Eng.Pt A-Syst.143.
[8] Possel, B., Wismans, L.J.J., Van Berkum, E.C., Bliemer, M.C.J. (2018) The
multi-objective network design problem using minimizing externalities as
Objectives:comparison of a genetic algorithm and simulated annealing
Framework.Transportation 45,545-572.
Summary of the invention:
Technical problem: there are problems that at least three in practical work previous.Firstly, about transportation network safety is improved
The optimal pricing method of performance using less, this is a major issue in traffic programme and management.Secondly, lower layer's mould
The traveler behavior reaction model of type has limitation, and the selection of traveler route is usually indicated using only user equilibrium.This hair
It is bright to propose a kind of four-phase model with feedback mechanism, to realize that the traffic system in underlying model balances.Model fortune
Traffic distribution is carried out with logit type destination preference pattern, so as to sufficiently reflect the decision behavior of traveler.Finally, existing
Some derivation algorithms or global optimum can not be found or extremely complex gradient is needed to calculate.
Technical solution: the optimal pass cost pricing problem based on traffic safety is expressed as one as shown in Figure 1 by the present invention
Bilayer model system, specifically includes the following steps:
Step 1: transportation network manager, using road toll as policy instrument, is built using network security as policy goals
Upper layer mathematical programming model under Liru:
Wherein z (p) is target function value, and A is the section set in transportation network, paIt is section a paying price, pmaxIt is
Maximum Charge price in allowed band, vaIt is link flow, caIt is road section capacity, β1、β2And β3It is empirical parameter, gives
After determining charging mode p, road traffic flow va(p) it is determined by underlying model；
Step 2: underlying model is the combination die that traffic generation, traffic distribution, traffic modal splitting and traffic flow distribute
Type reaches traffic system balance by feedback iteration, road section traffic volume flow and transit time when can be with calculated equilibrium state,
The underlying model is as shown in Fig. 2；
Wherein OiIt is the trip generation of departure place i, qijIt is the trip requirements between departure place i and destination j, βjIt is trip
Person can also be interpreted as the inherent attraction of destination j, t ' for the representative preference of destination jijIt is departure place i and purpose
Broad sense most short travel time between ground j, popjIt is the size of population of destination j, empjIt is employee's quantity of destination j, βt,
βpAnd βeIt is corresponding coefficient, vaIt is the magnitude of traffic flow of section a, its vector form is v, taIt is the transit time of section a, it
It is the function of the magnitude of traffic flow and the traffic capacity,It is the magnitude of traffic flow on the path k for connect departure place i and destination j,For
Road-path relation indicates are as follows:
Step 3: to the model foundation iterative feedback relationship in step 1 and step 2, for the road given in step 1
Road charging mode p calculates traffic system equilibrium state at this time in step 2, which, which calculates, hands over
The safety performance of open network, shows according to it and updates p, such iterative feedback, until p obtains optimal solution.
Further, it for the upper layer model in step 1, is solved using random feasible direction method, algorithm flow such as Fig. 3 institute
Show, specific calculate is not walked as follows:
Step 1: one feasible starting point p of input0；It is generated at random from area of feasible solutions, in entire area of feasible solutions
Need to generate multiple starting points to guarantee global optimization；
Step 2: generating random feasible direction；M >=100 vector is randomly generated in being uniformly distributed U (- 1,1), to its into
Row standardization；
Step 3: determining the descent direction s of steepest1；A small sample perturbations a will be used0Carry out all random directions of comparison, it is false
If most fast feasible descent direction is s1If going to step 6 without feasible descent direction；
Step 4: linear search；In steepest direction s1On with fixed step size a0Constantly advance, until feasibility or lower decreasing concentration
Condition is not being met, it is assumed that optimal step size a1；
Step 5: updating p0, go to step 1；p0Calculating step see below formula:
Step 6: stopping iterative process and export traffic safety performance z (p0)。
For the underlying model in step 2, algorithm flow chart is as shown in figure 4, specific calculating process is as follows:
Step 1: charge collection pricing p is inputted from upper layer model；
Step 2: trip distribution matrix is initialized by equally distributed methodIf n=0, the number of iteration is indicated；
Step 3: initialization trip distribution；By Frank-Wolfe algorithm, it is based on user equilibrium, will initially go on a journey distribution
Matrix allocation is to transportation network, to calculate the magnitude of traffic flow and the broad sense travel time on each section a, starting point i and destination
The broad sense most short travel time between j, i.e.,It can be calculated by dijkstra's algorithm；
Step 4: updating trip distribution；It is based onTrip distribution matrix is updated using destination preference pattern
Step 5: the iteration weighting method that using weights are successively decreased, average travel matrixWith
Step 6: the convergence of trip matrix is examined using opposite root square error approach (RRSE)；
If meeting the condition of convergence, step 8 is gone to；Otherwise turn step 7；
Step 7: trip distribution；Based on user equilibrium, by Frank-Wolfe algorithm, by distribution matrix of going on a journeyDistribution
To transportation network, to calculate the broad sense travel time of trip flow and section a, then, the broad sense in departure place i and destination j
The most short travel time, i.e.,Calculating will be calculated by dijkstra's algorithm, and feed back to step 4；
Step 8: output magnitude of traffic flow va(p), the supreme layer model of a ∈ A；In fact, trip distribution matrixThe departure place and
The broad sense travel time in i and destination jIt can be calculated simultaneously out.
The utility model has the advantages that congestion, exhaust emissions and injury accident are three big primary outers of traffic system.Congestion Toll and
The problem of tail gas pollution charge (usually carbon dioxide), has been widely studied, still, to reduce the safety of traffic accident
Pricing problem is but seldom studied, and the security pricing for reducing transportation network risk needs to obtain the attention of height.The present invention proposes
One completely new bilayer model system, the government in upper layer model is the leader with best safety performance target, lower layer
Traveler in model is the follower that target is maximized with personalistic utility.
It is well known that bilayer model system is a challenging problem.For the security performance for accurately measuring section,
The present invention extracts a complicated section security performance function from " highway safety handbook " (HSM), this makes bilayer model
It is more difficult.In order to solve the mould
A pass cost pricing model is given, the traffic system balance in underlying model is then for calculating the magnitude of traffic flow.This
It is the four stage progressive die types for having feedback mechanism.In trip distribution, multinomial logit model is instead of traditional weight
Power model, because the latter cannot accurately reflect the decision behavior of traveler.Research has shown that, many with aobvious in the selection of destination
The key factor for writing convincingness is not included in Gravity Models.On the contrary, multinomial logit model is but suitable for selecting
The attribute of item and individual.Subsequently, based on Frank-Wolfe algorithm, user equilibrium will be used to calculate the magnitude of traffic flow and broad sense is handed over
The logical time.The Generalized Shortest Path diameter time obtained with dijkstra's algorithm will be fed back to trip distribution.This feedback procedure
It will continue to that convergence requires to be met.Finally, the magnitude of traffic flow in equilibrium state can feed back to layer model, network security
Performance can also obtain herein.
Random feasible direction method has the risk of local minimum, it is therefore desirable to a series of starting point, to reduce error.
After more all network security performances, it may be determined that optimal security performance.Use the mould of Nguyen-Dupuis network
Draft experiment can verify the effect of the method for proposition, and the result is encouraging.Model framework proposed by the present invention can become one
A useful tool uses in pass cost price design for policy maker, to reduce the risk of transportation network.
Detailed description of the invention:
Fig. 1 is the bilayer model system for pass cost pricing problem.
Fig. 2 is the four-phase model with feedback.
Fig. 3 is the algorithm flow chart of upper layer model.
Fig. 4 is the algorithm flow chart of underlying model feedback procedure
Fig. 5 is Nguyen-Dupuis test network.
Specific embodiment:
Nguyen-Dupuis network as shown in Figure 5 is widely used in traffic study to test various methods.Table 1 is listed
The road parameters such as free flow running time and road passage capability in the network.
The road parameters of 1 Nguyen-Dupuis test network of table
In Nguyen-Dupuis network, there are two starting points 1 and 4, two destinations 2 and 3.Assuming that in time to peak
Interior, it is respectively 1500pcu/h and 1000pcu/h that the trip of starting point 1 and 4, which generates,.That is, O1=1500pcu/h, O4=
1000pcu/h.The candidate road section for needing pass cost to fix a price is 3,4,5,9,13,16,19.Problem is according to security performance come really
Fixed best section pricing model.Since random feasible direction method is there are the risk of local optimum, it can be produced in feasible zone
10 starting points of raw random distribution.The security performance of these starting points will mutually compare, and obtain optimal security performance to ensure
Global optimization.Small disturbance a0Value is 0.1, and the quantity M of random feasible direction is 100.Fix a price p in maximum sectionmaxIt is 3 beauty
Member, the time value are 0.3 dollar per minute.
It is well known that the trip distribution phase in underlying model, many has the key variables of significant convincingness cannot
Be comprised in traditional Gravity Models, most influential one be exactly traveler destination preference.For example, compared with new
Development area, traveler prefer traditional destination.Therefore, destination selection will be using multinomial with traveler preference
Formula logit model.Destination preference pattern in feedback procedure is reduced to:
Wherein, βjIt is preference of the traveler to destination j, βtIt is the path transit time between starting point i and destination j
Coefficient.βjAnd βtValue can be calibrated by real example data.We set β herein2=0, β3=1, βt=-0.1.This just anticipates
Taste, traveler is 0 to the preference of destination 2, and the preference to destination 3 is 1, and traveler more has a preference for destination 3.Broad sense goes out
The coefficient of row time is -0.1, this means that the broad sense travel time is disutility.
In the trip allocated phase of underlying model, this research is using classical user equilibrium method, and this method is by section property
Energy function is dissolved into equilibrium state.The common section performance function developed by Bureau of Public Roads (BPR) is as follows:
Wherein, ta(va) be the magnitude of traffic flow be vaGiven section a impedance function, caIt is road section capacity,It is road
The free flow time of section a, α and β are the flow/retardation coefficients that can be calibrated by real example.Traditional α and β value is 0.15 He respectively
4.0, these data will also be used for our analog study.Therefore, we can obtain road by Frank-Wolfe algorithm
The section magnitude of traffic flow.
If convergence RRSE is 0.01, i.e. ε=0.01.Pass through the pass cost price p setting to giving in upper layer model
Above-mentioned parameter, the available solution single, stable with consistent travel time/cost and trip distribution matrix.In addition,
The Generalized Shortest Path diameter transit time between dijkstra's algorithm calculating i and j can be used.Finally, volume of traffic va(p), a ∈ A
Layer model is fed back to calculate transportation network security performance z (p).
After the network security performance of 10 starting points is all listed, security performance value is the smallest to be determined,
Its annual average total number of accident per hour is 37.7.It note that if there will be 41.5 accidents, institutes without secure charge
With the effect of pass cost price is obvious.The charging mode in section is as shown in table 2.In this case, traffic system
System has optimal security performance.Flow, travel time (non-broad sense) and the service level in each section are shown in table 2.
The charge of the best transportation network of table 2 and section performance
Claims (3)
1. the present invention establishes the bilayer model system of the optimal pass cost pricing problem based on traffic safety, which is specifically wrapped
Include following steps:
Step 1: transportation network manager is using network security as policy goals, using road toll as policy instrument, establishes such as
Under upper layer mathematical programming model:
s.t.pa≤pmax, a ∈ A
pa>=0, a ∈ A
Wherein z (p) is target function value, and A is the section set in transportation network, paIt is section a paying price, pmaxIt is to allow model
Enclose interior Maximum Charge price, vaIt is link flow, caIt is road section capacity, β1、β2And β3It is empirical parameter, gives charge mould
After formula p, road traffic flow va(p) it is determined by underlying model；
Step 2: underlying model is the built-up pattern that traffic generation, traffic distribution, traffic modal splitting and traffic flow distribute, and is led to
It crosses feedback iteration and reaches traffic system balance, road section traffic volume flow and transit time when can be with calculated equilibrium state, the lower layer
Model such as Figure of description (Fig. 2) is shown, wherein OiIt is the trip generation of departure place i, qijIt is between departure place i and destination j
Trip requirements, βjIt is representative preference of the traveler for destination j, the inherent attraction of destination j can also be interpreted as,
t′ijIt is the broad sense most short travel time between departure place i and destination j, popjIt is the size of population of destination j, empjIt is mesh
Ground j employee's quantity, βt, βpAnd βeIt is corresponding coefficient, vaIt is the magnitude of traffic flow of section a, its vector form is v, taIt is
The transit time of section a, it is the function of the magnitude of traffic flow and the traffic capacity,It is the path k for connecting departure place i and destination j
On the magnitude of traffic flow,For road-path relation, indicate are as follows:
Step 3: to the model foundation iterative feedback relationship in step 1 and step 2, the road given in step 1 is received
Take mode p, traffic system equilibrium state at this time is calculated in step 2, which calculates transportation network
Safety performance, according to its show update p, such iterative feedback, until p obtain optimal solution.
2. being solved for the step one (upper layer model) in right 1 using following random feasible direction method:
Step 1: one feasible starting point p of input0；It is generated at random from area of feasible solutions, needs to give birth in entire area of feasible solutions
At multiple starting points to guarantee global optimization；
Step 2: generating random feasible direction；M >=100 vector is randomly generated in being uniformly distributed U (- 1,1), it is marked
Standardization；
Step 3: determining the descent direction s of steepest1；A small sample perturbations a will be used0Carry out all random directions of comparison, it is assumed that most
Fast feasible descent direction is s1If going to step 6 without feasible descent direction；
Step 4: linear search；In steepest direction s1On with fixed step size a0Constantly advance, until feasibility or the condition of lower decreasing concentration
It is not being met, it is assumed that optimal step size a1；
Step 5: updating p0, go to step 1；p0Calculating step see below formula:
p1=p0+a1s1
p0=p1
Step 6: stopping iterative process and export traffic safety performance z (p0)。
3. for the step two (underlying model) in right 1, using following calculating process:
Step 1: charge collection pricing p is inputted from upper layer model；
Step 2: trip distribution matrix is initialized by equally distributed methodIf n=0, the number of iteration is indicated；
Step 3: initialization trip distribution；By Frank-Wolfe algorithm, it is based on user equilibrium, will initially go on a journey distribution matrix
Transportation network is distributed to, to calculate the magnitude of traffic flow and the broad sense travel time on each section a, between starting point i and destination j
The broad sense most short travel time, i.e.,It can be calculated by dijkstra's algorithm；
Step 4: updating trip distribution；It is based onTrip distribution matrix is updated using destination preference pattern
Step 5: the iteration weighting method that using weights are successively decreased, average travel matrixWith
Step 6: the convergence of trip matrix is examined using opposite root square error approach (RRSE)；
If meeting the condition of convergence, step 8 is gone to；Otherwise turn step 7；
Step 7: trip distribution；Based on user equilibrium, by Frank-Wolfe algorithm, by distribution matrix of going on a journeyDistribute to friendship
Open network, to calculate the broad sense travel time of trip flow and section a, then, the broad sense in departure place i and destination j is most short
Travel time, i.e.,Calculating will be calculated by dijkstra's algorithm, and feed back to step 4；
Step 8: output magnitude of traffic flow va(p), the supreme layer model of a ∈ A；In fact, trip distribution matrixWith departure place i and mesh
Ground j in the broad sense travel timeIt can be calculated simultaneously out.
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