CN110309962A - Railway stroke route method and device for planning based on time extended model - Google Patents

Abstract

The present invention provides a kind of railway stroke route method and device for planning based on time extended model, by comparing the difference of standard time extended model and Chinese railway networks actual conditions, the time extended model of standard is improved, the time extended model for being suitable for Chinese Railway net is obtained, and with establishing combined airway railway traffic model and empty iron based on the time extended model through transport model based on this model；It is then based on improved model and solves railway stroke planning optimum path problems using dijkstra's algorithm, and railway stroke planning K shortest path problem is solved based on backtracking algorithm idea；Acceleration processing finally is carried out to stroke planning algorithm using model compression and A* algorithm, makes algorithm that the real-time calculating of travelling scheme may be implemented, compared with prior art, railway stroke route planing method efficiency provided by the invention significantly improves.

Description

Railway stroke route method and device for planning based on time extended model

Technical field

The invention belongs to rail paths to optimize field, in particular to a kind of railway stroke route based on time extended model Method and device for planning.

Background technique

With the development of society, the trip requirements of people are gradually increased.Railway has valence as one of basic mode of transportation The features such as lattice are low, fast speed, therefore the passenger traffic volume that it is born also becomes increasing.It is announced according to China National Bureau of Statistics of China " national economy and social development statistical communique in 2018 " obtain: China's whole year in 2018 transport total amount (railway, highway, water Fortune, civil aviaton) 17,900,000,000 person-times, wherein 33.7 hundred million person-times of total volume of railway freight, increase by 9.4% compared with last year.Railway has become people's One of important trip mode.Obviously, according to the trip needs of passenger (transfer is minimum, admission fee is minimum and the time is minimum etc.) come It is the matter of utmost importance that passenger selects railroad mode trip to need to face to the railway riding scheme between two places.

All transportation departments are serviced according to timetable both at home and abroad.All vehicles are had recorded in timetable The time of departure and intermediate stop etc., so-called stroke planning, be exactly according to the demand of timetable and passenger itself, it is all can One or more optimal solution is found in the scheme of energy.

One typical schedule planning system, should can solve the optimum path problems under following target: at least change Multiply problem, passenger removes Target Station from initiating station, it is desirable that be transfer number it is minimum；Shortest route matter of time, target be so that Passenger's the time it takes (time waited in station) in stroke is most short；Problem is reached earliest, and target is so that trip Visitor can reach Target Station earliest；Multi-objective optimization question comprehensively considers above several targets, realizes Pareto optimality.

Chinese railway networks have particularity and complexity, need to time extended model and calculation disclosed in the prior art Method improves the stroke planning to realize Chinese Railway path.

Summary of the invention

In order to solve the problems in the existing technology, the present invention provides a kind of railway stroke based on time extended model Route planning method.

Specific technical solution of the present invention is as follows:

The present invention provides a kind of railway stroke route planing method based on time extended model, and this method includes following step It is rapid:

Building is suitable for the time extended model of the railway network；Wherein, the railway network is preferably Chinese Railway net；Constitute time expansion The time expander graphs G=(V, E) of model is opened up, V indicates node set, and E indicates that line set, node set include reaching node, going out Send out node and transfer node；And have any one node v ∈ V, v with properties: ATTR (v) shows that v is any section Point；TIME (v) indicates that v represents the number of minutes of Time To Event relative to earliest time t；STATION (v) indicates the affiliated vehicle of v It stands；TRAIN (v) indicates full train number representated by v；CITY (v) represents city belonging to v；If (u, v) ∈ E, centainly has TIME (u)≤TIME (v), line set include reach node be directed toward transfer node while, reach node be directed toward set out node while, Transfer node be directed toward transfer node when, transfer node is directed toward the node that sets out and the node that sets out is directed toward the side for reaching node；

In time expander graphs, it is the smallest that search follow node is directed toward weight in the path for reaching each side composition of node Path obtains optimal path.

Further to improve, the time extended model that the building is suitable for the railway network includes the following steps:

It reads in station and urban information: establishing station and the index in city, stand and the relation table in city and can starting station table；

It reads in train and starts the period: extension timetable being obtained according to the period of starting of train, is established according to extension timetable The blank of time extended model；

Addition station in change to side: for each allow change to station S, by belong to station S all transfer nodes according to when Between sort, the node after sequence be v₁..., v_k, add side (v_i, v_i+1)1≤i≤k-1；The arrival node in S is traversed, for every One meets STATION (u)=S arrival node u, finds the smallest i and meets TIME (v_i)-TIME(u)≥TRANSFER (S), side (u, v are added_i)；

Addition changes to side with city: stand S₁With station S₂Between allow with city change to, traversal station S₁In all arrival nodes, it is right Each meets STATION (u)=S₁Arrival node, station S₂Transfer node sequence v₁..., v_kIn, find the smallest i Meet TIME (v_i)-TIME (u) >=t, add side (u, v_i), wherein t is the least transfer time changed to city.

It is further to improve, optimal path is obtained based on time extended model operation dijkstra's algorithm and is specifically included:

To side, weight is set；

It is scanned in time expander graphs with dijkstra's algorithm, obtains optimal path.

Further to improve, the method also includes it is excellent to obtain K using backtracking algorithm on the basis of the optimal path of acquisition Path.

Further to improve, the method also includes constructing base on the basis of being suitable for the time extended model of the railway network In the combined airway railway traffic model of time extended model and/or empty iron through transport model.

It is further to improve, the data structure that operation dijkstra's algorithm uses includes Dial barrels, N member heap, Radix heap, Fib heap or binary heap.

It is further to improve, it obtains K shortest path and includes the following steps:

One-to-all: the optimal path weight for solving starting point to other points；

Backtracking: preceding K shortest path is obtained by reversely searching.

Further to improve, obtaining K shortest path using backtracking algorithm further includes the optimization to K shortest path algorithm, including right Time expander graphs are carried out compression or are accelerated using A* algorithm to the one-to-all process in backtracking algorithm.

Further to improve, the present invention also provides a kind of, and the Chinese Railway stroke route based on time extended model plans dress It sets, which includes:

Model construction component: the model construction component is configured as the time extended model that building is suitable for the railway network, The time expander graphs G=(V, E) of time extended model is constituted, V indicates node set, and E indicates that line set, node set include arriving Up to node, set out node and transfer node；And have any one node v ∈ V, v with properties: ATTR (v) shows that v is Any node；TIME (v) indicates that v represents the number of minutes of Time To Event relative to earliest time t；STATION (v) is indicated The affiliated station v；TRAIN (v) indicates full train number representated by v；CITY (v) represents city belonging to v；If (u, v) ∈ E, that Centainly there is TIME (u)≤TIME (v), line set includes that arrival node is directed toward the side of transfer node, arrival node direction is set out Node when, transfer node is directed toward transfer node, transfer node is directed toward the side for the node that sets out and the node that sets out is directed toward and reaches The side of node；

Searching component: described search component is configured as in time expander graphs, and search follow node, which is directed toward, reaches section The smallest path of weight in the path of each side composition of point, obtains optimal path.

The present invention provides a kind of railway stroke route method and device for planning based on time extended model, and this method is being examined On the basis of considering the problems such as starting the period with city transfer, clearing station, train, the time for establishing suitable Chinese Railway application demand expands Model is opened up, and the ticket journey based on time extended model plans computation model, proposed optimal based on dijkstra's algorithm acquisition Path and K shortest path is obtained based on backtracking algorithm, compared with prior art, Chinese Railway stroke route provided by the invention planning Efficiency of algorithm significantly improves.

Detailed description of the invention

Fig. 1 is basic time extended model；

Fig. 2 is the time extended model read in after schedule data；

Fig. 3 is the time extended model for being suitble to Chinese Railway net；

Fig. 4 is the efficiency of dijkstra's algorithm under plurality of data structures；

Fig. 5 is influence of the n to dijkstra's algorithm efficiency in N member heap；

Fig. 6 is algorithm examples figure；

Fig. 7 is label figure of the One-to-all step to each point；

Fig. 8 is the variation of R in trace-back process；

The time extended model of Fig. 9 combined airway railway traffic；

Figure 10 sky iron ground three layers of time extended model of through transport；

Figure 11 simple bus model；

Figure 12 sky iron ground through transport time extended model

Figure 13 is the time extended model after improving；

Figure 14 is influence of the compact model to response efficiency；

Figure 15 is influence of the A* algorithm to response efficiency；

K shortest path algorithm experimental result under tetra- kinds of targets of Figure 16；

The comparison of Figure 17 backtracking algorithm and MS algorithm；

The comparison of Figure 18 backtracking algorithm and YEN algorithm；

The comparison of YEN algorithm after Figure 19 recalls algorithm and accelerates；

Figure 20 Train delay algorithm response efficiency；

Figure 21 ticket journey planning algorithm efficiency.

The step of process of attached drawing illustrates can hold in a computer system such as a set of computer executable instructions Row.It, in some cases, can be to be different from sequence execution institute herein although logical order is shown in flow charts The step of description.

Specific embodiment

Since method description of the invention realizes that the computer system, which can be set, to be serviced in computer systems In device or the processor of client.Such as method described herein can be implemented as that software can be performed with control logic, It is executed by the CPU in server.Function as described herein can be implemented as being stored in readable Jie of non-transitory tangible computer Program instruction set in matter.When implemented in this fashion, which includes one group of instruction, when the group is instructed by counting It promotes computer to execute the method that can implement above-mentioned function when calculation machine is run.Programmable logic can be installed temporarily or permanently In non-transitory visible computer readable medium, such as ROM chip, computer storage, disk or other storages Medium.In addition to software come other than realizing, logic as described herein can use discrete parts, integrated circuit, patrol with programmable The programmable logic that equipment (such as, field programmable gate array (FPGA) or microprocessor) is used in combination is collected, or including it Any other equipment of any combination embody.All such implementations are each fallen within the scope of the present invention.

Before understanding the present application main points, need first to understand the following contents:

The main thought of time extended model modeling is each of railway network to be dispatched a car and arrived at a station event as figure A node；The node for belonging to different websites is connected, and represents a train and runs between two stations；Node in same website It is connected in chronological order, represents waiting of the passenger in station.Such a website was just unfolded to obtain multiple nodes according to the time, often A node contains spatial information (affiliated website) and temporal information (dispatch a car or arrival time) simultaneously, and railway network is by structure It builds as a time-space network, referred to as time extended model, as shown in Figure 1.

Dijkstra's algorithm is very representational shortest path algorithm.Traditional dijkstra's algorithm is for seeking from fixation For starting point to the shortest path of remaining each point, it is that the order of increasing lengths by path generates the algorithm of shortest path.

The basic thought of dijkstra's algorithm is to generate a most short-path spanning tree to fix starting point as root.Root to tree In the path of each node be shortest path of the root to the point because in the network of problem required by traditional dijkstra's algorithm not There are negative power, thus this most short-path spanning tree in generating process by each node by its distance away from fixed starting point and Syntople between point is one by one added in tree, after first close remote.

Illustrate the claimed content of the present invention in conjunction with specific embodiments below.

One embodiment of the present of invention provides a kind of railway stroke route planing method based on time extended model, the party Method includes the following steps:

S1: building is suitable for the time extended model of Chinese Railway net；

Building has the time extended model suitable for Chinese Railway net of following time expander graphs in step S1, wherein Time expander graphs G=(V, E), V represent node set, and E represents line set, and G has the property that

There are three types of nodes in V: arrival node, set out node and transfer node；And have for any one node v ∈ V, v With properties: ATTR (v) shows that v is any node；TIME (v) indicate v represent Time To Event relative to it is earliest when Between t the number of minutes；STATION (v) indicates the affiliated station v；TRAIN (v) indicates full train number representated by v；CITY (v) represents v Affiliated city.

If (u, v) ∈ E, centainly there is TIME (u)≤TIME (v)；Side in E is divided into following five class:

(a) side that node is directed toward transfer node is reached.The side represents the generation of transfer event.If two nodes are same In one station, transfer in station is indicated, which can change to；Otherwise same city transfer is represented, the two stations are that can change to city 's.

(b) side that node is directed toward the node that sets out is reached.The side represents passenger and does not get off at the station, directly sit same coastiong from Open the station.

(c) transfer node is directed toward the side of transfer node.The side represents the arrival that passenger waits next coastiong in station.

(d) transfer node is directed toward the side for the node that sets out.The side represents vehicle and has been prepared for setting out, and passenger gets on the bus outbound.

(e) set out node to reach node side.The side represents traveller's and goes to the next stop.

For example, the building for describing the time extended model suitable for Chinese Railway net includes such as in other embodiments Lower step:

S11: station and urban information are read in

Station and the index in city are established, stand and the relation table in city and can starting station table.It is stored using Hash table All stations and city.City indicates that the information for including has city code, city name, the transfer node for belonging to city with a structural body Set.Standing also is indicated with a structural body, and the information for including has station yard, station name, affiliated city, label, transfer node set, arrives Up to node set.It wherein marks and is used to indicate whether the station can starting station, transfer node set and arrival node set expression Belong to all transfer nodes at this station and reaches node set.

S12: it reads in train and starts the period

Start the period come the timetable that is expanded, then according to extension timetable settling time extended model according to train Blank.As shown in Fig. 2, each of figure node is all indicated by a structural body, comprise the following information that node is compiled Number, station, the time of node on behalf, the full train number of train of node on behalf, the train station train number of node on behalf, node category belonging to node Property.Such as in preferred embodiment, node can represent arrival node there are three types of attribute, 1, and 2 represent transfer node, and 3 represent out Send out node.

For each record in extension timetable, node each one of three types is generated, and it is corresponding to fill in node Information, the point set structure in last extension station and city structural body.Each point can be added to the point concentration stood accordingly and go, but Only when station belong to can starting station when, point can just be added to corresponding city point and concentrate.Whenever all nodes for having traversed a coastiong When, the corresponding arrival node of this coastiong and set out node and transfer node and the node that sets out are connected with a line.

S13: addition changes to side in station

For each allow change to station S, by belong to station S all transfer nodes (this can be by the structural body at station Directly obtain) according to time-sequencing, the node after sequence is v₁..., v_k, add side (v_i, v_i+1)1≤i≤k-1。

Finally, the arrival node in traversal S, meets STATION (u)=S arrival node u for each, finds most Small i meets TIME (v_i)-TIME (u) >=TRANSFER (S), add side (u, v_i)。

S14: addition changes to side with city

The transfer process on side is similar in standing with addition, if station S₁With station S₂Between allow same city to change to, traversal station S₁ In all arrival nodes, STATION (u)=S is met to each₁Arrival node, station S₂Transfer node sequence v₁..., v_kIn, it finds the smallest i and meets TIME (v_i)-TIME (u) >=t, add side (u, v_i), wherein t is to change to most with city The small transfer time.

Finally, the time extended model of acquisition is as shown in Figure 3.There are three the A, B, C of standing altogether in figure.Wherein A and B is fair Perhaps transfer and also can with city change to, C is then not allow to change to.

S2: the time extended model operation dijkstra's algorithm based on step S1 building obtains optimal path.

In step S2, the time extended model operation Dijkstra suitable for Chinese Railway net based on step S1 building is calculated The problem of method acquisition optimal path, describes are as follows: in time [t₁, t₂] from city S₁Leave for city S₂There are many kinds of schemes, use

F=(ST_1a, ST_1d, Z₁, t_1a, t_1d, ST_2a, ST_2d, Z₂, t_2a, t_2d..., ST_(n-1)a, ST_(n-1)d, Z_n-1, t_(n-1)a, t_(n-1)d) indicate a feasible scheme, illustrate passenger in t_1dMoment takes Z₁Slave station ST_1dIt sets out, in moment t_1aIt reaches ST_1a.Then in moment t_2dTake Z₂Slave station ST_2dIt sets out, in moment t_2aReach ST_2a... ... finally in moment t_(n-1)dTake Z_n-1 It sets out, in moment t_(n-1)aReach ST_(n-1)a.In order to guarantee the reasonability of the program, it is necessary to meet the following conditions:

ST_1d=S₁

ST_(n-1)a=S₂

t_1d∈[t₁, t₂]

ST_ia≡ST_(i+1)dOr ST_iaWith ST_(i+1)dIt can carry out same city transfer

Enable F=f | and f be in time [t₁, t₂] from S₁Leave for S₂Scheme, i.e. F is all in time [t₁, t₂] from city City S₁Leave for city S₂The set of scheme wherein just there is some schemes to be an advantage over other schemes, used for passenger Value (f) indicates evaluation of the passenger under certain judgment criteria to scheme f, asks then optimal problem is converted into an optimization Topic:

Since the preference of passenger is different, to the calculating of Value (f) there are many kinds of different standards, these standards are drawn Different stroke planning problems is gone out.

Most common standard is divided into following:

(a) hourage

According to the difference of Value (f) calculation, which can be divided into two sub-problems again:

Problem: Value (f)=t is reached earliest_(n-1)a

Shortest route matter of time: Value (f)=t_(n-1)a-t_1d。

(b) number of transfer

Reversing is often made troubles and some new expenses to passenger, so most of passenger is biased into number of transfer Less scheme.Least bus change problem can be drawn by this judgment criteria.Definition Transi table Passenger is illustrated in ST_iaWhether move backward；Least bus change problem is desirable

(c) admission fee

For certain passengers, saving money, it is most important to be only, they be ready to save some money and select it is some fall Train number number or hourage very long scheme.Lowest fare problem can be introduced by this judgment criteria；Use price_iExpression multiplies Sit Z_iFrom STi_dTo ST_iaPrice, lowest fare problem is desirable

(d) comprehensively consider the above four factors

Passenger when selecting riding scheme will not only one judgment criteria, various standards can be comprehensively considered, then Select a satisfied scheme.The optimal stroke planning problem of pareto can be introduced by this judgment criteria.Use λ₁, λ₂, λ₃, λ₄Point Not Biao Shi passenger to arrival time, the journey time, reversing number, admission fee preference, then the optimal stroke planning problem of pareto It is desirable

In order to use time extended model solve propose optimization problem, need to obtain one from scheme f to time The one-to-one relationship of a path P in expander graphs.

Each point represents the generation of an event in time expander graphs, and uniquely to have corresponded to 2 (n-1) a by scheme f The generation of event connects the path of this 2 (n-1) a point composition, so that it may obtain the corresponding path P (f) of scheme f.

Suitable weight is set in time expander graphs and makes cost (P (f))=Value (f), so that it may be utilized Dijkstra's algorithm solves the optimization problem proposed.Result in the basic flow that optimization problem is solved using time extended model Journey is as follows:

Suitable weight is set to side and makes cost (P (f))=Value (f)；

It is scanned in time expander graphs with dijkstra's algorithm, obtains optimal path.

The factor for influencing dijkstra's algorithm mainly has: the scale of figure, the selection of Priority Queues and point pair it is practical away from From.

Frequently-used data structure suitable for dijkstra's algorithm has N member heap, Radix heap, Fib heap, binary heap and Dial Bucket, the time complexity of plurality of data structures are as shown in the table:

The time complexity of 1 plurality of data structures of table compares

As can be seen from the above table, the complexity of Dial barrels of operations is all minimum, and therefore, Dial barrels are most suitable Data structure.It is bright to name illustration.

Dijkstra's algorithm is realized with plurality of data structures, and is tested, one in time expander graphs used in test 1513754 points, 2575593 sides are shared, the optimization aim selected is the shortest route time.Test result is shown in Fig. 4 and Fig. 5.

Each data structure all corresponds to a box in figure, and each box has five lines, is from top to bottom respectively to survey Try minimum value, a quarter value, median, 3/4ths values, maximum value in data.Rectangle is then the main distribution of test point Region.Wherein, median reflects average response efficiency, and the difference of maxima and minima reflects the fluctuation model of response time It encloses.

It can be seen from the figure that Dial barrels of efficiency highest, as long as average 14ms responds primary request, and right In different points pair, Dial barrels of response time variation range is also the smallest.Due to Dial barrels with minimum complexity and Highest efficiency, it is final to use Dial barrels to realize dijkstra's algorithm.

The path optimization under dijkstra's algorithm realization various criterion is run, is specifically included as follows:

1. shortest route time algorithm obtains shortest route time path

The present invention handles shortest route matter of time by judgment criteria of the journey time.

Shortest route matter of time: two city S are given₁And S₂An and departure time section [t₁, t₂], target is Find the shortest path of journey time.

This problem is equivalent to following optimization problem:

(u, v) ∈ E is enabled, cos t (u, v)=TIME (v)-TIME (u) is set, then there is cos t (P (f))=Value (f)

It proves: enabling P (f)={ v₁, v₂..., v_m, since P (f) and f is mutual corresponding, therefore following equation is set up:

TIME(v₁)=t_1d, TIME (v_m)=t_(n-1)a

To v ∈ V, the weight of point v is indicated with cost (v), and to (u, v) ∈ E, the power of side (u, v) is indicated with cost (u, v) Value, therefore for path P={ v₁, v₂..., v_n, have

TIME(v₁)=t_(n-1)a-t_1d+cos t(v₁)

Therefore if choose cost (v₁Just there is cost (P (f))=Value (f) in)=0.

Shortest route matter of time is transformed into for a shortest route problem, Dijkstra can be used in this problem Algorithm is solved, and indicates that Priority Queues, T.insert indicate to be inserted into an element into T with T, T.deleteMin expression is deleted Except the smallest element of weight in T, T.decreaseKey indicates to reduce the weight that element is specified in T, and each point is recorded with pre It is preceding after node.By the available shortest path P of dijkstra's algorithm, P mapping is then become a scheme f, i.e., Obtain shortest route time path.

Path is reached earliest 2. reaching stroke planning algorithm earliest and obtaining

Earliest arrival problem is handled as judgment criteria using the journey time.

Problem is reached earliest: giving two city S₁And S₂An and departure time section [t₁, t₂], target is to find The shortest path of journey time.

This problem is equivalent to following optimization problem:

(u, v) ∈ E is enabled, cos t (u, v)=TIME (v)-TIME (u) is set, then there is cos t (P (f))=Value (f)。

It proves: enabling P (f)={ v₁, v₂..., v_m, since P (f) and f is mutual corresponding, therefore following equation is set up:

TIME(v₁)=t_1d, TIME (v_m)=t_(n-1)a。

To v ∈ V, the weight of point v is indicated with cos t (v), and to (u, v) ∈ E, the power of side (u, v) is indicated with cos t (u, v) Value, therefore for path P={ v₁, v₂..., v_n, have

Therefore if choose cos t (v₁)=TIME (v₁)=t_1d, just there is cos t (P (f))=Value (f).

Earliest arrival problem is transformed into for a shortest route problem, this problem is similar with the shortest route time, It can also be solved using dijkstra's algorithm, only difference is that, it is initial to weigh when point v needs to be added to Priority Queues Value be TIME (v) rather than 0.

3. least bus change stroke planning algorithm obtains least bus change path

Least bus change problem is handled as judgment criteria using number of transfer.

Least bus change problem: two city S are given₁And S₂An and departure time section [t₁, t₂], target is to find Change to least scheme.

This problem is equivalent to following optimization problem:

(u, v) ∈ E is enabled, is arrangedSo cos T (P (f))=Value (f).

It proves: enabling P (f)={ v₁, v₂..., v_m, it is clear that scheme f is divided into multistage, as follows: f={ (ST_1a, ST_1d, Z₁, t_1a, t_1d), (ST_2a, ST_2d, Z₂, t_2a, t_2d) ..., (ST_(n-1)a, ST_(n-1)d, Z_n-1, t_(n-1)a, t_(n-1)d) investigateIt can be found that trans_iExactly illustrate whether (i-1)-th section and i-th section of train number Z is identical.It is assumed that Point u, which is represented, takes Z_i-1Reach ST_(i-1)a, point v, which is represented, takes Z_iLeave STi_d, then centainly having one in P (f) from u to v Subpath P '.If Z_i≠Z_i-1, it is evident that P ' has the side for removing transfer node from arrival node, if Z_i=Z_i-1, that There is no such a lines.Therefore, under the setting of this weight, cos t (P (f))=Value (f) is to set up.

Least bus change is transformed into for a shortest route problem.It can also be solved using dijkstra's algorithm.

4. the optimal stroke planning algorithm of multiple target pareto obtains optimal path

Single target is difficult accurately to describe the demand of passenger, it is therefore desirable to when comprehensively considering number of transfer and stroke Between scheme is compared.

Pareto optimal problem is handled as judgment criteria using number of transfer and journey time.

Pareto optimal problem: two city S are given₁And S₂An and departure time section [t₁, t₂], target is to look for The smallest scheme of weight is integrated to transfer and stroke.

This problem is equivalent to following optimization problem:

(u, v) ∈ E is enabled, is arranged

V is transfer node, then There is cos t (P (f))=Value (f)

Dijkstra's algorithm can be used also to realize in this algorithm.

Another embodiment of the present invention provide the railway stroke route planing method based on time extended model further include Time extended model based on building obtains K shortest path using backtracking algorithm.

The excellent road problem of K in stroke planning is as follows:

The excellent Lu Wenti of K: in all scheme set F, k is found and makes the smallest scheme f of Value (f).

A set Fk is exactly found to meet:

1.If | F |≤k, F_k=F, otherwise | F_k|=k；

2. couple any f₁∈F_k, f₂∈F-F_k, there is Value (f₁) < Value (f₂)。

With the difference of Value (f) value, the excellent road problem of K can be divided into K short stroke problem, K morning arrival problem, K and change to less Problem and the excellent Lu Wenti of multiple target pareto K.

Time expander graphs are actually the digraph of a non-negative weight, therefore solve K using time extended model The basis of excellent road problem is exactly the excellent Lu Wenti of point-to-point K of non-negative weight digraph.

The excellent Lu Wenti of point-to-point K of non-negative weight digraph: in figure G=(V, E), two points s, t are given, are searched for from s Into all paths of t, the smallest K paths of weight.

Indicate that the set in all paths from s to t, target are to find a set P with P_kMeet:

1.If | P |≤k, P_k=P, otherwise | P_k|=k；

2. couple any p₁∈P_k, p₂∈P-P_k, there is cos t (p₁) < cos t (p₂)。

The point-to-point K shortest path algorithm of non-negative weight digraph is described below:

The algorithm, which is first solved, to be marked from starting point to other shortest path distances put then from the reversed lookup of terminal The point crossed, which is concentrated, finds preceding K short path.

Given digraph G=(V, E), source point s and terminal t indicate the weight of side (u, v) with cos t (u, v), wherein u, v ∈ V, (u, v) ∈ E.Arbitrary u ∈ V.Distance (u) is indicated from point s to the shortest path distance of point u.Q indicates open Table, T indicate close table.R indicates set of paths, and each of R element is by triple (P (s, a v₁, t), key, PostKey it) forms, wherein P (s, v₁, t) it is one from s to t and passes through v₁Shortest path, with { v₁..., v_k, t } and it indicates, Key indicates that the total weight value of this paths, postKey are indicated from v₁To the total weight value of the subpath of t, num indicates the road found Diameter number.

The algorithm is divided into two steps, one-to-all and backtracking.Wherein one-to-all is for solving starting point to other points Optimal path weight；Trace-back process is to determine preceding K short path by reversely searching.

With short distance problem in order to, introduce one-to-all and backtracking the step of concrete operations.

1.one-to-all

It is determined with dijkstra's algorithm from source point s to the shortest path distance Distance (u) of other arbitrary node u, is used The mode of open table and close table realizes dijkstra's algorithm.

2. backtracking

Initialization R is the set for containing only a triple ({ t }, Dis tan ce (t), 0), and initializing variable num= 0.Assuming that having traced back to point v at present₁, we use set { v₁..., v_k, t } and indicate v₁To the path of t.Therefore, the road of s to t Diameter is formed by two sections, and front half section is from s to v₁Shortest path, this paths is determined during one-to-all, later half Section path is { v₁..., v_k, t }.

Then it repeats the steps of:

Delete the smallest element of key value in R.

If v₁=s, then record has found the n-th um short path, then num adds 1.

If v₁≠ s, then, for all satisfaction (v, v₁) ∈ E point v, if v is obtained during one-to-all One apart from label Dis tan ce (v), by b=({ v, v₁..., v_k, t }, Dis tan ce (v)+postKey+cos t (v, v₁), postKey+cos t (v, v₁)) be inserted into R.If the element number in R has been more than K, delete R in key value most Big element is K until the element number in R.

When(at this time without more paths for search) or num=K (K short path before having been found at this time) When, trace-back process terminates.

Correctness of algorithm proves:

Lemma one: each of set R triple ({ v₁..., v_n, t }, key, postKey) all represent a paths And the routine weight value is key.

It proves: by dijkstra's algorithm it is found that there are one from s to v₁Path { s, u₁..., u_n, v₁, total weight value For Distance (v₁), it is assumed that v₁To the path t { v₁..., v_n, t } weight be postKey.Consider following formula:

Key=postKey+Distance (v₁)

Then have, path { s, u from s to t₁..., u_n, v₁..., v_n, t } weight be key.

Lemma two: the triple obtained by R.deleteMin (), key value will not reduce.

Enable ({ v₁... v_n, t }, key, postKey)=R.deleteMin (), then for any one triple in R Its key value key₁Certainly it is greater than equal to key's.So key value is also big as long as proving the triple that R is next added In equal to key.From the step of recalling it is found that the triple being newly added has following form: ({ u, v₁... v_n, t }, key₁, postKey₁), wherein

PostKey=COST { v₁... v_n, t }, key=DISTANCE (v₁)+postKey

postKey₁=COST { u, v₁... v_n, t } and=cos t (u, v₁)+postKey, key₁=DISTANCE (u)+ postKey₁Then, key₁- key=DISTANCE (u)+cos t (u, v₁)-DISTANCE(v₁)；

Because DISTANCE (u) indicates s to u shortest path length, then DISTANCE (u)+co st (u, v₁) indicate s to v₁ A paths length.DISTANCE (v again₁) indicate s to v₁Shortest path length, then have key₁- key= DISTANCE (u)+cos t (u, v₁)-DISTANCE(v₁) >=0, lemma must be demonstrate,proved.

The K paths acquired by backtracking algorithm are preceding K short paths.

It proves: it is by the step of recalling it is recognised that infinitely great if R is allowed to gather, i.e., key value in R is not deleted in algorithm Maximum element, then actually backtracking is to enumerate all feasible paths from s to t.It in this case, can by lemma two To know, the path of slave s to the t obtained for the first time by R.deleteMin () is shortest path, and second by obtaining Path from s to t is second shortest path, and so on.

At most save K paths in present R, as long as proving, in R unsaved path will not be certainly preceding K short path i.e. It can.By lemma one it is recognised that corresponding to the key of any one triple in R, its weight there are a paths that is bound to is key.When a certain paths are deleted from R by R.deleteMax (), centainly there are K element, and these elements in R Key value be respectively less than the weight in deleted path.Then, when a paths are deleted by R.deleteMax (), This paths will not be centainly one in preceding K short path.

In conclusion the path of slave s to the t obtained every time by R.deleteMin () belongs to K short circuit, and rear primary Obtained path length is more than or equal to the preceding path length once obtained.

Algorithm examples explanation

For example shown in fig. 6, it is assumed that starting point is 0, and terminal is 7, our target is two before finding from 0 to 7 Shortest path.

After by one-to-all step, the label of each point is as shown in Figure 7.

The variation for recalling step R is as shown in Figure 8.

It can be seen that algorithm has eventually found shortest path { 1,2,3,4,7 } and second shortest path { 1,2,3,6,4,7 }.

Different from the algorithm introduced before, city can be regarded as set a little, so this is actually between point set Preceding K shortest path searches for problem, moreover, because arrival time be it is uncertain, therefore, can only actually determine the point set that sets out, and Point of arrival collection is not can determine that.

K short path stroke planning algorithm includes the following:

1.K short stroke planning algorithm obtains k shortest path

Value (f)=t is chosen between while taking a bus in K short stroke problem_(n-1)a-t_1d, solution was extended in the time The initial weight that weight cos t (u, v)=TIME (the v)-TIME (u) on side is arranged in figure, and starting point is arranged is 0.

With { s₁, s₂... s_kIndicate point set of setting out, with { t₁, t₂... t_mIndicate sets of target points.One simplest Idea is exactly that point set is converted to a little.Two new point S and T can be increased as new source point and target point, and add side (S, s_i) 1≤i≤k and (T, t_i) 1≤i≤m, while the weight on these newly added sides is both configured to zero.Then point set { s₁, s₂... s_kArrive point set { t₁, t₂... t_mPreceding K short circuit path search be then converted to the preceding K short circuit path search of point S to T.For most The path P obtained afterwards=(S, v₁, v₂..., v_n, T), it is only necessary to remove the point S and T of head and the tail two sides.

It next is exactly the determination of the two point sets.City is indicated by a structural body, has recorded city in the structural body All in city, which set out, node and to be reached node (these nodes may adhere to different stations separately, but must be can starting station).So Set out point set determination it is very simple, as long as traversal city S₁Node set of setting out, find out all point u for meeting TIME (u) > t, The set that they form is exactly point set of setting out.It reaches point set then to need to be dynamically determined, for city S₂Arrival node set in Each point just add it in and reach in node set if it has been obtained during one-to-all apart from label.

Above-mentioned algorithm there are the problem of are as follows: needs are changed figure, add new side, and time expander graphs are as global Variable cannot be changed.It is found that during one-to-all, point S can be deleted parser from Priority Queues at the very start It removes, then will set out point set { s₁, s₂... s_kBe added in Priority Queues；In trace-back process, point T at the very start can be from R It deletes, then arrival point set { t₁, t₂... t_mBe added in R.So consideration is slightly modified to algorithm, point S and T is skipped.

In the part one-to-all, the behavior that joined S is imitated, no longer S is added in Priority Queues, directly just out Send out point set { s₁, s₂... s_kIt is added to Priority Queues, weight is set as 0.In backtracking part, initial R do not add T, arriving Up to point set { t₁, t₂... t_mIn point be all added in R, then start to recall.Because source point S is simultaneously not present, when recalling The standard that a paths are found in judgement is also required to change.As the point v ∈ { s of deletion₁, s₂... s_kWhen, it is believed that have found Yi Tiaolu Diameter.

2.K early reaches stroke planning algorithm and obtains the early arrival path K

Value (f)=t is chosen between while taking a bus in K short stroke problem_(n-1)a, solution is in time expander graphs The initial weight that weight cos t (u, v)=TIME (the v)-TIME (u) on side is arranged, and starting point v is arranged is TIME (v).

As K morning arrival problem with K short stroke problem is for the setting of side right value, therefore the algorithm of the two is similar. But due to the initial weight of starting point difference, this makes the difference for having certain between the two.Problem is early reached for K, is held very much If can be marked in one-to-all step, this label is bound to be TIME (v) easily proof arbitrary point v, and And the problem of there is no weight reductions.

It follows that not needing the weight for saving all nodes in one-to-all, close table only needs to record institute There is the state of node, greatly reduces the space complexity of algorithm.Moreover, because this process is reduced there is no node weight, The also available certain raising of the time complexity of algorithm.The backtracking part of algorithm is consistent with K short stroke problem.

3.K changes to stroke planning algorithm acquisition K less and changes to path less

It is chosen in K less transfer problemIts solution is arranged in time expander graphs The weight on sideAnd the initial weight that starting point v is arranged is 0。

Early arrival is just the same by algorithm and K, and only weight is different.

4. admission fee K low row journey planning algorithm obtains admission fee K low path diameter

For passenger propose K lowest fare query demand, provide be based on least bus change under the conditions of minimum ticket The strategy of valence.Due to the more train number of transfer coefficient, price affirmative is more expensive than the through train of ad eundem very much, and in booking hardly possible In terms of degree, transfer difficulty, scheme practicability, advantage is all no longer obvious, therefore based on the minimum strategy of admission fee under least bus change It is reasonable and practical.The strategy of K lowest fare to be obtained first uses least bus change algorithm by the strategy of preceding K ' least bus change (K ' is more than or equal to K and is integer) is found out, then admission fee engine is called to obtain the admission fee weight of each route, is finally counted It calculates, the lower strategy of K admission fee before being filtered out by admission fee.

The thus obtained minimum algorithm of admission fee is as follows:

(a) operation K changes to algorithm less, finds out the path of the most short transfer of preceding K ' item；

(b) weight of the preceding K ' paths searched out is calculated；

(c) path of the smaller weight of K item is required before.

5. the excellent stroke planning algorithm of multiple target pareto K obtains multiple target pareto K shortest path

The pareto optimization that journey time and number of transfer are only considered for multiple target pareto K shortest path, in more mesh It is chosen in the mark excellent route problem of pareto KSide right value is setV is transfer node

Algorithm and K short stroke are completely the same, it follows that as selection λ₁=0, λ₂It is exactly K short stroke problem when=1, is elected to Take λ₁=1, λ₂It is exactly that K changes to problem less when=0.

It is noted that K changes to weight setting less, new problem can be introduced in K less transfer problem: stop timeout issue and It tries to go south by driving the chariot north problem.

So-called stop timeout issue refers to that passenger has stopped the time more than one day in a station.It is assumed that timetable is such as Shown in following table:

Table at the time of 2 one hypothesis of table

Tianjin goes to Beijing to have two coastiongs, T1 and T2, and Beijing goes to Shanghai there was only a coastiong T3, but it can all be transported at this two days Row.Obviously, two paths of reasonable least bus change should be T1 or T2 to reach Beijing, then take the T3 on the same day from Beijing Go to Shanghai.But may actually obtain such two paths: take T1 and go to Beijing, then take the same day T3 go Shanghai or Beijing etc. one day, takes second day T3 and go to Shanghai.Obviously, although second scheme be in mathematical meaning correctly, It is unreasonable, it is necessary to be given up.

Solution: when searching some station S for the first time with dijkstra's algorithm, one, station time tag t is given (S), indicate that passenger can reach earliest at time t (S).In next search process, if some point u meets STATION (u)=S, TIME (u)-t (S) > 1440, algorithm directly skips u, is not arranged it apart from label.This can effectively solve to stop Timeout issue.But this method will also result in the loss of optimal solution.

So-called problem of trying to go south by driving the chariot north, that is passenger is first far from destination, then goes to destination.This either journey time Or admission fee expense is all relatively high, it is clear that it is unreasonable scheme, but its number of transfer may be fewer, thus This scheme can not be excluded in the algorithm.Such as, it is assumed that Beijing goes to Shanghai not have through train, then changing to is once most It is excellent as a result, first go to the Inner Mongol from Beijing then it is likely used only to providing, then go the scheme in Shanghai from the Inner Mongol.Though this scheme It is so correct in mathematical meaning, but for passenger, the quality of this scheme is very low, should be excluded.It can examine Worry limits search range using the longitude and latitude at each station, and the vehicle for not allowing passenger to take can be made far from target cities, but equally The loss of optimal solution out.

It is too long and try to go south by driving the chariot north problem that residence time can be well solved using multiobjective optimization.

It is that schedule planning system does not account for caused by journey time because of the appearance of both of these problems.When for stopping Between it is too long and try to go south by driving the chariot north problem, although the number of transfer of scheme is that the same, second-rate scheme frequently can lead to go The journey time is very long, in this way, second-rate scheme weight will be bigger than normal, to reach screening in the excellent problem of pareto K Purpose.

It should be noted that the quality of the solution obtained due to simple shortest route time and least bus change is too low, so real Simple shortest route time and least bus change are not used on border, but simulates both of these problems with multiple-objection optimization.

For K short stroke problem, λ is chosen₁=10, λ₂=1 is simulated.Why λ is not chosen₂=0, be because by Result is ranked up according to number of transfer.In view of journey time can be much larger than number of transfer, knot caused by this parameter selection Fruit is that journey time accounts for main influence, can the less scheme of preferential recommendation number of transfer when journey time is the same.

Problem is changed to for K less, chooses λ₁=1, λ₂=7200.Passenger can reach Anywhere within five days, so, This parameter selects meeting so that number of transfer is major influence factors, because journey time does not exceed 7200.And it is changing to In the same path of number, the shorter path of journey time can be preferential.

6. specified transfer city stroke planning algorithm

Sometimes, passenger may think that some city is first gone to do something, then go to destination again.In such case Under, the request of passenger will become (S₁, S₂, t₁, t₂, t₃, t₄, S₃, t₅, t₆), indicate that passenger wishes in moment (t₁, t₂) from city S₁ It sets out, in (t₃, t₄) reach city S₃, then in (t₅, t₆) from city S₃Leave for destination S₂.Target is then still and finds Preceding K shortest path.

In view of passenger generally can be in city S₃Do something, time passenger of this part not on the road, So passenger is in city S₃Residence time is calculated in the time loss of scheme.It is therefore intended that transfer city Algorithm can be split as two parts.

First part is exactly that common transfer K lacks algorithm, is found out respectively from S₁To S₃Preceding K short path and from S₃To S₂ Preceding K short path.This part is equivalent to calling, and transfer K lacks algorithm twice.

The problem of second part is then a combination of paths.The preceding K short path of above-mentioned two can have K*K altogether with combination producing Then paths select the smallest K item of weight as final result in this K*K paths.Use F_1kIt indicates from S₁To S₃ Preceding K scheme, F_2kIt indicates from S₃To S₂Preceding K scheme.

7. specified evacuation city stroke planning algorithm

Sometimes, passenger may be not desired to by some city.In this case, the request of passenger will become (S₁, S₂, t₁, t₂, S₃), indicate that passenger wishes in moment (t₁, t₂) from city S₁It sets out, purpose city is S₂, and passenger wish without Cross city S₃.Target is then the preceding K short path found out in this case.

In planning algorithm in front, when carrying out one-to-all, there is no the City attribution of consideration point, (point belongs to Which city).Due to being needed now without city S₃, therefore, need to carry out CITY (v) when one-to-all Consider.If CITY (v) is exactly S₃, then directly skipping point v.

In this way, during due to one-to-all, it is all to belong to S₃Node will not all be labeled, therefore backtracking when It waits, all paths will not be by city S₃, meet the requirements.

8. ticket journey planning algorithm

Ticket journey algorithm needs to call stroke planning algorithm and calls the database at storage seat, return the scheduled date, train number, The other remaining ticket information of seat, remaining ticket information and query result are returned simultaneously.

The planning of ticket journey includes two relatively independent parts, stroke planning and remaining ticket library inquiry.Stroke is same as above, and remaining ticket library is looked into Inquiry process is as follows:

Remaining ticket library stores the daily remaining ticket information of each coastiong, all seats and correspondence possessed including the train number Remaining poll mesh.Remaining ticket library stores these information using ORACLE database, and algorithm calls remaining ticket using fixed interface Information query function, query function are obtained remaining ticket information in real time by access database, return to all remaining ticket information. The inquiry of train is divided into ticket inquiry more than ticket inquiry and non-whole multiplexing train more than whole multiplexing train, for non-whole multiplexing train For, need to guarantee when inquiry initiating station along stringent equal, terminate station along between the genial farthest station in the station recently of ticketing along between； For whole process is multiplexed train, termination station is suitable constant along between the genial farthest station in the station recently of ticketing, and start-stop station is suitable can It is suitable to be more than or equal to the initiating station that inquires, by the had a surplus ticket information for the condition that meets by seat not Qiu He after, return the result.Remaining ticket The input parameter format of query function is as follows: full train number | the time of departure | initiating station is suitable | and it is suitable to terminate station | whole process multiplexing mark |.It returns The result parameter returned is JSON array, the Format Object of the inside storage are as follows: Xi Bie and corresponding remaining poll amount.

After journey inqiuiry, remaining ticket query interface is called, query function returns to real time information after voluntarily inquiring database, and Ticket information more than these and stroke planning are packaged return together afterwards, passenger is according to the stroke planning route and correspondence searched Remaining ticket information can voluntarily plan preferably route.

By taking the ticket journey planning algorithm under K is early reached as an example, detailed algorithm flow is as follows:

(a) it calls K early to reach algorithm, calculates in given departure time section, given starting point to the end arrives earliest Up to path；

(b) for every riding scheme of each path, remaining ticket information query interface is called, returns to remaining ticket information；

(c) remaining ticket information and corresponding route scheme are returned as a result.

9. Train delay algorithm

All algorithms before assume that timetable is right-on, that is to say, that in the case of whatsoever, if when Illustrate that the vehicle can arrive at a station in 18:00 on quarter table, then this coastiong is just bound to arrive at a station in 18:00.But in fact, this is assumed Be it is difficult to ensure that, no matter use how many method, Train delay is a realistic problem being difficult to avoid that, in some cases, It is late that result even in some schemes infeasible.Than timetable as shown in Table 2, if not occurring any accident, passenger is taken After D29 reaches Tianjin, D195 can be changed to and go to Shanghai.But if for some reason, D29 late hour, In this way, passenger, which can not just take D195, goes to Shanghai, if still recommending D29 to change to passenger after learning that D29 is late The scheme of D195, it is clear that be incorrect.Since Train delay is objective reality, so at must be to Train delay Reason, after learning that a certain coastiong is late, in next suggested design, just must take into account late situation.

In order to handle Train delay problem, it is necessary first to estimate the influence after a coastiong is late.This influence is can not Estimation, because a coastiong is late, it will lead to the variation of entire railway dispatching system, to influence other train numbers, Railway Bureau It may select to allow this coastiong to accelerate, so that the vehicle is not late in next website, it is also possible to which selection allows this coastiong Slow down or avoid other train numbers, to guarantee the normal operation of other train numbers.This brings very big to processing Train delay problem Difficulty, make the following assumptions:

Train delay is assumed: if a coastiong is t minutes late in station S, in next all stations, and the Che Douhui It is t minutes late.

It is that known late do later to figure updates in view of handling late situation in practice all, it is possible to which processing is every respectively Column Train delay situation, therefore model update method research can be carried out based on the hypothesis.

Next, should just handle late problem in time extended model.It should be noted that every in time expander graphs One point all represents train arrival or the generation for event of setting out, and when Train delay, corresponding node no longer can Represent the arrival of train and event of setting out, it is therefore desirable to be modified to these nodes and its corresponding side.Assuming that train is in station S It is t minutes late, arrival node of the train in station is indicated with v, and u indicates transfer node of the train in station, a city The chain of interior all transfer node compositions is known as changing to chain, then as follows to the processing of station S:

(a) TIME (v)=TIME (v)+t, TIME (u)=TIME (u)+t；

(b) for each side (k, u) ∈ E, this edge is deleted, if k is to reach node, k is added to one In set T；

(c) u is deleted from transfer chain；

(d) adjacent two nodes s, t are found in transfer chain, meets TIME (s) < TIME (u) < TIME (t), in s, U is inserted among t；

(e) for each of T element k, the smallest point t of TIME (t) is found in transfer chain and meets TIME (k) + TRANSFER (S) < TIME (t) is inserted into side (k, t).

In view of Train delay is assumed, it is only necessary to all stations of process be executed above-mentioned step to station S and following train It is rapid.

Third embodiment of the invention provide the railway stroke route planing method based on time extended model further include The time extended model suitable for Chinese Railway net based on building constructs combined airway railway traffic model.

The combined airway railway traffic model of building is as follows: for time expander graphs G=(V, E), wherein V represents vertex set, E ' generation Table line set, G have the property that

There are three types of nodes in 1.V: arrival node, set out node and transfer node；And have for any one point v ∈ V, v These labels: ATTR (v) shows that v is any node；TIME (v) indicate v represent Time To Event relative to it is earliest when Between the number of minutes；STATION (v) indicates station belonging to v；TRAIN (v) indicates full train number or aircraft shift representated by v；CITY (v) city belonging to v is represented；LEVEL (v) indicates layer belonging to v.

2. (if u, v) ∈ E, centainly there is TIME (u)≤TIME (v).Side in E is divided into five classes, as follows:

(a) side that node is directed toward transfer node is reached.The side represents the generation of transfer event；If two nodes are same In one station, transfer in station is indicated, which must can change to；Otherwise same city transfer is represented, the two stations must be can With city transfer.

(b) side that node is directed toward the node that sets out is reached.The side represents passenger and does not get off at the station, directly sit same coastiong from Open the station.

(c) transfer node is directed toward the side of transfer node.The side represents the arrival that passenger waits next coastiong in station.

(d) transfer node is directed toward the side for the node that sets out.The side represents vehicle and has been prepared for setting out, and passenger gets on the bus outbound.

(e) set out node to reach node side.The side represents traveller's and goes to the next stop.

Combined airway railway traffic model is as shown in Figure 9.

Model is divided into two layers.First layer is railway model；The second layer is model airplane.The inside of layer is all time expanded mode Type.Connection is carried out between layers in form that same city is changed to.That is: airport, airport are gone to by the transfer of same city in railway station It gos to the railway station also by the transfer of same city.In order to enable between layers can be with connection, increase and assume: all airports are all " major station " as destination and can change to city.

Therefore, simple railway model and simple model airplane are just merged into for a combined airway railway traffic model.When When handling railway planning, only scanned in first layer；When handling aviation planning only in the second layer Search；When handling combined airway railway traffic, all scanned in two layers.

Four embodiment of the invention provide the railway stroke route planing method based on time extended model further include The time extended model suitable for Chinese Railway net based on building with constructing empty iron through transport model.

Since bus is also based on timetable to provide service, with establishing one three layers of empty iron through transport to passenger Model, as shown in Figure 10.

It can be seen from the figure that bus is also modeled as a time expanded mode in three layers of time extended model Type, and being added in combined airway railway traffic model as new one layer then in empty iron one shares three layers in through transport model: iron Road floor, aircraft floor and bus floor.It is similar with combined airway railway traffic model, in order to enable communicating between layers, also assume that Connection is carried out by the way of the transfer of same city between bus layer and railway layer and aircraft layer, and selects some long-distance stations and makees For the station that can be changed to city.

When constructing bus model, it is assumed that starting time, the period of starting and starting route all for bus is determining, and from The A that stands goes whether station B has through bus.

In bus model, one station of each node on behalf.As soon as when thering is a bus to pass through between two stations, Increase a line between node.

Bus model are as follows: for time expander graphs G=(V, E), arbitrary node v ∈ V represents a station, any side (u, V) ∈ E has represented a bus slave station u and has removed station v.There may be multiple summits between two nodes.

Simple bus model is as shown in figure 11.

The empty iron of building through transport model it is as follows, model is divided into three parts: bus model, combined airway railway traffic model and model Connecting line.The connecting line of model is the side of some CFSs to CFS, if S₁Only bus, then (S₁, S₂) indicate from the station Take bus energy destination S₂, (S₂, S₁) indicate from S₂It sets out and takes bus and can reach the station.

Empty iron through transport time extended model it is as shown in figure 12.

Red line indicates, when inception point does not have train and aircraft, passenger's seating bus, which goes one, to be had train or fly The website of machine.Black line indicates, when terminus does not have train and aircraft, passenger takes bus and goes to terminus.

Fifth embodiment of the invention provides the optimization to algorithm, specific as follows:

The compression of 5.1 time expander graphs

In order to improve the efficiency of algorithm, the time suitable for Chinese Railway net that step S1 in embodiment 1 is constructed is extended Model optimizes, and specific Optimization Steps are as follows:

Then all nodes that sets out in erasing time expander graphs add corresponding side to guarantee the topological structure of figure not Become.Model after finally improving is as shown in figure 13.

The A that stands in figure is the major station that can be changed to, and the B that stands is the station for not allowing to change to.The knot removal that sets out all in figure, Corresponding transfer node is handled as node is set out.Then for each node u that sets out, if (v, u) ∈ E, (u, k) ∈ E deletes point u and associated all sides, then adds side (v, k), and the topological structure to guarantee figure is constant.

For time extended model, after having done improvement as above, the variation of figure scale is as shown in the table:

Influence of 3 model refinement of table to figure scale

It can be found that compact model (model after improvement), the number at figure midpoint reduce 33.3%, the number on side subtracts Lack 22.7%, this will greatly accelerate the response time.

Above-mentioned model is tested, is tested as shown in the table using 21 days Chinese Railway net scales.

21 days Chinese Railway network planning moulds in 4 model of table

K=15 is chosen, test carries out on railway model, has chosen λ in K short stroke problem₁=10, λ₂=1, test As a result as shown in figure 14.

It can be seen from the figure that the point of time expander graphs reduces 33.3%, while reducing 22.7% after compression.It is right In shortest route matter of time, 43.2% efficiency is improved.

The improvement of searching algorithm in 5.2 time expander graphs

Accelerating algorithm is mainly set about in terms of following three:

1.A* algorithm accelerates

In A* algorithm, most important is exactly the selection of A* table.In the A* algorithm of standard, need to each point between The shortest distance makes an estimation, and so as to form an A* table.But when figure is when being on a grand scale, this A* table is just shown Must be very big, need a large amount of exceptional space.So figure is divided into several parts, only stored between these parts most in A* table Short-range estimated value.Due to the information containing station in time expander graphs, it may be considered that according to the belonging station of point come to the time Expander graphs are divided.

Use S_iStation is indicated, with Dis tan c e (S_i, S_j) indicate station S_iArrive at a station S_jThe estimation of required time lower bound.Most open When beginning, if there is train slave station S_iDestination S_j, select wherein time-consuming least the time it takes as Dis tan c e(S_i, S_j).And if without train slave station S_iArrive at a station S_j, Dis tan c e (S is set_i, S_j) it is infinity.

Next, Floyd algorithm is carried out to obtained A* table, for any three stations S_i, S_j, S_k, meet following triangle not Equation:

Dis tan c e(S_i, S_j)+Dis tan c e(S_j, S_k)≥Dis tan c e(S_i, S_k)

Obviously, the estimated value of the A* table obtained in this way does not exceed actual value, thus can guarantee that optimal solution will not be lost. However, in order to solve city C_iTo city C_jK short path problem, it is contemplated that often have multiple stations in city, so this A* table It is unable to meet demand.It is slightly modified.With Dis tan c e (S_i, C_j) indicate station S_iTo city C_jShortest path Lower bound.Dis tan c e(S_i, C_j) determined by following formula:

It thus generates and solves the problems, such as the required A* table of this paper, be the estimation the time required to standing to city in table.

2. reducing target point set

From the backtracking part of algorithm, as long as that is in trace-back process it can be found that putting on K short path all has apart from label In would not lose solution.Therefore, when carrying out one-to-all, as long as all the points on K short path are marked, So can estimate the number of passes K ' found during one-to-all, as K ' > K, one-to-all process is just It can finish.

In dijkstra's algorithm, the preceding after may finally come before one after table in this way of lower each point can recorde Directly obtain shortest path.It, can be by recording multiple marks to each point in algorithmic procedure if shortest path more than one After obtaining all shortest paths before number identical.For time extended model, Target Station, which corresponds to multiple nodes, (indicates different Arrival time).This operation can be done to these nodes respectively, label range is estimated with this.Specific practice is as follows:

Whenever searching the arrival node v in a Target Station_iWhen, traverse this point it is preceding after table, so that it may obtain from Source point reaches the number of the shortest path of the point, is denoted as NUM (v_i).If dijkstra's algorithm label Target Station in node according to Secondary is v₁, v₂... v_mIfThen labeling algorithm stops.

After this label range estimation method, when searching for K=15, as long as the average Target Station that finds reaches section 5 to 6 points that point is concentrated can terminate label procedure, substantially increase efficiency of algorithm.

3. reducing time expander graphs

Subgraph G ' interior to time expander graphs G=(V, E)=(V ', E ') is scanned for.Wherein, V ' is in V within five days The set of all the points, and E ' is that in five days corresponding side in E.The departure time is set as t, if node v meets TIME (v)-t > 7200, just not to node v apart from label.

The improved example of searching algorithm:

It is as shown in the table using 21 days Chinese Railway network data scales:

Railway network scale in 5 A* algorithm of table

Model size is as follows:

Scale of model in 6 A* algorithm of table

By the acceleration of above method, the efficiency of algorithm is as shown in figure 15, for shortest route matter of time, selects λ₁= 10, λ₂=1；For least bus change problem, λ is selected₁=1, λ₂=7200, select K=15.

The acceleration effect of three steps more than it can be seen from upper figure is it is obvious that for K short stroke problem, acceleration efficiency is 54.7%, problem, acceleration efficiency 28.3% are changed to less for K.

Sixth embodiment of the invention compares optimum route search efficiency, specific as follows:

It is as shown in the table that 6.1 experiment conditions test hardware and software environment:

Table 7 tests environment

The scale of model is as shown in the table:

8 time of table expander graphs scale

The searching request format of passenger is (city of setting out reaches city, Earliest Start Time, at the latest departure time).It is real It tests and uses 440 group searching request for test data altogether, search for 15 schemes.

K shortest path algorithm experimental analysis under 6.2 4 kinds of targets

Test that the early arrival of K, K short stroke, K are changed to less and the efficiency of the low algorithm of admission fee K under time extended model.It calculates Dijkstra's algorithm in method has carried out altogether two groups of tests using Dial barrel experiments: test 1 be in time extended model into Row search, the result of railway model is simulated with this；Test 2 in combined airway railway traffic model to railway layer and aircraft layer simultaneously into Row search.Test data is 440 groups of requests that front is chosen, and test result is as shown in figure 16.

Algorithm response average value under four kinds of targets is as shown in the table:

The excellent road algorithm response average value of K under 9 four kinds of targets of table

Across comparison, it can be seen that the response efficiency of the low algorithm of admission fee K is minimum, this is because needing in the low algorithm of admission fee K Far beyond K scheme is found out, then these schemes are ranked up, have seriously affected the efficiency of algorithm.K changes to calculation less Method efficiency is far below K short stroke, this is because when choosing number of transfer is optimization aim, once search reaches certain A transfer node, then being just bound to traverse all transfer nodes after the transfer node, because of the side between transfer node Weight is 0, greatly expands search range, therefore to change to algorithm response efficiency less relatively low by K.K short stroke and K early reach algorithm Efficiency is highest, and the two algorithms only only have the initial weight of start node different, but K early reaches efficiency of algorithm To be much higher than K short stroke, the reason is that, K is early reached in algorithm, for arbitrary node v, the value in close table is exactly TIME (v), this makes the weight for not needing record close table interior joint, has saved a large amount of time.

Longitudinal comparison needs to consider two kinds of influences: popularization bring influences so that efficiency of algorithm is lower, because of test 2 need to simultaneously scan for railway layer and aircraft layer, this virtually increases the range of search；Optimal solution numerical value, which reduces bring, to be influenced So that efficiency of algorithm is got higher, this is because the speed of aircraft can be far longer than train, the reduction of optimal solution numerical value will lead to, therefore calculate Method can terminate earlier, to improve efficiency of algorithm.For K short stroke and K early reach, the influence of optimal solution numerical value reduction It is more obvious, therefore the efficiency of test 2 is higher than test 1.It is to be changed less based on K since admission fee K is low but for low for admission fee K Multiply, changed in algorithm less in K, if having searched a transfer node, all sections after this transfer node can be traversed Point, therefore in the low algorithm of admission fee K, the influence of popularization be it is prevailing, this makes the efficiency of test 2 lower than test 1.For K changes to algorithm less, two kinds of influences are almost balanced, therefore it is almost consistent with the efficiency of test 2 to test 1.

6.3 backtracking algorithms and the analysis of MS algorithm experimental

Comparison backtracking algorithm and MS algorithm K short stroke, K change to less and K early reach algorithm under efficiency, test exist It carries out on combined airway railway traffic model, but is scanned for only for railway layer, obtained experimental result is as shown in figure 17:

The average response time comparison for recalling algorithm and MS algorithm is as shown in the table:

Table 10 recalls algorithm and MS algorithm average response time compares

As can be seen from the above table, K short stroke, K are changed to less and K early reaches problem, backtracking algorithm is better than MS algorithm.

6.4 backtracking algorithms and the analysis of YEN algorithm experimental

Comparison recalls algorithm and YEN algorithm and changes to the efficiency under algorithm less in K short stroke, K, tests in combined airway railway traffic model Lower progress, but scanned for only for railway layer.Obtained test result is as shown in figure 18:

The average time comparison for recalling algorithm and YEN algorithm response is as shown in the table:

Table 11 recalls algorithm and YEN algorithm average response time compares

It can be seen that backtracking algorithm is better than YEN algorithm for K short stroke and K are changed to less.

Certain acceleration has also been carried out to YEN algorithm, A* algorithm is also used in its one-to-all process, reduces mesh The methods of punctuate collection is accelerated, and obtained test result is as shown in figure 19.

The comparison of the average response time of backtracking method and YEN algorithm is as shown in the table:

YEN algorithm average response time compares after table 12 is recalled algorithm and accelerated

It can see by upper table, similarly add even if being used in backtracking method during the one-to-all of YEN algorithm Fast means, the efficiency of backtracking method are still higher than YEN algorithm.

6.5 Train delay test of heuristics

The data for assuming a Train delay reach node for each of time expander graphs, it is assumed that have's Probability chooses the node, and thinks that vehicle representated by the node is 60 minutes late, finally has chosen 883 nodes, and think The vehicle of this 883 node on behalf is 60 minutes late, this 883 nodes are carried out with the processing of Train delay algorithm, response diagram As shown in figure 20.

It can be seen that the average response time of each column Train delay Processing Algorithm is musec order, ticket journey can satisfy Planning system practical application request.

The test of 6.6 ticket journey planning algorithms

After it joined remaining ticket information, due to requiring to inquire remaining ticket information to all schemes, so this will lead to Searching algorithm efficiency reduces.Test the efficiency of algorithm after remaining ticket inquiry is added.Test carries out on combined airway railway traffic model, but only Railway layer is scanned for.Test result is as shown in figure 21.

It can be seen from the figure that influence of the remaining ticket inquiry for efficiency of algorithm is it will be apparent that in order to more accurately analyze This influence, data preparation is at following table:

More than 13 ticket of table inquires the influence to algorithm

Inside the difference as can be seen that remaining ticket inquire and K low on admission fee K change to less algorithm influence it is almost the same, to the short row of K It is almost the same that journey and K early reach algorithm influence.This is because changing to inside the scheme low with admission fee K less in K, obtained solution is big Majority is only one scheme twice of transfer, and the number for needing to carry out remaining ticket inquiry in this way is fewer, therefore, remaining ticket inquire to this two A algorithm influences almost the same.And early reach in K in K short stroke algorithm, obtained solution is often changed to four or five times, thus So that the number of remaining ticket inquiry becomes more, so that the inquiry of remaining ticket is almost the same on the influence of the two algorithms, and make the two calculations Method efficiency reduces more obvious, since it is desired that the number for carrying out remaining ticket inquiry is more.But these influence at 10ms grades, It is acceptable in the application such as actual internet.

Claims (9)

1. a kind of railway stroke route planing method based on time extended model, which is characterized in that the method includes as follows Step:

Building is suitable for the time extended model of the railway network, constitutes the time expander graphs G=(V, E) of time extended model, and V is indicated Node set, E indicate line set, and node set includes arrival node, set out node and transfer node；And for any one section Point v ∈ V, v are with properties: ATTR (v) shows that v is any node；TIME (v) indicates that v represents Time To Event phase For the number of minutes of earliest time t；STATION (v) indicates the affiliated station v；TRAIN (v) indicates full train number representated by v； CITY (v) represents city belonging to v；If (u, v) ∈ E, centainly there is TIME (u)≤TIME (v), line set includes reaching Node be directed toward transfer node while, reach node be directed toward set out node while, transfer node be directed toward transfer node side, transfer section Point be directed toward set out node while and set out node be directed toward reach node while；

In time expander graphs, search follow node is directed toward the smallest road of weight in the path for reaching each side composition of node Diameter obtains optimal path.

2. the railway stroke route planing method based on time extended model as described in claim 1, which is characterized in that described Building be suitable for the railway network time extended model include the following steps:

It reads in station and urban information: establishing station and the index in city, stand and the relation table in city and can starting station table；

It reads in train and starts the period: extension timetable being obtained according to the period of starting of train, according to extension timetable settling time The blank of extended model；

Addition changes to side in station: the station S for allowing to change to for each arranges all transfer nodes for belonging to station S according to the time Sequence, the node after sequence are v₁,…,v_k, add side (v_i,v_i+1)1≤i≤k-1；The arrival node in S is traversed, for each Meet STATION (u)=S arrival node u, finds the smallest i and meet TIME (v_i)-TIME (u) >=TRANSFER (S), add Edged (u, v_i)；

Addition changes to side with city: stand S₁With station S₂Between allow with city change to, traversal station S₁In all arrival nodes, to each It is a to meet STATION (u)=S₁Arrival node, station S₂Transfer node sequence v₁,…,v_kIn, it finds the smallest i and meets TIME(v_i)-TIME (u) >=t, add side (u, v_i), wherein t is the least transfer time changed to city.

3. the railway stroke route planing method based on time extended model as claimed in claim 2, which is characterized in that described On time extended model, the smallest path of weight in the path formed follow node to each side for reaching node is searched for, is obtained Optimal path is taken to specifically include:

To side, weight is set；

It is scanned in time expander graphs with dijkstra's algorithm, obtains optimal path.

4. the railway stroke route planing method based on time extended model as claimed in claim 3, which is characterized in that described Method further includes obtaining K shortest path using backtracking algorithm on the basis of the optimal path of acquisition.

5. the railway stroke route planing method based on time extended model as described in claim 1, which is characterized in that described Method further includes that the combined airway railway traffic based on time extended model is constructed on the basis of being suitable for the time extended model of the railway network Model and/or empty iron ground through transport model.

6. the railway stroke route planing method based on time extended model as claimed in claim 3, which is characterized in that operation The data structure that dijkstra's algorithm uses includes Dial barrels, N member heap, Radix heap, Fib heap or binary heap.

7. the railway stroke route planing method based on time extended model as claimed in claim 4, which is characterized in that obtain K shortest path includes the following steps:

One-to-all: the optimal path weight for solving starting point to other points；

Backtracking: preceding K shortest path is obtained by reversely searching.

8. the railway stroke route planing method based on time extended model as claimed in claim 7, which is characterized in that described Obtaining K shortest path using backtracking algorithm further includes the optimization to K shortest path algorithm, including carries out compression or benefit to time expander graphs The one-to-all process in backtracking algorithm is accelerated with A* algorithm.

9. a kind of railway stroke route device for planning based on time extended model, which is characterized in that described device includes:

Model construction component: the model construction component is configured as the time extended model that building is suitable for the railway network, constitutes The time expander graphs G=(V, E) of time extended model, V indicate node set, and E indicates that line set, node set include reaching section Point, set out node and transfer node；And have any one node v ∈ V, v with properties: ATTR (v) shows which v is Kind node；TIME (v) indicates that v represents the number of minutes of Time To Event relative to earliest time t；STATION (v) indicates v institute Belong to station；TRAIN (v) indicates full train number representated by v；CITY (v) represents city belonging to v；If (u, v) ∈ E, one Surely there is TIME (u)≤TIME (v), line set includes that arrival node is directed toward the side of transfer node, arrival node is directed toward the node that sets out When, transfer node is directed toward transfer node, transfer node is directed toward the side for the node that sets out and the node that sets out is directed toward and reaches node Side；

Searching component: described search component is configured as in time expander graphs, and search follow node, which is directed toward, reaches node The smallest path of weight in the path of each side composition, obtains optimal path.