CN111651844A - Algorithm for calculating multiple bus paths between two bus stops - Google Patents

Algorithm for calculating multiple bus paths between two bus stops Download PDF

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CN111651844A
CN111651844A CN201911227817.1A CN201911227817A CN111651844A CN 111651844 A CN111651844 A CN 111651844A CN 201911227817 A CN201911227817 A CN 201911227817A CN 111651844 A CN111651844 A CN 111651844A
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path
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route
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CN111651844B (en
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陈�光
王三秀
崔跃利
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Taizhou University
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Abstract

The invention provides an algorithm for calculating a plurality of bus paths between two bus stops, which comprises the following steps in sequence when calculating the plurality of bus paths from one stop o to one stop d in a bus network: setting parameters; establishing a riding network NETB; establishing a pedestrian network NETW; calculating low-cost riding paths of a plurality of minimum-cost bus route sections from a station o to a station d based on the networks NETB and NETW; for each bus route, each bus route section in the route is replaced by each route section with the same bus getting-on and getting-off station to generate a new bus route, and then the bus routes passing through the same station for multiple times or the bus routes with high cost in the route are filtered; and for each bus taking path, marking each line section in the path by using each line name passing through the line section respectively to generate a new bus taking path containing the information of the specific bus taking line name, and keeping the obtained path as a result when the obtained path does not pass through the same bus line for multiple times.

Description

Algorithm for calculating multiple bus paths between two bus stops
Technical Field
The invention relates to the field of urban public transport network and network path calculation, in particular to an algorithm for calculating a plurality of bus paths between two bus stops.
Background
The public transport network is a common appearance mode for urban residents, and the development of the public transport network plays an important role in relieving urban traffic congestion and saving social operation energy consumption.
The basic units of the public transportation network are public transportation stops and public transportation lines, and passengers can arrive at a destination stop from a departure stop by taking one or more public transportation lines in the network coverage range. In addition, in order to save travel time and other costs, passengers often also can save the number of bus routes to be taken by a way of arriving at another nearby station from a certain station by walking in the bus travel process.
It is worth noting that in a medium and large-sized city public transportation network, a passenger often has multiple riding paths from a starting station to a destination station, that is, the selection of which lines the passenger specifically rides on, which stations of the lines get on or off the vehicle, which short-distance stations walk between, and the like in the traveling process is various. The reasons for this phenomenon are mainly: firstly, in order to ensure the accessibility between a coverage range and a plurality of stops, a public transportation network is often provided with more annular structures, namely, passengers can get back to the same stop by taking a public transportation or walking between short-distance stops from one stop; secondly, due to the consideration of the improvement of the transport capacity of the line section and the redundancy configuration, a plurality of bus lines are usually arranged between a pair of bus through stops in the bus network, namely, a passenger can select a plurality of different bus lines by taking one bus from one stop and arriving at another stop.
Nowadays, public transport network riding path algorithms applied to public transport travel navigation are widely researched and used in applications such as network maps, and the algorithms can calculate one or a few low-cost suggested riding paths from a travel starting point to a travel destination for passengers. Along with the increase of the demand of people on intelligent buses, the problem of prediction of space-time distribution of passenger flow in a bus network draws attention of people. Different from bus travel navigation, the bus traffic prediction method needs to fully consider each riding path possibly selected by a passenger when the passenger goes out, and can further give accurate traffic prediction of the bus network at different time intervals, different stops and line sections according to factors such as travel demand distribution, passenger travel behavior modes and the like. At present, research on calculating all riding paths possibly selected by passengers between a pair of bus stops is not fully developed, and the existing algorithm has some defects in the aspects of operation efficiency and the like. For example, multiple route transfers are often involved in traveling of a departure station far away from a destination station, according to a mathematical combination theory, the number of all reachable riding paths between a pair of stations and the number of route transfers in the paths are in a power law increasing relationship, and how to screen out all low-cost riding paths acceptable to passengers in a large reachable riding path set in a short time is a key problem to be solved.
In view of the above background, the present invention provides an algorithm for calculating multiple bus routes between two bus stops. The technical idea of the algorithm is as follows: the basic composition unit 'bus line section' in the riding path is hierarchically divided, the bottommost layer is called 'line section', and passengers can ride the line on one stop in one line and get off the line on another stop; the middle layer is a 'station line section', and one 'station line section' is a collective name of different 'line sections' passing through the same station; the highest layer is a 'direct line section', and one 'direct line section' is a collective name of different 'station line sections' with the same getting-on and getting-off stations. On the basis of the division, firstly, a line section with the minimum cost is used as a representative of a direct line section to simplify the public transport network, and a plurality of low-cost riding paths from a starting station to a target station, which only pass through the line section with the minimum cost, are calculated by adopting the ideas of path expansion and dynamic programming; then, respectively aiming at each riding path in the result set, replacing each minimum cost line section in the path by using each station line section corresponding to the direct line section to which the minimum cost line section belongs, and generating and reserving a plurality of low-cost riding paths passing through the station line sections; and finally, respectively aiming at each riding path in the result set, replacing each 'station line section' in the path by using each 'line section' corresponding to the 'station line section', and generating and reserving a plurality of low-cost riding paths passing through the 'line sections' as the result riding path set returned to the user.
Based on the above description, it can be seen that the proposed algorithm adopts a reduction and enlargement mapping mechanism (from a minimum cost "line segment" to a "direct line segment" to a "site line segment" and finally to a "site line segment") to reduce the complexity of the operation, and finally, a plurality of riding paths with lower traveling cost from a starting site to a destination site can be quickly given.
Disclosure of Invention
The invention provides an algorithm for calculating a plurality of bus paths between two bus stops, which comprises the following steps of 1-7 in sequence when calculating the plurality of bus paths from one stop o to one stop d in a bus network:
step 1: setting a parameter theta and a parameter phi which are larger than zero;
step 2: establishing a ride network NETB, wherein NETBi,jIs a set of public communication sides from a station i to a station j, and each communication side in the set is a public communication line segment [ i->…->tk->…->j]Wherein t iskThe k-th bus stop is a passing bus stop except an upper bus stop i and a lower bus stop j in the process of starting from the stop i, taking the route section and arriving at the stop j; at the same time, for each of the NETBsi,jEach connecting edge C in the system establishes a public traffic line name set LCThe set comprises all the bus route names of the bus route sections corresponding to the route C;
and step 3: establishing a pedestrian network NETW, wherein NETWi,jThe short-distance walking connecting edge from the station i to the station j is the shortest walking path with the walking distance from the station i to the station j smaller than theta;
and 4, step 4: on the basis of the network NETB and the network NETW, calculating a riding path set from the station o to all other stations, wherein the steps are 4.1-4.5:
step 4.1: establishing an initially empty ride path set OS; establishing an initially empty riding path set P for each station k except the station o in the networko,kAnd a variable C initially being positive infinityo,k
Step 4.2: traversing each neighboring site k of the site o in the network NETB, using the set NETBo,kMinimum cost in (E) connecting edgeo,kGenerating a ride path' o->Eo,k->k ", adding the path to the set Po,kAnd a collection OS;
step 4.3: traversing each neighbor site k of the site o in the network NETW, and using the edge NETWo,kGenerating a ride path' o->NETWo,k->k ", join the path to the set PSo,kAnd a collection OS;
step 4.4: when the set OS is not empty, sequentially and circularly executing the step 4.4.1 to the step 4.4.3:
step 4.4.1: taking out the least expensive ride path P from the set OSo,x
Step 4.4.2: traversing each neighbor station y of the station x in the network NETB, if the station y does not belong to the path Po,xThe passing site is at Po,xOn the basis of using the set NETBx,yMinimum cost in (E) connecting edgex,yGenerating a ride path 'P' from a station o to a station yo,x->Ex,y->y' when the cost of the path is less than Co,yAdd it to the PS set at + phio,yWith the set OS, when the cost of the path is less than Co,yTime update Co,yThe cost for that path;
step 4.4.3: traversing each neighbor station y of the station x in the network NETW if the station y does not belong to the path Po,xStations on the way, and Po,xThe last connecting edge of the route does not belong to the connecting edge of the NETW, and then the last connecting edge of the route is Po,xOn the basis of using the edge-connected NETWx,yGenerating a ride path 'P' from a station o to a station yo,x->NETWx,y->y' when the cost of the path is less than Co,yAdd it to the PS set at + phio,yWith the set OS, when the cost of the path is less than Co,yTime update Co,yThe cost for that path;
step 4.5: traverse each site k except site o, in set PSo,kThe cost of medium deletion is greater than Co,kA + Φ path;
and 5: traverse set PSo,dIn each route P, taking P as a blue book to pass through each bus passing through P and connecting edges Em,nUsing sets NETB respectivelym,nWhen the P1 does not pass through the same station for many times and the cost is less than Co,dAdding P1 to P at + phio,d
Step 6: establishing a riding path set PDS which is initially empty and traversing a set PSo,dIn each route P, taking P as a blue book, and respectively using a set L for each cross connecting edge C of the route PCMarking each line name in the PDS to generate a riding path PD containing information of the specific riding bus line name, and adding the PD into the PDS when the PD does not pass through the same bus line for multiple times;
and 7: the PDS is returned as the result set.
In the above steps, the cost of a bus connecting edge or a bus path is defined as (W/α)μ+X/β+Y/γ+(Z/)νWherein W is the number of passing bus lines, X is the length of passing bus lines, Y is the number of passing bus stations except the station where the bus gets on or off the bus, Z is the total walking distance, and α, β, gamma, mu and v are parameters greater than zero.
The invention has the beneficial effects that: the algorithm for calculating the multiple bus taking paths between the two bus stops can calculate all bus taking paths between a pair of bus stops according with parameter limitation quickly.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention. In the accompanying drawings, fig. 1 shows a schematic diagram of a public transportation network according to an embodiment of the present invention, wherein different bus stops are marked by circles with different numbers, different bus routes are marked by line segments with different patterns, and an ellipse with a dashed frame indicates that two bus stops inside the bus stops can realize non-co-stop transfer by short-distance walking.
Detailed Description
The invention is further described with reference to the accompanying drawings and an embodiment.
Example 1: referring to fig. 1, the steps of the algorithm provided by the present invention when calculating a plurality of riding paths from a station 1 to a station 9 are in sequence step 1 to step 7:
step 1: setting a parameter theta and a parameter phi which are larger than zero;
step 2: establishing a ride network NETB, wherein NETBi,jIs a set of public communication sides from a station i to a station j, and each communication side in the set is a public communication line segment [ i->…->tk->…->j]Wherein t iskThe k-th bus stop is a passing bus stop except an upper bus stop i and a lower bus stop j in the process of starting from the stop i, taking the route section and arriving at the stop j; at the same time, for each of the NETBsi,jEach connecting edge C in the system establishes a public traffic line name set LCThe set comprises all the bus route names of the bus route sections corresponding to the route C;
and step 3: establishing a pedestrian network NETW, wherein NETWi,jThe short-distance walking connecting edge from the station i to the station j is the shortest walking path with the walking distance from the station i to the station j smaller than theta;
and 4, step 4: on the basis of the network NETB and the network NETW, calculating a riding path set from the station 1 to all other stations, wherein the steps are step 4.1-step 4.5:
step 4.1: establishing an initially empty ride path set OS; establishing an initially empty riding path set P for each station k except station 1 in the network1,kAnd a variable C initially being positive infinity1,k
Step 4.2: traversing each neighboring site k of the site 1 in the network NETB, using the set NETB1,kMinimum cost in (E) connecting edge1,kGenerating a ride path '1' from a station 1 to a station k>E1,k->k ", adding the path to the set P1,kAnd a collection OS;
step 4.3: traverse site 1 atEach neighbor site k in the network NETW uses the edge-connected NETW1,kGenerating a ride path '1' from a station 1 to a station k>NETW1,k->k ", join the path to the set PS1,kAnd a collection OS;
step 4.4: when the set OS is not empty, sequentially and circularly executing the step 4.4.1 to the step 4.4.3:
step 4.4.1: taking out the least expensive ride path P from the set OS1,x
Step 4.4.2: traversing each neighbor station y of the station x in the network NETB, if the station y does not belong to the path P1,xThe passing site is at P1,xOn the basis of using the set NETBx,yMinimum cost in (E) connecting edgex,yGenerating a ride path 'P' from station 1 to station y1,x->Ex,y->y' when the cost of the path is less than C1,yAdd it to the PS set at + phi1,yWith the set OS, when the cost of the path is less than C1,yTime update C1,yThe cost for that path;
step 4.4.3: traversing each neighbor station y of the station x in the network NETW if the station y does not belong to the path P1,xStations on the way, and P1,xThe last connecting edge of the route does not belong to the connecting edge of the NETW, and then the last connecting edge of the route is P1,xOn the basis of using the edge-connected NETWx,yGenerating a ride path 'P' from station 1 to station y1,x->NETWx,y->y' when the cost of the path is less than C1,yAdd it to the PS set at + phi1,yWith the set OS, when the cost of the path is less than C1,yTime update C1,yThe cost for that path;
step 4.5: traverse each site k except site 1, in set PS1,kThe cost of medium deletion is greater than C1,kA + Φ path;
and 5: traverse set PS1,dIn each route P, taking P as a blue book to pass through each bus passing through P and connecting edges Em,nUsing sets NETB respectivelym,nWhen the P1 does not pass through the same station for multiple times and the cost is less than C, the connecting edges are replaced to generate a new riding path P11,dAdding P1 to P at + phi1,d
Step 6: establishing a riding path set PDS which is initially empty and traversing a set PS1,dIn each route P, taking P as a blue book, and respectively using a set L for each cross connecting edge C of the route PCMarking each line name in the PDS to generate a riding path PD containing information of the specific riding bus line name, and adding the PD into the PDS when the PD does not pass through the same bus line for multiple times;
and 7: the PDS is returned as the result set.
In the above steps, the cost of a bus connecting edge or a bus path is defined as (W/α)μ+X/β+Y/γ+(Z/)νWherein W is the number of passing bus lines, X is the length of passing bus lines, Y is the number of passing bus stations except the station where the bus gets on or off the bus, Z is the total walking distance, and α, β, gamma, mu and v are parameters greater than zero.
In the present embodiment, it is assumed that after step 4.5 is performed, the set P is1,9The method comprises the following riding paths:
(1)“1->[1->2->3->6]->6->[6->7->9]->9”;
(2)“1->[1->2]->2->NETW2,5->5->[5->6->7->9]->9”。
after step 4.5 is performed, the set P is completed1,9The method comprises the following riding paths:
(1’)“1->[1->2->3->6]->6->[6->7->9]->9”;
(2’)“1->[1->2->3->6]->6->[6->7->8->9]->9”;
(3’)“1->[1->2]->2->NETW2,5->5->[5->6->7->9]->9”;
(4’)“1->[1->2]->2->NETW2,5->5->[5->6->7->8->9]->9”。
in the above path, (1 ') and (2') are generated by (1) route segment replacement via route, and (3 ') and (4') are generated by (2) route segment replacement via route.
After step 5 is executed, the result set PDS includes the following riding paths:
(1 ")" 1- > [1- >2- >3- >6] (line 1) - >6- > [6- >7- >9] (line 2) - >9 ";
(2 ")" 1- > [1- >2- >3- >6] (line 1) - >6- > [6- >7- >9] (line 3) - >9 ";
(3 ")" 1- > [1- >2- >3- >6] (line 1) - >6- > [6- >7- >8- >9] (line 4) - >9 ";
(4”)“1->[1->2](line 1)>2->NETW2,5->5->[5->6->7->9](line 2)>9”;
(5”)“1->[1->2](line 1)>2->NETW2,5->5->[5->6->7->9](line 3)>9”;
(6”)“1->[1->2](line 1)>2->NETW2,5->5->[5->6->7->8->9](line 4)>9”。
In the above path, (1 ") and (2") are generated by the route segment line name label (1 '), and (3 ") is generated by the route segment line name label (2'), and (4") and (5 ") are generated by the route segment line name label (3 '), and (6") is generated by the route segment line name label (4').
The foregoing is illustrative of embodiments of the present invention and is provided for the purpose of clarity. Any modification and equivalent substitution made of the present invention within the spirit and scope of the claims will fall within the scope of the present invention.

Claims (2)

1. An algorithm for calculating multiple bus paths between two bus stops, characterized in that: the steps of calculating a plurality of riding paths from one stop o to one stop d in the public transport network are sequentially from step 1 to step 7:
step 1: setting a parameter theta and a parameter phi which are larger than zero;
step 2: establishing a ride network NETB, wherein NETBi,jA set of public connecting edges from site i to site j, wherein each connecting edge in the set is from site i to site jOne bus line segment [ i->…->tk->…->j]Wherein t iskThe k-th bus stop is a passing bus stop except an upper bus stop i and a lower bus stop j in the process of starting from the stop i, taking the route section and arriving at the stop j; at the same time, for each of the NETBsi,jEach connecting edge C in the system establishes a public traffic line name set LCThe set comprises all the bus route names of the bus route sections corresponding to the route C;
and step 3: establishing a pedestrian network NETW, wherein NETWi,jThe short-distance walking connecting edge from the station i to the station j is the shortest walking path with the walking distance from the station i to the station j smaller than theta;
and 4, step 4: on the basis of the network NETB and the network NETW, calculating a riding path set from the station o to all other stations, wherein the steps are 4.1-4.5:
step 4.1: establishing an initially empty ride path set OS; establishing an initially empty riding path set P for each station k except the station o in the networko,kAnd a variable C initially being positive infinityo,k
Step 4.2: traversing each neighboring site k of the site o in the network NETB, using the set NETBo,kMinimum cost in (E) connecting edgeo,kGenerating a ride path' o->Eo,k->k ", adding the path to the set Po,kAnd a collection OS;
step 4.3: traversing each neighbor site k of the site o in the network NETW, and using the edge NETWo,kGenerating a ride path' o->NETWo,k->k ", join the path to the set PSo,kAnd a collection OS;
step 4.4: when the set OS is not empty, sequentially and circularly executing the step 4.4.1 to the step 4.4.3:
step 4.4.1: taking out the least expensive ride path P from the set OSo,x
Step 4.4.2: traversing each neighbor station y of the station x in the network NETB, if the station y does not belong to the path Po,xThe passing site is at Po,xOn the basis of usingSet NETBx,yMinimum cost in (E) connecting edgex,yGenerating a ride path 'P' from a station o to a station yo,x->Ex,y->y' when the cost of the path is less than Co,yAdd it to the PS set at + phio,yWith the set OS, when the cost of the path is less than Co,yTime update Co,yThe cost for that path;
step 4.4.3: traversing each neighbor station y of the station x in the network NETW if the station y does not belong to the path Po,xStations on the way, and Po,xThe last connecting edge of the route does not belong to the connecting edge of the NETW, and then the last connecting edge of the route is Po,xOn the basis of using the edge-connected NETWx,yGenerating a ride path 'P' from a station o to a station yo,x->NETWx,y->y' when the cost of the path is less than Co,yAdd it to the PS set at + phio,yWith the set OS, when the cost of the path is less than Co,yTime update Co,yThe cost for that path;
step 4.5: traverse each site k except site o, in set PSo,kThe cost of medium deletion is greater than Co,kA + Φ path;
and 5: traverse set PSo,dIn each route P, taking P as a blue book to pass through each bus passing through P and connecting edges Em,nUsing sets NETB respectivelym,nWhen the P1 does not pass through the same station for multiple times and the cost is less than C, a new riding path P1 is generated in a mode of replacing each connecting edgeo,dAdding P1 to P at + phio,d
Step 6: establishing a riding path set PDS which is initially empty and traversing a set PSo,dIn each route P, taking P as a blue book, and respectively using a set L for each cross connecting edge C of the route PCGenerating a riding path PD containing information of the specific riding bus line name in a mode of marking each line name in the PDS, and adding the PD into the PDS when the PD does not pass through the same bus line for multiple times;
and 7: the PDS is returned as the result set.
2. The method of claim 1 for calculating multiple rides between two bus stopsThe algorithm of the vehicle path is characterized in that the cost of a bus connecting edge or a vehicle path is defined as (W/α)μ+X/β+Y/γ+(Z/)νWherein W is the number of passing bus lines, X is the length of passing bus lines, Y is the number of passing bus stations except the station where the bus gets on or off the bus, Z is the total walking distance, and α, β, gamma, mu and v are parameters greater than zero.
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