CN114564809B - Bus network optimization method considering current network structure - Google Patents
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Abstract
The invention discloses a bus network optimization method considering a current network structure, which comprises two parts of station optimization and network optimization, wherein the station optimization is carried out by constructing a 0-1 integer programming model, the selection and combination of stations are involved to reduce station redundancy, and the network optimization is carried out based on the bus network after the station optimization. In the network optimization part, the skeleton continuous edge and the secondary skeleton continuous edge of the current wire net are identified by combining the PageRank algorithm, and the weights of the skeleton continuous edge and the secondary skeleton continuous edge are adjusted so that more optimized wire nets pass through the skeleton continuous edge and the secondary skeleton continuous edge, thereby keeping the similarity and stability of the wire nets before and after optimization. The method is beneficial to implementation of a network optimization scheme, cannot cause excessive influence on resident traveling, can assist a public transport group to implement large-scale network optimization under the condition of keeping the whole network stable, reduces station redundancy, and improves resident traveling experience and public transport competitiveness.
Description
Technical Field
The invention relates to the technical field of public transportation information processing, in particular to a public transportation network optimization method considering a current network structure.
Background
With the development of social economy, the demands of residents on trips are increased and changed, the urban traffic flow is saturated, the traffic problem not only hinders the development of the economic society, but also brings great pressure and challenges to urban traffic planning and management. Good public transportation is a necessary condition for survival and healthy development of cities, and is an important means for solving the urban transportation problem. Ground public transport is an important component of urban public transport, and the foundation of ground public transport development is a public transport network carrying heavy passenger flow. Therefore, reasonable wire network planning can improve the efficiency and the service level of a public transportation system, scientifically and reasonably service the travel demands of residents and simultaneously reduce the transport resource waste, and has very important significance for society, enterprises and individuals.
Along with the continuous change of the time-space distribution of the resident trip, the public transportation network also needs to be continuously adjusted and optimized to reasonably configure public transportation resources, so that the operation efficiency of the public transportation system is improved. However, the large city public transportation network has the characteristics of numerous and complicated stations and multiple lines, and due to the problems of resident travel path dependence, enterprise operation, capital construction cost and the like, the current public transportation network structure needs to be considered in the optimization scheme, so that the implementation of the optimization scheme and the overall view of the optimization scheme do not influence resident travel.
Therefore, how to optimize the public transportation network as a whole is a problem to be solved by the person skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a bus network optimization method considering the current network structure, namely, the network has certain similarity and stability from the whole angle before and after optimization, thereby being beneficial to implementation and application of an optimization scheme and not causing excessive influence on resident traveling. The optimization method provided by the invention is divided into two parts of station optimization and network optimization, wherein the station optimization is used as a basis of subsequent network optimization, and relates to station selection and combination. Connecting the station optimized result from the first station to the last station according to the line, and obtaining a public transportation network for network optimization; in network optimization, combining a PageRank algorithm to identify a framework connecting edge, a secondary framework connecting edge and a common connecting edge of a current wire network, and adding alternative connecting edges by adopting a driving path planning function provided by an open-platform API; and finally, establishing a 0-1 integer programming model of network optimization and solving.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A bus network optimization method considering the current network structure comprises the following steps:
Step 1: acquiring line basic information, and constructing a bus network topology diagram which takes an actual physical space platform as a node and distinguishes the uplink and the downlink of a line; determining the range of a used line and a related station, and arranging basic information of the line; visually displaying a bus network;
Step 2: performing station optimization pretreatment to obtain a station optimization pretreatment result; determining a coverage rate verification area according to the actual space distribution condition of the bus stations, and determining the coverage rate verification area according to the actual space distribution condition of the bus stations so that the optimized coverage rate of 500 meters of the bus stations meets the national requirements by using national related documents to make certain regulations on the coverage rate of 500 meters of the bus stations in the region; selecting a plurality of pairs of stations with the same name and the same direction, calculating merging stations corresponding to the names of the stations by adopting a weighted average method, and generating a merging station set according to all the merging stations;
Step 3: constructing a platform optimization model, setting constraint conditions of the platform optimization model, and solving the platform optimization model by adopting an operation study solver or an intelligent algorithm according to a platform optimization pretreatment result to obtain a platform optimization result; an operation study solver or an intelligent algorithm is utilized to solve the optimal solution of the constructed platform optimization model, and the common operation study solver comprises Gurobi, cplex and the like; the constraint conditions comprise a station conservation constraint, a bus station conservation constraint, a station abandon constraint, a station merge constraint with the same name and the same direction, a 0-1 variable constraint and the like, and the value coefficient before each decision variable in the objective function of the station optimization model can be designed according to actual needs; the platform optimization model is a 0-1 integer programming model; determining the most suitable station conservation amount constraint according to the station conservation amount constraint and a station 500m coverage rate calculation result circulation verification mode;
Step 4: performing network optimization pretreatment based on the platform optimization result and the bus network topological graph to obtain a network optimization pretreatment result; the network optimization preprocessing comprises the steps of connecting stations according to a line to obtain a new bus network topology graph according to a station optimization result, defining each connecting edge weight w ij and node weight sw i in the new bus network topology graph according to requirements, obtaining a skeleton connecting edge and a secondary skeleton connecting edge of the current bus network topology graph by adopting a PageRank algorithm, and adding alternative connecting edges by adopting a driving path planning function provided by a Gaode open platform API.
Step 5: constructing a network optimization model, setting constraint conditions of the network optimization model, and solving the network optimization model by adopting an operation study solver or an intelligent algorithm according to the platform optimization result and the network optimization pretreatment result to obtain a final optimized bus network;
the network optimization model is a 0-1 integer programming model, and constraint conditions of the network optimization model comprise linear constraint, platform passing constraint, nonlinear coefficient constraint, complex line number constraint, 0-1 variable constraint and the like; the value coefficient before each decision variable in the objective function can be designed according to the weight of the edge node and the actual requirement.
Preferably, in the step 3, the platform optimization model is expressed as follows:
Max(∑i∈Icixi+2∑i∈Fcixi) (1)
wherein x i is a 0-1 variable indicating whether station i is selected; c i is the value coefficient of the i-th station; i represents a current bus stop set; f represents the calculated merging station set;
The station keeping amount constraint is expressed as:
s.t. ∑i∈(I∪F)xi≤a (2)
Wherein a is the number of stations after station optimization; the value a is used for limiting the number of optimized stations, but the requirement of the coverage rate of 500 meters of the stations is met, so that the determination of the value a is a repeated cycling process to find the most suitable value a;
bus station reservation constraints are expressed as:
wherein T is the first and last station set of all public transport lines
Station dropping constraints are expressed as:
Wherein B is a set of abandoned stations;
the homonymous and unidirectional station merge constraint is expressed as:
Wherein x nj represents a j-th station with the name n and the same name and the same direction, and x nf represents a calculated merging station; formula (5) represents that at most two stations with the same name and the same direction and a merging station are selected, and formula (6) and formula (7) represent that the merging station and any station with the same name and the same direction can only keep one station;
The 0-1 variable constraint is expressed as:
wherein, whether a station is selected is represented by a 0-1 variable x i, 0 represents non-selected, and 1 represents selected;
And solving the platform optimization model to obtain a platform optimization result, and screening the access selection platform.
Preferably, the network optimization preprocessing comprises orderly connecting stations in the station optimization result according to the screened selected stations by lines to obtain a new bus network topology diagram.
Preferably, defining a connecting edge weight w ij and a node weight sw i in the new public transportation network topological graph according to the requirement;
preferably, the specific process of obtaining the frame connecting edge and the secondary frame connecting edge of the current wire net by adopting the PageRank algorithm is as follows:
step 411: identifying important nodes in a state of running to be stable under network evolution by adopting a random browsing model of PageRank, thereby classifying the importance degree of continuous edges; the random browsing model definition for PageRank is as follows:
Wherein PR (u) represents the influence of node u; u is the node to be evaluated; b u is an incoming edge set of the node u; PR (v) represents the influence of a node; l (v) represents the number of outgoing edges of the node v; n represents the total number of nodes; d represents a damping factor, and is usually 0.85; the method comprises the steps of obtaining a relatively stable P scale value of each node, namely the influence of a final node in a network in a multi-iteration mode, starting a PageRank algorithm calculation process by taking a node weight sw i as a PR initial value of each node, and finally obtaining the influence of each node;
Step 412: dividing each node into important nodes or common nodes according to the influence of each node; the connecting edge between the two important nodes is a skeleton connecting edge, the connecting edge between the two common nodes is a common connecting edge, and the connecting edge between the important nodes and the common nodes is a secondary skeleton connecting edge;
And adjusting weights of the skeleton continuous edge and the secondary skeleton continuous edge, wherein the formula is as follows:
rwij＝α*wij (10)
wherein rw ij is the adjusted edge weight, namely the edge weight applied to the network optimization model; alpha is a set adjustment coefficient, and the values of the adjustment coefficients are set according to the classification of the frame continuous edge, the secondary frame continuous edge and the common continuous edge, so that the three types of continuous edge weights have a certain degree of distinction.
Preferably, the driving path planning function provided by the open platform API of the german is added with an alternative continuous edge, which comprises the following specific steps:
Step 421: screening out a connecting edge which is not in the current network and is formed by connecting the connecting edge and a non-current line separating station, wherein the difference value between the linear distance between two stations and the average linear distance between bus stations of the initial network before station optimization is within a set threshold value;
Step 422: the selected continuous edges are subjected to driving planning by adopting an open platform API, continuous edges in which the driving actual distance is within 1.25 times of the straight line distance are selected, and the continuous edges are considered to be in accordance with traffic rules and do not have the condition of far detour or turning around; obtaining an alternative connected edge set to be added; and setting the average value of all the edge weights in the network optimization model as the adjusted edge weight rw ij value of the alternative edge.
Preferably, a network optimization model is constructed by setting network constraints, wherein the network constraints comprise line constraints, platform path constraints, nonlinear coefficient constraints, complex line number constraints, 0-1 variable constraints and the like; the network optimization model is a 0-1 integer programming model;
The value coefficient before each decision variable in the objective function of the network optimization model can be designed according to the weight of the edge node and the actual requirement, and the objective function of the network optimization model is expressed as follows:
Min∑(i,j)∈Edgeset,k∈Linesetrwijxijk (11)
Wherein rw ij is the weight obtained after various continuous edge adjustment according to formula (10), x ijk represents whether continuous edge ij is in optimized line k, lineset represents line set, edgeset represents continuous edge set;
The line constraints are expressed as:
∑jxjik-∑jxijk＝-1,i∈{sourcek}，(i，j)∈Edgeset，k∈Lineset (13)
∑jxjik-∑jxijk＝1,i∈{targetk}，(i，j)∈Edgeset，k∈Lineset (14)
wherein source k represents the start station of line k, i.e., the first station of the line, target k represents the end station of line k, i.e., the last station of the line, lineset represents the line set, x ijk represents whether the border ij is in the optimized line k;
The station routing constraints are expressed as:
Wherein Lineset denotes a line set, edgeset denotes a link set, stopset denotes a station set, x ijk denotes whether a link ij is in an optimized line k;
The nonlinear coefficient constraint is expressed as:
Wherein d ij represents the actual path distance between the links ij obtained by the Goodyear API, road_dis k represents the shortest road distance between the first and last stations of the line k, and g represents the nonlinear coefficient specified in the model;
The complex line number constraint is expressed as:
wherein c ij represents the maximum number of complex lines which can be borne by the connecting edge ij, and can be set according to actual needs, and Lineset represents a line set;
The 0-1 variable constraint is expressed as:
a 0-1 variable x ijk is used to indicate whether the connecting edge ij is in the optimized line k, 0 indicates that the connecting edge ij is not in the optimized line k, and 1 indicates that the connecting edge ij is in the optimized line k;
and solving the network optimization model to obtain an optimized public transportation network.
Compared with the prior art, the invention discloses a bus network optimization method considering the current network structure, which divides the bus network optimization into two parts of platform optimization and network optimization, decouples the platform from the line, optimizes the platform and then optimizes the network. Meanwhile, the connected edges of the bus network topological structure are divided into skeleton connected edges, secondary skeleton connected edges and common connected edges by combining the PageRank algorithm, and more points of the optimized network are connected by the skeleton connected edges and the secondary skeleton connected edges, so that the network has certain similarity and stability before and after optimization, and the implementation of an optimization scheme is facilitated. The optimization method provided by the invention can be connected with a bus network evaluation system, and the bus network evaluation result can provide basis for calculating the edge and node weights and determining the value coefficient of the objective function in the optimization model.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of the method provided by the invention;
FIG. 2 is a diagram showing cyclic verification of station coverage and station coverage constraints provided by the present invention;
FIG. 3 is a schematic diagram of two classical distribution forms of the same-name and same-direction platforms provided by the invention;
FIG. 4 is a schematic diagram of a distribution diagram of 580 buses and 6446 stations according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a region in which a station optimizing section verifies a hold quantity constraint set in an embodiment provided by the present invention;
FIG. 6 is a diagram illustrating coverage of 500 meters for a regional bus station with different station coverage amounts according to an embodiment of the present invention;
FIG. 7 is a schematic diagram of a connective classification visualization in an embodiment of the present invention;
FIG. 8 is a diagram showing a comparison of the net before and after optimization in accordance with an embodiment of the present invention;
Fig. 9 is a schematic diagram of a 19-way bus network before and after optimization in accordance with an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention discloses a bus network optimization method considering a current network structure, which comprises the following specific steps:
S1: determining the range of a used line and a related station, arranging basic information of the line, and constructing a bus network topological graph which takes an actual physical space station as a node to distinguish the uplink and the downlink of the line; because the specific uplink and downlink paths of the public lines in the large city are not completely consistent, if the uplink and downlink paths are regarded as one line, certain errors are brought to the construction and subsequent optimization of the line network, so that a bus network topological graph which takes an actual physical space platform as a node and distinguishes the uplink and downlink paths is required to be constructed, and the bus network is more truly depicted;
S2: performing preparation work before station optimization, and performing station optimization pretreatment to obtain station optimization pretreatment results, wherein the preparation work comprises the steps of determining coverage rate verification areas and merging station set generation; in the platform optimization model, the determination of the platform conservation quantity constraint is performed in a mode of circularly verifying the coverage rate of the platform 500 meters in the area, so that the optimal platform conservation quantity constraint is obtained, and the flow is shown in figure 2. Therefore, a coverage rate calculation range needs to be defined according to the space distribution condition of the platform;
The invention refers to station merging, which means that stations A and B with the same name and the same direction are merged, the connection relation of A is added to B, and related information is updated by adopting a weighted average method, so that the merging station can be obtained. In large cities, a situation that a plurality of stations in actual physical space correspond to each other in the same name and the same direction is frequently caused, so that congestion caused by the fact that too many lines stop at the same place is avoided, certain station redundancy is brought, and whether the stations in the same name and the same direction need to be combined can be judged through a model so as to reduce the station redundancy;
The number and spatial distribution of the same-name and same-direction stations are different, and since the number of the same-name and same-direction stations is 2, which is a more common condition, and the distance relationship between the stations can be utilized to identify the same-name and same-direction stations under the condition that the distribution form of the stations is simplified and the stations are not dependent on a geographic base map, only the condition that the number of the same-name and same-direction stations is 2 is considered and the distribution is simplified into two distribution forms as shown in fig. 3:
one is that as shown in fig. 3 (a), A1 and A3 are stations with the same name and the same direction, A2 is an opposite station with the same name, the shortest distance is opposite, the distance between A1 and A2 is short, and the distance between A1 and A3 is long; as shown in fig. 3 (b), A1 and A3 are stations with the same name and the same direction, wherein A1 is located on a secondary road, A3 is located on a main road, the shortest distance is the same direction, A1 and A3 are closer, and A2 is a station with the same name and the opposite direction and is farther from A1 and A3;
Selecting a plurality of pairs of stations with the same name and the same direction according to actual needs, calculating to obtain merging stations corresponding to the names of the stations, collecting all merging stations as merging stations, and constructing merging station related data according to the actual needs;
If some evaluation indexes exist in each station, the merging station calculates the following process:
S21: screening out stations with the same name and the same direction and with index difference of more than 3 times (which can be set according to actual conditions) as a merging basis;
s22: in each pair of stations with the same name and the same direction, the connection relation of the stations with small passenger flow is overlapped with the stations with large passenger flow to obtain a merging station, and various indexes of the merging station are calculated by adopting a weighted average method of passenger flow;
S23: taking all calculated merging stations as a merging station set;
S3: constructing a platform optimization model; it is necessary to determine whether the station selects the optimization result, so that a 0-1 integer programming model can be constructed, and the model is shown in the formulas (1) to (8).
Max(∑i∈Icixi+2∑i∈Fcixi) (1)
s.t.∑i∈(I∪F)xi≤a (2)
(1) Optimization objective
The optimization goal of the platform optimization model is to select the appropriate platform based on the value coefficient c i under the condition of minimizing redundancy, so that the optimization direction is maximized, similar to the problem of aggregate coverage in operational research, as shown in the formula (1). Wherein x i is 0-1 variable, c i is a value coefficient of the ith station, I is a current bus station set, and F is a calculated merging station set. The meaning of the second half of the optimization target is that when the selected station is the merging station, the value coefficient in the optimization target is multiplied by 2 to balance the target value gap caused by the different numbers of stations before and after merging. Unselected stations in the optimization result can be represented as station hops or station withdrawals in the actual operation process. The value coefficient c i needs to be set according to the data and the actual requirement.
(2) Station keeping amount constraint
At present, bus stations mostly have redundancy problems, and in order to directly reduce station redundancy, the maintenance amount of the overall stations needs to be restrained. As shown in formula (2), wherein x i is 0-1 variable to indicate whether a station I is selected, a is the number of stations after station optimization, I is the current bus station set, and F is the calculated merging station set. This constraint directly limits the number of stations, but the optimized number of stations a needs to be verified according to the flow of fig. 2 to ensure that the coverage of 500 meters of the optimized regional stations meets the local requirements.
(3) Bus station reservation constraints
The bus station is a place where buses are parked and a collecting and distributing place of related staff, plays an important role in the operation process of a bus line, and the first and the last stations of the line are often close to or positioned at the bus station. In the invention, the first station and the last station of each line are regarded as bus stations, namely, the first station and the last station of each line are expected to be selected, so that the constraint is set as shown in a formula (3). Wherein x i is 0-1 variable, which indicates whether the station i is selected, and T is the set of the first station and the last station of all bus routes. In addition, the optimization result of the entering stations of the first station and the last station of each line is kept, so that the network optimization part is beneficial to being connected with the first station and the last station of each line in the network optimization part unchanged, and the stability of the network can be kept to a certain extent.
(4) Platform abandonment constraint
Some stations which obviously cannot be selected for optimization result can be directly removed according to actual needs, as shown in a formula (4). Wherein x i is a 0-1 variable indicating whether station i is selected and B is a set of dropped stations.
(5) Merging constraint for stations with the same name and the same direction
The merging constraint of the stations with the same name and the same direction is expected to automatically judge whether the merging is needed or the current situation is kept through an operation planning model, and the constraint is set as shown in the formulas (5) to (7). Wherein N represents a set of station names in the set of merging stations, only stations with the same name and the same direction number of 2 are considered in the present invention; x nj denotes the j-th station of the same name and direction, and x nf denotes the calculated merging station. Equation (5) indicates that at most two of the two co-directional stations and the merging station are selected, and equations (6) and (7) indicate that the merging station can only remain one with any one of the original co-directional stations.
(6) 0-1 Variable constraint
Whether a station is selected is indicated by a 0-1 variable x i, 0 indicates no selection, and 1 indicates selection, so that a constraint is set as shown in formula (8).
And solving the platform optimization model to obtain a platform optimization result.
S4: preparing work before network optimization is carried out;
after the platform optimization result is obtained, the platforms are orderly connected according to the lines, and a new bus network topology diagram after the platform optimization can be obtained.
And defining a calculation method of the edge weight w ij and the node weight sw i in the new bus network topological graph according to actual requirements. The calculated node weight and the edge weight can be considered as a result under a static network, and the public transportation network operates at moment, so that the conditions of all nodes in the network can be considered from the network evolution and operation angles, the importance of all edges under the network evolution and operation angles is obtained, and the whole public transportation network can maintain certain similarity and stability as long as the important edges are kept in the optimized public transportation network. In the invention, a random browsing model of PageRank is adopted to identify important nodes in the state that the network evolution runs to a stable state, so that the importance degree of the continuous edge is classified. The definition of the random browsing model of PageRank is shown as a formula (9), wherein PR (u) represents influence of the node u, u is a node to be evaluated, B u is an incoming edge set of the node u, PR (v) represents influence of the node, L (v) represents the number of outgoing edges of the node v, N represents the total number of the nodes, d represents a damping factor, and the average value is 0.85. The definition of the PageRank random browsing model is constructive, i.e. the definition itself gives the calculation method. At present, a more stable PR value of each node is obtained in a multi-iteration mode, and the PR value is the influence of the final node in the network. And starting the PageRank algorithm calculation process by taking the node weight sw i as the initial value of each node, and finally obtaining the influence of each node.
After the node influence is obtained, the important nodes and the common nodes can be divided according to the influence. The connecting edge between the two important nodes is a skeleton connecting edge, the connecting edge between the two common nodes is a common connecting edge, and the connecting edge between the important nodes and the common nodes is a secondary skeleton connecting edge. The skeleton connecting edge and the secondary skeleton connecting edge are important in the current network and play a role of 'compendium and tie' in a public transportation network. Therefore, the weights of the skeleton continuous edge and the secondary skeleton continuous edge can be adjusted so as to be as much as possible in the optimized wire net, thereby keeping certain similarity and stability of the wire net before and after optimization. Specifically, the adjustment method is as shown in the formula (10), and the alpha values of the connecting edges of different types are set, so that the frame connecting edges and the secondary frame connecting edges are enabled to appear in the optimized wire net as much as possible. And rw ij is the edge weight applied to the network optimization model.
rwij＝α*wij (10)；
In order to increase certain flexibility for network optimization, the connecting edges which are not in the current network structure need to be added, but the straight line distance of the newly added connecting edges needs to be consistent with the average straight line distance of the current bus network platform, and the corresponding actual paths need to be consistent with the current traffic regulations. In order to generate alternative continuous edges which accord with traffic rules more conveniently, the invention obtains the alternative continuous edges by means of the driving path planning function of the Goldd open platform, and the steps are as follows: (1) Screening out a connecting edge which is consistent with the average linear distance between bus stations of the initial line network and is not in the current line network, and ensuring that the connecting edge is also formed by connecting non-current line stations; the two stations are approximately equal, the difference value is within a certain threshold value, for example, the average linear distance between bus stations of an initial network is 600 meters, and the threshold value is set to be-100 m, so that the stations with the linear distance between the two stations within the range of 500-700 meters can be screened out; (2) And (3) taking the edge selected in the step (1) as a driving plan by adopting a Gaoder open platform API, and selecting the edge with the driving actual distance within 1.25 times of the straight line distance, wherein the edge is considered to be in accordance with traffic rules and is not in the condition of too far detour or turning around. Through the two steps, the alternative continuous edge set to be added can be obtained. The adjusted link weight rw ij value of the alternative link may be assigned as the mean of the current link weights rw ij.
S5: and constructing a network optimization model to obtain a final network optimization result. In the invention, whether the connecting edge is in a certain optimized line is determined, so that a 0-1 integer programming model can be constructed by utilizing 0-1 variables with three subscripts, and the model is shown in the formulas (11) to (18):
Min∑(i,j)∈Edgeset,k∈Linesetrwijxijk (11)
∑jxjik-∑jxijk＝-1,i∈{sourcek}，(i，j)∈Edgeset，k∈Lineset (13)
∑jxjik-∑jxijk＝1,i∈{targetk}，(i，j)∈Edgeset，k∈Lineset (14)
(1) Optimization objective
The optimization target of the network optimization model is to minimize the sum of weights of the integral continuous edges of the network under the condition of meeting constraint, so that the optimization direction is minimized, the optimization target is shown as a formula (11), wherein rw ij is the weight obtained after various continuous edge adjustment according to a formula (10), x ijk represents whether continuous edge ij is in an optimized line k, lineset represents a line set, and Edgeset represents the continuous edge set.
(2) Wire-forming constraint
The connection with the station optimizing part keeps the first station and the last station of each line unchanged, so that the first station and the last station can form lines. Considering the out-edge and in-edge cases of the nodes, the constraint is set as shown in equations (12) to (14). Where source k represents the start station of line k, i.e., the first station of the line, target k represents the end station of line k, i.e., the last station of the line, lineset represents the line set, and x ijk represents whether or not the border ij is in the optimized line k. For the stations of the non-line head and tail stations, the number of incoming sides and the number of outgoing sides are equal, for the originating station, the value obtained by subtracting the number of outgoing sides from the number of incoming sides is-1, and for the destination station, the value obtained by subtracting the number of incoming sides from the number of outgoing sides is 1.
(3) Station approach constraint
Since stations have been screened by station optimisation, it is necessary to ensure that each station has a line passing during the network optimisation phase, the constraint is set as shown in equation (15) which indicates that there is at least one line passing for each station. Wherein Lineset denotes a line set, edgeset denotes a link set, stopset denotes a station set, x ijk denotes whether a link ij is in the optimized line k.
(4) Nonlinear coefficient constraint
The nonlinear coefficient is in a reasonable range, so that the serious detour condition of the bus can be avoided, and the good nonlinear coefficient is favorable for improving the traveling experience of passengers. The denominator of the nonlinear coefficient definition in the invention adopts the shortest road distance between the head station and the tail station, can reflect the degree of the deviation of the line from the shortest path of the road network, and is set as shown in a formula (16). Where d ij denotes the actual path distance between the links ij obtained by the GoldAPI, road_dis k denotes the shortest road distance between the first and last stations of line k, and g denotes the nonlinear coefficient specified in the model.
(5) Complex line number constraint
In the actual operation process of buses, the number of public lines between two stations is related to the road carrying capacity, the surrounding traffic conditions and the number of resident trips. If the road carrying capacity of the actual path between the two stations is poor and the actual path is not located in the area with higher travel demand, the arrangement of too many bus routes between the two stations causes resource waste and the problems that the road sections are blocked and the like possibly caused by the stop of more buses at the stations during commuting peaks, therefore, the number of the compound lines between the two stations needs to be limited to a certain extent, and the constraint is set as shown in a formula (17). c ij represents the maximum number of complex lines that can be borne by the connecting edge ij, and can be set according to actual needs, and Lineset represents a line set.
(6) 0-1 Variable constraint
The invention adopts a 0-1 variable x ijk to indicate whether the continuous edge ij is in the optimized line k, 0 indicates that the continuous edge ij is not in the optimized line k, and 1 indicates that the continuous edge ij is in the optimized line k, so that constraint is set as shown in a formula (18).
And solving the model to obtain the optimized public transportation network.
Examples
In this embodiment, a public line network comprising 580 non-loop public lines and 6446 physical stations is selected, and is optimized. Fig. 4 shows the bus route distribution and the station distribution used in the example, fig. 4 (a) shows 580 bus route distribution diagrams, and fig. 4 (b) shows 6446 station distribution thermodynamic diagrams.
In this embodiment, the value coefficient c i and the obsolete station set B in the station optimization model, the merge station set F, the edge weight w ij and the node weight sw i in the network optimization, the rw ij used for solving the edge weight after adjustment and the maximum complex line number c ij of each edge have been calculated according to the actual needs and the data conditions.
Firstly, optimizing the platform, and defining a verification range of the coverage rate of the restraint of the maintenance quantity according to the actual distribution condition of the platform, as shown in a red line frame part in fig. 5. The lower boundary of the area is a first line of 'Che Gongzhuang street-north of the stadium of workers', the upper boundary is five loops, and the area of the area is 230.02 square kilometers. The coverage rate of the current station 500 m in the area is 83.95%, and the coverage rate of the station 500 m in the area after optimization is more than 82% (the average value in the city).
And finally determining that the retention constraint is 6280 through the cyclic verification of the retention amount of the station and the coverage rate of the regional station of 500 meters, wherein the retention amount of the station exceeds 96%, the coverage rate of the regional station of 500 meters is 83.26%, and 8 merging stations are selected exceeding the average level of the city. According to the coverage rate of 500 meters of the regional bus station under different station keeping amounts shown in fig. 6, when the station keeping amount is 6280, the coverage rate of 500 meters of the regional bus station is greatly improved, and at the moment, not only the redundant station with poor evaluation can be removed, but also the coverage rate of 500 meters can be kept higher. Most stations without the selected optimization result pass through one to two lines, the average peripheral speed of the stations is 7.56km/h, and the average station commute flow is only about 300 people, so that the station optimization model provided by the invention can effectively screen worse stations so as to improve the bus network. The unselected stations can be processed according to the station jump in the actual operation process of the line. The relevant constant and variable descriptions of the platform optimization model are shown in table 1.
Table 1 station optimization model related constant and variable description
| Constant or variable sign | Meaning of |
| I | Current actual bus station set |
| F | The calculated merging station set |
| T | First and last station set of all public transport lines |
| B | Discarding station set |
| N | Merging station name sets in station set |
| a | Number of stations after station optimization |
| ci | Obtaining the value coefficient of the ith station according to the data and the actual demand |
| xi | 0-1 Variable indicating whether the ith station is selected |
| xnj | The jth station with the name n and the same name and same direction |
| xnf | Merging station calculated by homonymous stations with n |
And (3) performing network optimization on the basis of the network after the station optimization. Substituting the calculated node weight sw i into the PageRank algorithm and setting the damping factor to be 0.85 to obtain the influence of each station. Stations with a pre-impact ranking 660 (approximately 10.5% of all stations) are considered important stations for the current net. The frame binder, the secondary frame binder and the common binder of the current wire network are determined based on 660 important stations, and the result is shown in fig. 7, wherein the result is shown in fig. 7 (a) is the frame binder, fig. 7 (b) is the secondary frame binder, and fig. 7 (c) is the common binder, wherein the frame binder has 542 pieces, the secondary frame binder has 1923 pieces, the common binder has 5958 pieces, and the total of 8423 pieces of binder. From fig. 7, it can be seen that the skeleton border grabs the state-to-country commuter corridor and the gyros-to-guancun commuter corridor of the current net well, and a certain number of skeleton borders exist in the urban area and the suburban area; the secondary skeleton links include, in addition to other links in the direction of the two commuting corridors, more links between stations in the urban area. According to the proposed alternative edge generation method, 400 alternative edges are added into the net. The straight line distance of the alternative continuous edges is between 400 meters and 600 meters, and the actual driving path distance is less than 1.25 times of the straight line distance.
To sum up, currently, 8823 links are used, 580 lines are generated under the condition that the head and the tail of the lines are kept unchanged, so that a network optimization model is constructed, and the aim is to minimize the weight sum of the links in the network. After about 400 ten thousand iterative solution calculations, the target value of the optimized net obtained by solving at the gap value of 0.0068% is 356845, and the target value of the current net is 419817, so that the optimized net is optimized by 15% compared with the current net target value, and the total of 7613 different connecting edges are used. The network optimization related constants and variable descriptions are shown in table 2;
table 2 network optimization related constants and variable description
| Constant or variable sign | Meaning of |
| Edgeset | Edge set |
| Lineset | Line set |
| Stopset | Bus stop set |
| sourcek | Line k starting station |
| targetk | Terminal station of line k |
| cij | Maximum number of complex lines of the connecting edge ij |
| dij | Actual path distance between links ij |
| rwij | Corresponding weight of continuous edge ij in network optimization model |
| road_disk | Shortest road distance between first and last stations of line k |
| g | Nonlinear coefficients specified in a model |
| xijk | 0-1 Variable, indicating whether the edge is in the optimized line |
As shown in fig. 8 (a) which shows the distribution diagram of the net before optimization, fig. 8 (b) which shows the distribution diagram of the net after optimization, fig. 8 (c) which shows the comparison distribution diagram of the net before and after optimization, the whole net before and after optimization can be found to be similar by comparing the net before and after optimization in fig. 8, the communication corridor from the general state to the national trade and the communication corridor from the gyros to the Zhongguancun can be marked, and part of suburban lines are completely consistent; the line focusing in urban areas has a certain degree of difference, and the net optimization flow provided by the invention can be considered to achieve the purposes of 'overall stability, redundancy removal and net optimization'. The optimized wire net is similar to the current wire net to a certain extent from the whole angle, so that the optimized wire net can be considered to not cause excessive influence on the traveling of residents, and meanwhile, the application and implementation of an optimization scheme are facilitated due to the fact that the current wire net is referenced.
Fig. 9 shows a comparison of the lines before and after the optimization by taking 19 lines (zoo terminal station-delrin district) as a single line example, fig. 9 (a) shows the line before the optimization of 19 lines, fig. 9 (b) shows the line after the optimization of 19 lines, and fig. 9 (c) shows the comparison diagram before and after the optimization, so that the head station and the tail station of the line before and after the optimization are not changed and most of the paths are relatively consistent, and only one part is obviously changed. Before optimization, the line is routed through 23 stations in total; after optimization, the line passes through 21 stations in total, and 19 optimized lines (zoo hub station-delrin district) skip the station of the exhibition hall and are different from the original line in the section of 'Dongkou-the Temple of Moon park in two-inner ditch'. The sum and the average value of the weight coefficients rw ij of 19 paths (zoo terminal station-delrin cells) for the network optimization model before and after optimization are calculated, 22 continuous edges are found in the path before optimization, the sum of the weight coefficients rw ij of all continuous edges for the network optimization model is 629.616, and the weight coefficient of the network optimization model of each continuous edge is 28.62; after optimization, the line has 20 continuous edges, the weight coefficient rw ij and 552.483 of the network optimization model of all continuous edges are improved compared with the prior optimization, and the average weight coefficient of the network optimization model of each continuous edge is 27.62, so that an optimization scheme of 19 paths (zoo terminal station-delphine district) can be considered to be reasonable and convenient to apply and implement.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (3)
1. The bus network optimization method taking the current network structure into consideration is characterized by comprising the following steps of:
Step 1: acquiring line basic information, and constructing a bus network topology diagram which takes an actual physical space platform as a node and distinguishes the uplink and the downlink of a line;
step 2: optimizing pretreatment is carried out on the platform to obtain a platform optimizing pretreatment result;
step 3: constructing a platform optimization model, setting constraint conditions of the platform optimization model, and solving the platform optimization model according to a platform optimization pretreatment result to obtain a platform optimization result;
Station constraint conditions comprise station conservation constraint, bus station conservation constraint, station disuse constraint, homonymous and same-direction station merging constraint and 0-1 variable constraint; the platform optimization model is a 0-1 integer programming model;
the objective function of the station optimization model is expressed as:
Max(∑i∈Icixi+2∑i∈Fcixi) (1)
Wherein x i is a 0-1 variable, indicating whether station i is selected; c i is the value coefficient of the i-th station; i represents a current bus stop set; f represents a merging station set; the value coefficient before each decision variable in the objective function of the platform optimization model is set according to actual needs;
The station keeping amount constraint is expressed as:
s.t.∑i∈(I∪F)xi≤a (2)
wherein a is the number of stations after station optimization;
bus station reservation constraints are expressed as:
Wherein T is a set of first stations and last stations of all public transport lines;
Station dropping constraints are expressed as:
Wherein B is a set of abandoned stations;
the homonymous and unidirectional station merge constraint is expressed as:
Wherein x nj represents a j-th station with the name n and the same name and the same direction, and x nf represents a calculated merging station; formula (5) represents that at most two stations with the same name and the same direction and a merging station are selected, and formula (6) and formula (7) represent that the merging station and any station with the same name and the same direction can only keep one station;
The 0-1 variable constraint is expressed as:
wherein, whether a station is selected is represented by a 0-1 variable x i, 0 represents non-selected, and 1 represents selected;
Solving the platform optimization model by adopting an operation study solver or an intelligent algorithm to obtain a platform optimization result;
Step 4: performing network optimization pretreatment based on the platform optimization result and the bus network topological graph to obtain a network optimization pretreatment result;
The network optimization pretreatment comprises the steps of connecting stations according to a line to obtain a new bus network topological graph according to a station optimization result, setting each connecting edge weight w ij and node weight sw i in the new bus network topological graph according to requirements, calculating a skeleton connecting edge and a secondary skeleton connecting edge of the current bus network topological graph by adopting a PageRank algorithm, and adding alternative connecting edges;
The specific process of obtaining the frame connecting edge and the secondary frame connecting edge of the current wire net by adopting the PageRank algorithm is as follows:
step 411: identifying important nodes in a state of running from network evolution to a stable state by adopting a random browsing model of PageRank, and classifying the importance degree of the continuous edges; the random browsing model of PageRank is as follows:
Wherein u is the node to be evaluated; PR (u) represents the influence of the node u to be evaluated; b u is an incoming edge set of the node u to be evaluated; PR (v) represents the influence of node v; l (v) represents the number of outgoing edges of the node v; n represents the total number of nodes; d represents a damping factor; the PR value of each node is obtained through multiple iterations and is used as the influence of the node in the network, the node weight sw i is used as the PR initial value of each node to start the PageRank algorithm calculation process, and finally the influence of each node is obtained;
step 412: dividing each node into important nodes or common nodes according to influence of each node, dividing the connecting edges according to the nodes, wherein the connecting edges between the two important nodes are skeleton connecting edges, the connecting edges between the two common nodes are common connecting edges, and the connecting edges between the important nodes and the common nodes are secondary skeleton connecting edges;
And adjusting weights of the skeleton continuous edge and the secondary skeleton continuous edge, wherein the formula is as follows:
rwij＝α*wij(10)
Wherein rw ij is the adjusted edge weight, which is used as the edge weight in the network optimization model; alpha is a set adjustment coefficient;
step 5: constructing a network optimization model, setting constraint conditions of the network optimization model, and solving the network optimization model according to the platform optimization result and the network optimization pretreatment result to obtain a final optimized bus network;
Constructing a network optimization model by setting network constraint conditions, wherein the network constraint conditions comprise line formation constraint, platform passing constraint, nonlinear coefficient constraint, complex line number constraint and 0-1 variable constraint; the network optimization model is a 0-1 integer programming model;
The value coefficient before each decision variable in the objective function of the network optimization model is set according to the edge weight, the node weight and the actual requirement, and the objective function of the network optimization model is expressed as follows:
Min∑(i,j)∈Edgeset,k∈Linesetrwijxijk (11)
Wherein rw ij is the edge weight after various edge adjustment obtained according to (10); x ijk represents whether the border ij is in the optimized line k; lineset denotes a line set; edgeset denotes a set of conjoined edges;
The line constraints are expressed as:
∑jxjik-∑jxijk＝-1,i∈{sourcek},(i,j)∈Edgeset,k∈Lineset (13)
∑jxjik-∑jxijk＝1,i∈{targetk},(i,j)∈Edgeset,k∈Lineset (14)
Wherein source k represents the starting station for line k; target k represents the destination station for line k; x ijk represents whether the border ij is in the optimized line k;
The station routing constraints are expressed as:
wherein Stopset denotes a set of stations; x ijk represents whether the border ij is in the optimized line k;
The nonlinear coefficient constraint is expressed as:
Wherein d ij represents the actual path distance between the edges ij obtained by the open platform API; road_dis k represents the shortest road distance between the first and last stations of line k; g represents nonlinear coefficients set in the network optimization model;
The complex line number constraint is expressed as:
wherein c ij represents the maximum number of complex lines that the connecting edge ij can bear;
The 0-1 variable constraint is expressed as:
a 0-1 variable x ijk is used to indicate whether the connecting edge ij is in the optimized line k, 0 indicates that the connecting edge ij is not in the optimized line k, and 1 indicates that the connecting edge ij is in the optimized line k;
And solving the network optimization model by adopting an operation study solver or an intelligent algorithm to obtain the final optimized public transportation network.
2. The method according to claim 1, wherein in the step 2, the platform optimization preprocessing result includes determining coverage rate verification area according to actual distribution condition of the platform, and generating a merging platform set; and determining coverage rate verification areas according to the spatial distribution of the stations, selecting a plurality of pairs of stations with the same name and the same direction, calculating merging stations corresponding to the names of the stations by adopting a weighted average method, and generating a merging station set according to all the merging stations.
3. The bus network optimization method considering the current network structure according to claim 1, wherein the driving path planning function provided by the open platform API of the german is added with an alternative connecting edge, which comprises the following specific steps:
Step 421: screening out the connecting edges which are not in the current network and are formed by connecting the screened connecting edges with non-current line separating stations, wherein the difference value between the linear distance between two stations and the average linear distance between bus stations of the initial network before station optimization is within a set threshold value;
Step 422: adopting a Gaoder open platform API to make driving planning for the selected connecting edges, and selecting the connecting edges with driving actual distances within a set multiple of the linear distances as alternative connecting edges to form alternative connecting edge sets; and setting the average value of all the edge weights in the network optimization model as the adjusted edge weight rw ij of the alternative edge.
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