CN115187158A - Rapid composite transport path planning method with limited loading and unloading times - Google Patents

Rapid composite transport path planning method with limited loading and unloading times Download PDF

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CN115187158A
CN115187158A CN202210673769.4A CN202210673769A CN115187158A CN 115187158 A CN115187158 A CN 115187158A CN 202210673769 A CN202210673769 A CN 202210673769A CN 115187158 A CN115187158 A CN 115187158A
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tuple
loading
path
unloading times
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卢文联
陈发君
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Fudan University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/08—Logistics, e.g. warehousing, loading or distribution; Inventory or stock management
    • G06Q10/083—Shipping
    • G06Q10/0835—Relationships between shipper or supplier and carriers
    • G06Q10/08355—Routing methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem

Abstract

The invention provides a rapid composite transport path planning method with limited loading and unloading times, which is used for outputting the shortest path between vertexes under the constraint condition of the appointed maximum loading and unloading times. The method increases the limit on the loading and unloading times on the basis of the Lewis algorithm, and realizes the rapid composite transportation path planning algorithm under the condition of limited loading and unloading times. Compared with the existing algorithm, the method for planning the rapid composite transport path not only solves the problem of solving the shortest path in composite transport, but also flexibly realizes the planning of the rapid composite transport path with limited loading and unloading times from the viewpoint of loading and unloading times under the condition of not introducing additional calculation complexity, reduces the cost of composite transport, provides convenience for composite transport and has higher applicability.

Description

Rapid composite transport path planning method with limited loading and unloading times
Technical Field
The invention belongs to the field of path planning, and particularly relates to a rapid composite transport path planning method with limited loading and unloading times.
Background
In the planning of the composite transportation path, more than two transportation modes exist, and the switching between different transportation modes requires loading and unloading operation, for example, the connection between road transportation and railway transportation requires the loading and unloading operation at a train station. At present, the general practice is to convert the handling operation into the cost of path planning, if the objective is to find the shortest path, the cost is converted into the length of the path, if the objective is to find the fastest path, the cost is converted into the time, and then the extended Dijkstra algorithm is used for path planning. However, in actual operation, the handling overhead is not a good measure, and is influenced by many factors, and users want to limit the handling times when they demand more.
Dijkstra algorithm [1 ]]Is an algorithm for solving the shortest path between two vertices in a network, the computational complexity without considering a special data structure is O (n) 2 ) The computational complexity is increased to O (m + nlog (n)) using heap structure-optimized ordering. The Dijkstra algorithm cannot solve the path planning problem in composite transportation, the length attribute of edges is mainly utilized, the path planning problem is accumulated and calculated in a network topological structure, the minimum value reaching a vertex is selected as the length of the shortest path, and therefore the vertex of each mark in the Dijkstra algorithm only has one shortest path value starting from a starting point.
The Dijkstra algorithm limits that each mark vertex only stores one optimal shortest path value, however, in the composite transport network, the shortest path values reaching the same position are different after different numbers of loading and unloading processes in different transportation ways, so the Dijkstra algorithm cannot be used for solving the composite transport path planning problem with limited loading and unloading times.
And Kirby-Potts expansion [2] expands each vertex in the road network into a plurality of virtual vertices according to different arrival or departure transportation modes, and each virtual vertex only allows one arrival or departure transportation mode, so when the Dijkstra algorithm is used for solving, the shortest path marked by the virtual vertex is the shortest path to the node by using the transportation mode, and cannot be other transportation modes. The Kirby-Potts expansion is schematically shown in FIG. 6, and for abstract description, different transportation modes are labeled with different colors, such as red (thick line segment in FIG. 6) for railway transportation, black (dotted line segment in FIG. 6) for road transportation, and the like, so that the Kirby-Potts expanded composite transportation network is also called a coloring network.
Although the Kirby-Potts extended network can be solved by using Dijkstra algorithm, the number of vertexes is increased by M times, so that the computational complexity is increased by M 2 And the computational complexity of the Kirby-Potts-based composite transportation path planning algorithm is O (M) 2 n 2 )。
Rhyd Lewis [3] proposes a space-time-changing strategy on the basis of analyzing Kirby-Potts expansion, and the algorithm calculates all virtual nodes simultaneously on the basis of marking whether the nodes or the original nodes, so the Lewis algorithm does not increase the calculation complexity of the Dijkstra algorithm, but needs more storage space, as shown in FIG. 7.
Although the Lewis algorithm improves the calculation efficiency compared with the Kirby-Potts expansion algorithm and can solve the problem of path planning of the composite transport network, the Lewis algorithm still only converts the loading and unloading expense into one cost and adds the cost to the path length to calculate the shortest path from the starting point to the end point, and the algorithm design is not carried out from the angle of the loading and unloading times.
Reference documents:
[1]E.W.Dijkstra,“A note on two problems in connexion with graphs,”Numer.Math.,vol.1,no.1,pp.269–271,Dec.1959,doi:10.1007/BF01386390.
[2]R.F.Kirby and R.B.Potts,“The minimum route problem for networks with turn penalties and prohibitions,”Transp.Res.,vol.3,pp.397–408,1969.
[3]R.Lewis,“Algorithms for Finding Shortest Paths in Networks withVertex TransferPenalties,”Algorithms,vol.13,no.11,p.269,Oct.2020,doi:10.3390/a13110269.
disclosure of Invention
In order to solve the problem of the composite transportation path planning with limited loading and unloading times, the invention provides a method for outputting the shortest path between vertexes under the constraint condition of the specified maximum loading and unloading times, which adopts the following technical scheme:
the invention provides a rapid composite transport path planning method with limited loading and unloading times, which is used for outputting the shortest path between vertexes under the constraint condition of the appointed maximum loading and unloading times and is characterized by comprising the following steps of: s1, performing Kirby-Potts expansion on all vertexes in the road network to generate respective corresponding tuples (v, c, i, l, n), wherein the tuples comprise elements with the transport v, the transportation mode c, the in-and-out direction i, the path length l from the starting point to the current vertex and the package passing from the starting point to the current vertexN times of unloading; step S2, selecting the maximum loading and unloading times n max Selecting a starting point v src And endpoint v dst Based on the starting point v src Constructing an initial tuple sequence Q with the direction of i = OUT by Kirby-Potts expansion; s3, judging whether the initial tuple sequence Q is empty or not; s4, when the judgment in the S3 is yes, the reachable path does not exist from the starting point to the end point, and planning is finished; step S5, when the judgment of the step S3 is no, selecting the tuple p (v, c, i, l, n) with the minimum value of l from the initial tuple sequence Q, and marking the tuple; s6, judging the direction of i in the marked tuple p (v, c, i, l, n); s7, when the judgment result IN the step S6 is IN, selecting a tuple which can be converted from IN to OUT, and marking the tuple as p2; s8, judging whether the transportation mode in the tuple p2 is the same as the transportation mode in the marked tuple; step S9, when the judgment in the step S8 is negative, recording the temporary path cost as c tmp ＝p(l)+c tx ，c tx For the transfer cost, and increasing the loading and unloading times n tmp = p (n) +1; step S10, when the judgment in the step S8 is yes, the transportation mode of entering the vertex and the transportation mode of leaving the vertex are the same, and the path cost and the loading and unloading times are not changed; step S11, judging the loading and unloading times n tmp >n max (ii) a Step S12, when the judgment of the step S11 is yes, the p2 group is not changed; step S13, when the judgment is no, judging c tmp <p2 (l), if yes, updating p2 (l) = c tmp Putting the updated p2 into the sequence Q and then entering the step S16; otherwise, the cost of the p2 path is unchanged, and the p2 tuple is unchanged; step S14, when the judgment IN the step S6 is OUT, selecting a tuple which can be converted from OUT into IN, has a consistent transportation mode and is not marked, and marking the tuple as p2, wherein p2 (c) = p (c); step S15, calculating the temporary conversion path cost c tmp = p (l) + w (p (v), p2 (v)), where w is the path cost (length) of the edge between vertices, and judges c tmp <p2 (l), when judged yes, putting p2 into the sequence Q and then proceeding to step S16; step S16, determine p2 (v) = v dst Whether the current vertex is the end point or not; step S17, when the judgment of step S16 is YES, the starting point v is shown src And endpoint v dst The shortest path exists, the total number of transfers is calculatedAnd total path cost; otherwise, repeating the steps S5 to S17 until the end.
The present invention also provides a computer-readable storage medium for storing a computer program, wherein the computer program is configured to implement the above-mentioned method for planning a rapid composite transportation path with limited loading and unloading times when executed.
Action and Effect of the invention
According to the rapid composite transport path planning method with limited loading and unloading times, the limitation on the loading and unloading times is added on the basis of a Lewis algorithm, and the rapid composite transport path planning algorithm is realized under the condition of limited loading and unloading times. Compared with the existing algorithm, the path planning method not only solves the problem of solving the shortest path in the composite transportation, but also flexibly realizes the rapid composite transportation path planning with limited loading and unloading times from the viewpoint of loading and unloading times under the condition of not introducing additional calculation complexity, reduces the cost of the composite transportation, provides convenience for the composite transportation, and has higher applicability.
Drawings
Fig. 1 is a schematic flow chart of a method for planning a rapid composite transportation path with limited loading and unloading times according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a shortest path result obtained without limitation of loading and unloading times and transfer cost in the embodiment of the present invention;
fig. 3 is a schematic diagram of a shortest path result obtained by limiting the maximum handling number to 2 and not limiting the transfer cost in the embodiment of the present invention;
figure 4 is a partial schematic view of the railway section of figure 3 in an embodiment of the present invention.
FIG. 5 is a diagram illustrating a shortest path result obtained when the transfer cost is 100 meters or the maximum handling time is limited to 0 according to an embodiment of the present invention;
FIG. 6 is a Kirby-Potts expansion diagram; and
FIG. 7 is a schematic diagram of the improved rendering Dijkstra algorithm by Lewis with space-time transformation.
Detailed Description
On the basis of a Lewis algorithm, the invention increases the limitation on the loading and unloading times in the algorithm step, does not introduce additional calculation complexity, and realizes the rapid composite transportation path planning algorithm under the condition of limited loading and unloading times.
In order to make the technical means, creation features, achievement purposes and effects of the present invention easy to understand, the following describes a fast composite transportation path planning method with limited loading and unloading times in detail with reference to the embodiments and the accompanying drawings.
< example >
Fig. 1 is a schematic flow chart of a rapid composite transportation path planning method with limited loading and unloading times in an embodiment of the present invention.
As shown in fig. 1, a method for planning a rapid composite transportation path with limited loading and unloading times includes the following steps:
in order to facilitate the user to select any starting point or ending point for path planning calculation, the Kirby-points expansion is performed on all vertexes in the road network in the embodiment, and the Kirby-points expansion is not only a local road network graph of the starting point and the ending point.
And S1, performing Kirby-Potts expansion on all vertexes in the road network graph G (V, E) to generate corresponding tuples, wherein the tuples at least comprise a transportation mode, an in-out direction, a path length from a starting point to the current vertex and loading and unloading times passing from the starting point to the current vertex.
IN this embodiment, the tuple is represented as (v, c, i, l, n), where v points IN reverse to its corresponding original vertex, c represents its corresponding transportation mode or edge color, i represents the IN-and-OUT direction, i = IN if it is an extension derived from "IN edge", otherwise i = OUT, i represents the path cost (length) from the origin to the current extended vertex, and n represents the number of passes of loading and unloading from the origin to the current node.
Step S2, selecting the maximum loading and unloading times n max Selecting a starting point v src And endpoint v dst Based on the starting point v src The construction direction of the Kirby-Potts expansion is i = OUT.
In the embodiment, a starting point and an ending point are selected from a road network comprising roads and railways, the position is represented by longitude and latitude coordinates, the longitude and latitude coordinates of the starting point (117.618164, 34.595214) and the longitude and latitude coordinates of the ending point (117.993164, 29.685058) are adopted. The initial tuple sequence Q contains a tuple p = { ((117.618164, 34.595214), "road", OUT, 0) } with the direction OUT.
And S3, judging whether the initial tuple sequence Q is empty or not.
In this embodiment, the sequence Q is now non-empty, containing a tuple from the beginning outward.
And S4, when the judgment in the step S3 is yes, finishing the path planning.
This step S4 is an exit condition, and when the condition of step S4 is triggered, there is no reachable path from the starting point to the end point in most cases.
And step S5, when the judgment of the step S3 is no, selecting the tuple p (v, c, i, l, n) with the minimum value of l from the initial tuple sequence Q, and marking the tuple.
In this embodiment, for the first iteration, the unique tuple is selected because the sequence Q has only one tuple; for the second iteration, p = { ((117.618164, 34.595214), "road", OUT, 0) } has 50 outgoing paths, so there are 50 new tuples added, the minimum tuple is: { (117.256880, 34.709827), "Highway", IN,35458.82 m, 0}.
Step S6, judging the direction of i in the tuple p (v, c, i, l, n) of the mark.
In this embodiment, the first iteration i = OUT; the second iteration i = IN. Subsequent iterations are also repetitions of similar phenomena, namely preceded by OUT and followed by IN.
And S7, when the judgment result IN the step S6 is IN, selecting a tuple which can be converted from IN to OUT, and marking the tuple as p2.
IN this embodiment, the second iteration i = IN, there is one OUT tuple connected to it, and the current value of the tuple is: { (117.256880, 34.709827), "Highway", OUT, + inf,0}, the initial cost of a non-origin tuple is noted as infinity.
Step S8, determine whether the transportation mode in the tuple p2 is the same as the transportation mode in the marked tuple, i.e. determine whether p (c) is equal to p2 (c).
IN this embodiment, the transportation mode of the OUT tuple is the same as that of the IN tuple IN the second iteration, and the transportation modes are roads.
Step S9, if different, i.e. p (c) ≠ p2 (c), then the temporary path cost is recorded as c tmp ＝p(l)+c tx And increasing the number of times of loading and unloading n tmp ＝p(n)+1。
Wherein, c tx Is the transfer cost. If the transfer cost is measurable and additive to the path cost, accumulating the transfer cost to obtain the optimal total cost (including the path transportation cost and the transfer cost); of course, if the transfer cost is unknown, then c is set tx =0, only accumulating the number of transfers, which is used to constrain the total number of transfers of the solution, and this is also one of the advantages of the path planning algorithm of the embodiment.
In step S10, if the transportation modes are the same, i.e., the transportation modes of the entering vertex and the leaving vertex are the same, the path cost and the loading and unloading times are not changed.
In this embodiment, the second iteration is performed in the same transportation mode, and the path cost and the loading and unloading times are kept unchanged.
Step S11, judging the loading and unloading times n tmp Whether or not it is greater than a defined maximum number n of handlings max 。
Step S12, when n is tmp >n max Then, the processing of the tuple is ignored, which is a key step that makes the final path solution not exceed the maximum load and unload times.
Step S13, when n is tmp ＜n max When it is, judge c tmp Whether it is less than p2 (l), if it is, the path cost of p2 is unchanged; if less than, update p2 (l) = c tmp The updated p2 tuple is put into the sequence Q and step S16 is entered.
IN this embodiment, for the second iteration, the OUT tuple path cost is modified from + inf, i.e. infinity, to 35458.82 meters, i.e. equal to the path cost of the IN tuple. The updated OUT tuple is: { (117.256880, 34.709827), "road", OUT,35458.82 m, 0}, and adding the OUT node corresponding to the tuple to the Q queue. The node still has a load and unload count of 0, and obviously an out-of-range condition of the maximum load and unload count is not triggered.
And step S14, when the node is judged to be OUT IN the step S6, selecting the conversion of the tuple which has the same direction as IN, the same color and is not marked from the corresponding node to all the neighbor nodes, and if the tuple is marked as p2, then p2 (c) = p (c) exists.
Step S15, calculating the temporary conversion path cost c tmp = p (l) + w (p (v), p2 (v)), where w is the path cost (length) of the edge between vertices, and c is judged tmp If it is less than p2 (l), and when it is less than p2 is put in the Q queue and then proceeds to step S16.
IN this embodiment, IN the first iteration, the current tuple is OUT, which corresponds to 50 IN tuples, and the path costs of modifying them are calculated to be 42784.44, 38224.95, \8230;, respectively. The minimum tuple path cost selected for the second iteration is 35458.82 meters.
Step S16, judging whether p2 (v) is equal to v dst I.e. whether the current vertex is an end point.
Step S17, if p2 (v) = v dst Then, it represents the starting point v src And endpoint v dst If the shortest path exists, the path planning is finished after the total transfer times and the total path cost are calculated and output, otherwise, the steps S5 to S17 are repeatedly executed until the path planning is finished.
In this embodiment, the end point, i.e. the target node tuple, is: { (117.993164, 29.685058), "Highway", IN,771450.16 m, 2}.
In summary, the result of performing the path planning on the starting point (117.618164, 34.595214) and the ending point (117.993164, 29.685058) by using the path planning method of the embodiment is: the transfer is done twice, the total path cost is 771450.16 meters.
As described above, the present embodiment provides a fast compound transportation path planning method with limited loading and unloading times, which may also be configured as a computer program and stored in a computer storage medium, where the computer program is used to make a computer execute the steps of the fast compound transportation path planning method with limited loading and unloading times.
In addition, in order to verify the necessity of limiting the number of loading and unloading times in the planning of the compound transportation route, the following tests were performed based on the starting point (117.618164, 34.595214) and the ending point (117.993164, 29.685058) in the present embodiment.
In fig. 2 to 5, a thick black line indicates a railway section, that is, the section of transportation is a railway, and a thin black line indicates a road section, that is, the section of transportation is a road.
Fig. 2 is a schematic diagram of a shortest path result obtained without loading and unloading times and without limitation of transfer cost in the embodiment of the present invention, and fig. 3 is a schematic diagram of a shortest path result obtained with limitation of a maximum loading and unloading time of 2 and without limitation of transfer cost in the embodiment of the present invention.
If the transfer times are not limited and the transfer cost is not set, the obtained shortest path result is shown in fig. 2. If the maximum transfer times are limited to 2 and no transfer cost (cost) is set, the obtained shortest path result is shown in fig. 3, and the partial schematic diagram of the railway section is shown in fig. 4.
Fig. 5 is a diagram illustrating the shortest path result obtained when the transfer cost is 100 meters or the maximum handling number is limited to 0 in the embodiment of the present invention.
If the shortest path algorithm can be operated by converting the transfer cost into the path length instead of adopting the path planning algorithm of the embodiment, tests show that if the set transfer cost is equivalent to a path of 10 meters, the planning result is the same as the result without the transfer cost. When the transfer cost is 100 meters, the planning result is only roads without railways. As shown in fig. 5, it is clear that the use of the maximum transfer number limit can more intuitively control the transfer scenario of the planning result than the transfer cost.
Examples effects and effects
According to the rapid composite transport path planning method with limited loading and unloading times, the limitation on the loading and unloading times is added on the basis of the Lewis algorithm, and the rapid composite transport path planning algorithm is realized under the condition of limited loading and unloading times. Compared with the existing algorithm, the path planning method of the embodiment not only solves the problem of solving the shortest path in the composite transportation, but also flexibly realizes the rapid composite transportation path planning with limited loading and unloading times from the viewpoint of loading and unloading times under the condition of not introducing extra calculation complexity, reduces the cost of the composite transportation, provides convenience for the composite transportation, and has higher applicability.
The above-described embodiments are merely illustrative of specific embodiments of the present invention, and the present invention is not limited to the scope of the description of the above-described embodiments.

Claims (2)

1. A fast composite transport path planning method with limited loading and unloading times is used for outputting the shortest path between vertexes under the constraint condition of the appointed maximum loading and unloading times, and is characterized by comprising the following steps:
step S1, performing Kirby-Potts expansion on all vertexes in a road network to generate respective corresponding tuples (v, c, i, l, n), wherein elements contained in the tuples have the original vertex transport v, the transport mode c, the in-and-out direction i, the path length l from a starting point to a current vertex and the loading and unloading times n passing from the starting point to the current vertex;
step S2, selecting the maximum loading and unloading times n max Selecting a starting point v src And endpoint v dst Based on the starting point v src Constructing an initial tuple sequence Q with the direction of i = OUT by Kirby-Potts expansion;
s3, judging whether the initial tuple sequence Q is empty or not;
s4, when the judgment in the S3 is yes, the reachable path does not exist from the starting point to the end point, and planning is finished;
step S5, when the judgment in the step S3 is negative, selecting a tuple p (v, c, i, l, n) with the minimum value of l from the initial tuple sequence Q, and marking the tuple;
s6, judging the direction of i in the marked tuple p (v, c, i, l, n);
s7, when the IN is judged IN the step S6, selecting a tuple which can be converted into OUT from the IN, and marking the tuple as p2;
s8, judging whether the transportation mode in the tuple p2 is the same as the transportation mode in the marked tuple;
step S9, when the judgment in the step S8 is negative, recording the temporary path cost as c tmp ＝p(l)+c tx ，c tx For the transfer cost, and increasing the loading and unloading times n tmp ＝p(n)+1；
Step S10, when the judgment in the step S8 is yes, the transportation mode of entering the vertex and the transportation mode of leaving the vertex are the same, and the path cost and the loading and unloading times are not changed;
step S11, judging the loading and unloading times n tmp >n max ；
Step S12, when the judgment in the step S11 is yes, the p2 tuple is not changed;
step S13, when the judgment is no, judging c tmp <p2 (l), if no, the path cost of p2 is not changed, if yes, p2 (l) = c is updated tmp Putting the updated p2 into the sequence Q and then entering the step S16;
step S14, when the judgment IN the step S6 is OUT, selecting a tuple which can be converted from OUT into IN, has a consistent transportation mode and is not marked, and marking the tuple as p2, wherein p2 (c) = p (c);
step S15, calculating the temporary conversion path cost c tmp = p (l) + w (p (v), p2 (v)), where w is the path cost of the edge between vertices, and c is judged tmp <p2 (l), when judged yes, put p2 into sequence Q and then go to step S16;
step S16, determine p2 (v) = v dst I.e. whether the current vertex is an end point;
step S17, when the judgment of step S16 is YES, the starting point v is shown src And endpoint v dst The shortest path exists, and the total transfer times and the total path cost are calculated; otherwise, repeating the steps S5 to S17 until the end.
2. A computer-readable storage medium storing a computer program, wherein the computer program is configured to implement a load-bound rapid composite transport route planning method as claimed in claim 1 when executed.
CN202210673769.4A 2022-06-15 2022-06-15 Rapid composite transport path planning method with limited loading and unloading times Pending CN115187158A (en)

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