WO2016188151A1

WO2016188151A1 - Searching method and device for optimal route of multiple meeting point applicable for real-time ride-sharing

Info

Publication number: WO2016188151A1
Application number: PCT/CN2016/073858
Authority: WO
Inventors: 李荣华; 邱宇轩; 毛睿; 秦璐; 钟舒馨
Original assignee: 深圳大学
Priority date: 2015-05-26
Filing date: 2016-02-16
Publication date: 2016-12-01
Also published as: CN104992044A; CN104992044B

Abstract

A searching method and device for an optimal route of multiple meeting points applicable for real-time ride-sharing. The method comprises: obtaining preset route searching information comprising a graph G = (V, E, W), a point set of U, α, a starting point s, and a destination point t; initializing a queue Q and a set D, and adding an initial state ((s, ∅), 0) into the queue Q; and if the queue Q is not empty, then repeating the following steps: (A) popping a first element ((v, X), cost) in the queue Q; (B) returning cost if both v = t and X = U; (C) adding a state (v, X) into the set D; (D) iterating through all edges (v, u) to update (Q, D, (v, X),cost + α × w(v, u)); (E) iterating through all points x in the set U-X to update (Q, D, (v, X∪{x}), cost + (1 - α) × dist(x, v)); and obtaining an optimal route upon completion of the iteration. The searching method for an optimal route of multiple meeting points can efficiently solve the technical difficulties unresolved in current real-time ride-sharing applications, namely, how to rapidly determine an optimal route for a driver to pick up all matched passengers after the driver and the passengers are matched, thus bridging the gap in the related art of the current real-time ride-sharing applications.

Description

Optimal multi-join point path searching method and device applied to real-time multiplication

Technical field

The invention relates to the field of real-time sharing application technology, in particular to an optimal multi-join point path searching method and device applied to real-time multiplication.

Background technique

Real-time multiplication, also known as dynamic carpooling, is a promising way to save fuel and reduce traffic congestion in modern transportation systems. Recently, many real-time ride-in applications, such as Uber (www.uber.com) and Lyft (www.lyft.com), have become increasingly popular among smartphone users as it helps them plan their journey. In a typical real-time ride-in system, there are two types of entities: the driver and the passenger. Passengers can book a car through their smartphone with a location function. They need to provide their geographic location information to the system, and then the system dynamically arranges for the driver to provide a ride for these passengers.

Setting up such a real-time ride system is not an easy task. The main technical difficulties are two: 1. How to quickly find the driver who can service the incoming user request; 2. After matching the driver and the passenger, how to quickly determine the optimal path for the driver to pick up All the matching passengers. In the literature, some of the existing research focuses on solving the first problem.

For example, in [2] "S. Ma, Y. Zheng, and O. Wolfson, "T-share: A large-scale dynamic taxi ridesharing service," in 2013 IEEE 29th International Conference on Data Engineering (ICDE), 2013, Pp.410–421” and [3] “S.Ma and O.Wolfson, “Analysis and evaluation of the slugging form of ridesharing,” in Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic In Information Systems, 2013, pp. 64–73, Shuo Ma et al. made a system called T-share for real-time matching of drivers and passengers in taxi-combining applications. [1] (Y. Huang, R. Jin, F. Bastani, and XSWang, "Large Scale Real-time Ridesharing with Service Guarantee on Road Networks," ArXiv 13026666Cs, Feb. 2013), Yan Huang et al. proposed an efficient The activity tree algorithm supports a match between a driver and a passenger with service guarantees. The work of these algorithms focuses on developing a practical algorithm to efficiently solve the matching problem between the driver and the passenger, ie The technical difficulties described above are 1. For the technical difficulties 2 described above, as far as we know, there are no related studies reported in the past. Similar studies include: OSR, KOR, and multiplication queries. Problems and OMP issues.

The OSR problem, the optimal sequenced route, is in the literature [4] (F.Li, D.Cheng, M.Hadjieleftheriou, G.Kollios, and S.-H.Teng, "On Trip planning queries in spatial databases," in Advances in Spatial and Temporal Databases, Springer, 2005, pp. 273-290) and [5] (M. Sharifzadeh, M. Kolahdouzan, and C. Shahabi, "The optimal sequenced route The query, "VLDB J., vol. 17, no. 4, pp. 765-787, 2008" was independently proposed and was promoted in later literature. According to the definition in [5], the goal of the OSR problem is to find a path with the shortest distance. This path starts from a source point and passes through several types of points in a certain order. This certain order is determined by the point. The type is applied and eventually reaches a target point. The OSR problem is different from ours. There are three main differences: 1. In our problem, these nodes do not have any type information, and the OSR passes through a series of points that belong to different types. 2. Unlike the OSR problem, our problem does not impose a type sequence constraint on the optimal path. 3. In the OSR problem, the optimal path must pass through these specific types of nodes, and our problem does not need to go through a specific point. Take Figure 1 as an example. Assuming that our source and destination nodes are v ₁ and v _{10 respectively} , we assume that the passengers travel to the path and the driver spends the same amount of time along the path, and assume that the passenger is at v ₆ points, ie U={v ₆ }. Then for this problem, the result of the OSR solution is the path (v ₁ , v ₃ , v ₆ , v ₈ , v ₁₀ ), and the result of our problem should be (v ₁ , v ₃ , v ₇ , v ₁₀ ). Because the results are so different, the techniques used to solve the OSR problem (see [4], [5], [9] (M. Sharifzadeh and C. Shahabi, "Processing optimal sequenced route queries using voronoi diagrams "GeoInformatica, vol.12, no.4, pp.411-433, 2008.)) cannot be used to solve this problem.

KOR problem (see [10]: X. Cao, L. Chen, G. Cong, and X. Xiao, "Keyword-aware optimal route search," Proc. VLDB Endow., vol. 5, no. 11, pp .1136–1147, 2012), the keyword-aware optimal route. The KOR problem aims to find an optimal s~t path that passes through all the given keywords, and it also satisfies some established constraints. Obviously, according to the definition, we can know that our problem is fundamentally different from the KOR problem. Therefore, the method of KOR problem in [10] can not be used to solve our problem.

The ride-sharing query is in the literature [11] (F. Drews and D. Luxen, "Multi-hop ride sharing," in Sixth Annual Symposium on Combinatorial Search, 2013.), [12] ( R. Geisberger, D. Luxen, S. Neubauer, P. Sanders, and L. Volker, "Fast detour computation for ride sharing," ArXiv Prepr. ArXiv 09075269, 2009). The goal of this problem is to find an optimal s~t return path, which contains a subpath s'~t', where s' and t' are given in the query. Obviously, the optimal s~t迂 path of the multiplicative query problem passes through the given points s' and t', and the path in our problem does not need to go through the query point. Because of this fundamental difference, the methods given in [11], [12] cannot be used for our problems.

OMP problem, optimal meeting point problem (see [13] (Z. Xu and H.-A. Jacobsen, "Processing proximity relations in road networks," in Proceedings of the 2010 ACM SIGMOD international conference on management of data, 2010, pp. 243–254), [14] (D. Yan, Z. Zhao, and W. Ng, “Efficient algorithms for finding optimal meeting point on road networks , "Proc. VLDB Endow., vol. 4, no. 11, 2011)). The problem is given a set of query points, requiring a rendezvous so that the sum of all query points to the rendezvous is the smallest. The OMP problem is also significantly different from ours. On the one hand, the OMP problem is aimed at finding a rendezvous point, and the result of our problem is a s~t path. On the other hand, in our problem, the objective function consists of two parts - the length of the path and the distance from all query points to the path. In the OMP problem, the objective function is only determined by the distance from the query point to the rendezvous point. Because of these differences, existing methods in OMP problems cannot be used to solve our problems. Moreover, [14] also illustrates that the assembly point of the OMP problem must be a node on the graph through a different proof than the one we use.

In addition, it is worth noting that the shortest path between the source node and the destination node is obviously not the solution to our problem. Therefore, the Dijkstra algorithm and many other index-based shortest path solutions cannot be applied to our problem.

Summary of the invention

It is an object of the present invention to provide an optimal multi-join point path search method and apparatus for real-time multiplication, which can quickly determine an optimal path for the driver to connect to all matching passengers.

The object of the present invention is achieved by the following technical solutions.

An optimal multi-join point path search method applied to real-time multiplication, including:

Obtain path search preset information, including: graph G=(V, E, W), point set U, α, starting point s, destination point t; wherein, V, E, and W are point sets, edge sets, and weights, respectively Collection

a subset of vertices; a parameter α ∈ (0, 1) for balancing the proportion of the distance between the point s to the path P _st and U in the graph G to the path P _st ;

Initialize queue Q and set D, initial state

Join the queue Q;

Repeat the following steps when the queue Q is not empty:

A. The first element ((v, X), cost) in the pop-up queue Q; where v is the end point of the sub-path, X is a subset of Us that are included in the sub-path, and cost is the cost of the state (v, X).

B. If v=t and X=U, return cost;

C, adding the state (v, X) to the set D;

D, for all (v, u) edge loops in set E, update (Q, D, (v, X), cost + α × w (v, u));

w(v, u) is the weight of the edge (v, u);

E. For all x-point loops in the set UX, update (Q, D, (v, X∪{x}), cost+(1-α)×dist(x,v)); where dist(x,v) The distance from point x to point v.

The optimal path is obtained after the end of the loop.

Preferably, in the method, if an optimal solution has not been found at the end of the cycle, then ∞ is returned.

Preferably, in the method, the operation of updating (Q, D, (v, X), cost) is as follows:

When the state (v, X) ∈ D, return directly;

When state

When the state ((v, X), cost) is pushed into the queue Q;

When cost<Q.cost((v,X)), Q.update((v,X), cost).

An optimal multi-join point path searching device for real-time multiplication is applicable to a mobile terminal, and the device includes:

Search information input unit: used to obtain path search preset information, including: graph G=(V, E, W), point set U, α, starting point s, destination point t; wherein, V, E, and W are points respectively a set of sets, edge sets, and weights;

a subset of vertices; the parameter α∈(0,1) is used to balance the distance and the proportion of the distance between the points P _St and U to P _st ;

a path searching unit: configured to search for preset information according to the path, and search for an optimal path from the starting point s to the destination point t in the graph G by using a best-priority dynamic programming strategy;

Search result output unit: for outputting an optimal path searched by the path search unit.

Preferably, the mobile terminal comprises: a mobile phone, a smart phone, a notebook computer, a personal digital assistant, a tablet computer.

Compared with the prior art, the present invention has the following advantages:

The optimal multi-joining point path searching method proposed by the invention can effectively solve the unsolved technical difficulties in the current real-time multi-function application, that is, how to quickly determine the optimal path for driving after matching the driver and the passengers It is possible to connect all the matching passengers and fill in the gaps in the related technologies in the current real-time sharing application.

DRAWINGS

1 is a schematic diagram of a road network according to an embodiment of the present invention;

2 is a schematic diagram of a path provided by an embodiment of the present invention, assuming that a meeting point x falls on an edge;

3 is a schematic diagram of a first path constructed according to an embodiment of the present invention, assuming that the meeting point is a node r;

4 is a schematic diagram of a second path constructed according to an embodiment of the present invention, assuming that its meeting point is a node v;

FIG. 5 is a schematic diagram of an extended manner of adopting edge growth for a state (v, X) according to an embodiment of the present invention; FIG.

FIG. 6 is a schematic diagram of an extended manner of adopting point growth for a state (v, X) according to an embodiment of the present invention.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It is understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

In view of the problem that the second technical difficulty in solving the real-time multiplication problem is not solved in the background art, the present invention 1) gives a specific definition of the second technical difficulty, and names it OMMPR (optimal multi-meeting-point) Query, the optimal multi-recovery path search problem; 2) An algorithm for solving the OMMRP problem is proposed, hereinafter referred to as the OMMRP algorithm. The algorithm can effectively solve the second technical difficulty in the real-time multiplication problem, namely the OMMRP problem.

First, define the OMMRP problem.

The present invention abstracts the road network into a weighted graph G(V, E, W), where V, E, and W are a set of points, sets of edges, and weights, respectively. Let n=|V| denote the number of points, and m=|E| denote the number of edges. On the right side (v _i, v _j) the value of w (v _i, v _j) represents the point to point distance between v _i v _j. The graph G is treated here as an undirected graph, but in practice the invention can be used to process directed graphs. The present invention records the s to t path as P _st = (s, v ₁ , ..., v _k-1 , t). Let v ₀ = s, v _k = t,

Is a collection of nodes on P _st , ie

You can record the total cost on the path as

Note that the path here is not necessarily a simple path with no repeating vertices. make

For a subset of vertices, for each u∈U we define a set of points from node u to path P _st

The distance is:

Here dist(u,v _i ) is the distance from node u to node v _i . Obviously, here

Indicates the distance from node u to path P _st . If a node

And there is

Then the present invention calls the node v the meeting point of the node u and the path P _st . As will be shown later, in the problem of the present invention, the meeting point is necessarily a point on the graph.

Definition of the invention

The sum of the distances from all points in the set U to the path P _st , ie

Then for a given s, t, U and α, the average cost function of the path P _st can be constructed:

Here, the parameter α ∈ (0, 1) is used to balance the specific gravity of the distance between the points in the paths P _st and U to P _st . Here, consider that the distance between all the points in U to P _st occupies the same specific gravity (1-α). However, the method of the present invention can be extended to support the handling of different points of gravity at different points. Obviously, in real-time multiplication applications, c(P _st ) represents the driver's cost.

Represents the cost of all passengers. The goal of the OMMPR search is to find a path P _st from the source node s to the destination node t in the graph G such that f(P _st ) is minimized.

The official definition of OMMPR search is as follows:

For a given road network G=(V, E, W), the goal of OMMRP to search for Q(s, t, U, α) is to find a s~t path P _st on graph G, such that f(P _st ) Minimal, ie

Minf(P _st )

stP _st ∈Ρ _st

Here Ρ _st is a collection of all paths from s to t.

As mentioned earlier, the meeting point must be a point on the graph. Below, proof will be given.

Restatement: For a given road network G=(V, E, W) and an OMMRP search Q(s, t, U, α), the convergence point of all nodes u∈U and the optimal path P _st is inevitable In the set V.

Proof: Use the counter-evidence method to prove this problem. For each node u∈U and the optimal s~t path P _st , without loss of generality, it is assumed that the meeting point of u and P _st falls on the edge (r, v), as shown in FIG. 2 . Record the meeting point as x. Then there are:

f(P _st )=α(c(P _sr )+c(P _rt )+2w(r,x))+(1-α)(dist(u,v)+w(v,x)).

In order to obtain contradictions, construct two paths

with

See Figure 3 and Figure 4, respectively. u and

The meeting point is node r, u and

The meeting point is node v. Then there is

If you do poor, you can find:

with

So there is

This means that

with

There must be a path better than P _st , which contradicts the condition P _st is the optimal path. So the proposition is proved.

Second, for the OMMRP problem, the present invention proposes an efficient algorithm - OMMPR algorithm.

The OMMPR algorithm is based on dynamic programming, using (u, X) to represent a state, where u represents the end node of a path and X is a subset of U. The algorithm finds the optimal path by extending the end node of a path and the subset X of U. When u=t, X=U, the optimal path is obtained. Let f(u,X) be the average cost of an OMMPR path, ie

When u = s, f(s, X) satisfies f(s, X) = (1 - α) × ∑ _{x ∈ X} dist (x, s). Because when u=s, the path from s to u contains only one point s, the cost on the path is 0, and the cost from the node in U to the path is ∑ _x∈X dist(x, s). Obviously, when

Time,

For each state (v, X), the invention has two modes of expansion, edge growing and node growing. As the side grows, the present invention extends the state (v, X) to the new state (u, X) with one edge (v, u) ∈ E. As the point grows, the present invention extends each state (v, X) to a new state (v, X ∪ {x}) with each node x ∈ U-X. Then the state transition equation is as follows:

The above formula is explained as follows: Let P _su denote the end from s to the end of u, considering the optimal path of point set X. f(u, X) represents the cost of P _su . Then f(u, X) can be obtained in the following two ways.

1. While growing. For the query point and the optimal path P _su in the set X, it is assumed that all the rendezvous points are on the set V _Psu -{u}. In this case, by extending the sub-path P _sv, at its top with the edge (v, u) ∈E, to obtain the optimal path P _su. Because all the rendezvous points fall on the optimal subpath P _sv at this time. Figure 5 shows the process of edge growth. Obviously, there is

2. Point growth. It is assumed that the meeting point of at least one point x ∈ X and the optimal path P _su falls at point u. In this case, the optimal path can be taken into account set X P _su extended by considering the set of X- {x} is the optimal path P _su. Figure 6 shows the process of point growth. Can get

Obviously, the present invention can take the minimum cost of the above two as f(u, X), that is, the state transition equation above.

Based on the above state transition equation, the present invention can solve the OMMRP search problem by a best-first dynamic programming strategy.

The detailed process of the OMMPR algorithm is as follows:

Input: Figure G = (V, E, W), point set U, α, starting point s, destination point t.

Output: Minimum cost.

(1) Initialize queue Q and set D, the initial state

Join queue Q.

(2) Repeat the following steps when queue Q is not empty:

(2.1) pop the first element in the queue Q ((v, X), cost);

(2.2) If v=t and X=U, return cost;

(2.3) adding the state (v, X) to the set D;

(2.4) For all (v, u) edge loops in set E,

(2.4.1) Update (Q, D, (v, X), cost + α × w (v, u));

(2.5) For all x-point loops in the set U-X,

(2.5.1) Update

(Q, D, (v, X ∪ {x}), cost + (1-α) × dist (x, v)).

(3) If all the above loops have not found the optimal solution, return ∞.

The operation of updating (Q, D, (v, X∪X'), cost') is as follows:

When the state (v, X) ∈ D, return directly;

When state

When the state ((v, X), cost) is pushed into the queue Q;

When cost<Q.cost((v,X)), Q.update((v,X), cost).

In the above algorithm, the present invention defines the state (v, X) and is represented by a tuple ((v, X), cost), where cost=f(v, X), from the point s to At the end of point t, consider the cost of querying the OMMRP problem of set X. In this algorithm, the present invention uses a priority queue Q to achieve the best priority strategy. Each element in Q is a tuple ((v, X), cost). In the priority queue Q, the cost in each element ((v, X), cost) is the priority order, and the element with the lowest cost is always at the head of the queue. Queue Q has three operations, pop, push, and update. The pop-up operation dequeues the leader element, which is the lowest cost element, from the queue. The push operation pushes an element into the queue. The update operation updates the cost of an element in the queue and adjusts the queue so that it stays in order of priority. A set D is also used in the algorithm to save the state that has been calculated.

Correspondingly, the present invention also provides an optimal multi-join point path searching device, including:

Search information input unit: used to obtain path search preset information, including: graph G=(V, E, W), point set U, α, starting point s, destination point t;

Search result output unit: used to output and display the optimal path; the display mode can adopt different ways according to the user's usage habits or individualized requirements.

The above-mentioned optimal multi-joining point path searching device can be applied to various mobile terminals, and specifically can be a mobile phone, a smart phone, a notebook computer, a personal digital assistant, a tablet computer, and the terminal can be used as long as a terminal equipped with a real-time sharing application can be used. .

In summary, the above algorithm efficiently solves the problem of optimal path determination in real-time multiplication applications, filling A gap in the prior art. Two examples will be enumerated below to illustrate the application of the above algorithm.

Example one

In this example, an example of an OMMRP problem and its result calculation method are introduced. Looking at the example diagram shown in Fig. 1, assume that s = v ₁ , t = v ₁₀ , α = 1/2, U = {v ₆ }. Then the optimal path of the OMMRP search is P _st = (v ₁ , v ₃ , v ₇ , v ₁₀ ), and the optimal average cost of the path is 3, that is, f(P _st )=3. The point of convergence of point v ₆ and path P _st is v ₃ because the path (v ₆ , v ₃ ) is from point v ₆ to the set

The shortest path.

Example two

In this example, the example in Example 1 is used to demonstrate the algorithm flow of the OMMRP algorithm in Figure 1 to solve the optimal multi-rejoin path. After changing the parameters s, t, α, U, the algorithm flow is similar to this example.

As shown in the example diagram shown in Fig. 1, it is assumed that s = v ₁ , t = v ₁₀ , U = {v ₆ }, and α = 1/2. First element

Join the priority queue Q. The least expensive element in the first iteration

Pop up from queue Q. Next, the algorithm expands the state with edge growth and point growth, respectively.

As the edge grows, the edge is expanded for all edges (s, v) ∈ E. When the point grows, for all points

There is only one point v ₆ here to extend this point. The expanded result generated 4 states

And ((v ₁ ,{v ₆ }), 3/2) and add them to the queue Q. Similarly, in the second iteration, the algorithm pops up the new least expensive element.

And extend the state in a similar way

When the algorithm pops up state (v ₁₀ , {v ₆ }), the algorithm ends. The optimal cost is 3, and the optimal path is (v ₁ , v ₃ , v ₇ , v ₁₀ ).

The above is only the preferred embodiment of the present invention, and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. Within the scope.

Claims

An optimal multi-join point path searching method applied to real-time multiplication, characterized in that the method comprises:

Obtain path search preset information, including: graph G=(V, E, W), point set U, α, starting point s, destination point t; wherein, V, E, and W are point sets, edge sets, and weights, respectively Collection
a subset of vertices; a parameter α ∈ (0, 1) for balancing the proportion of the distance between the points in the s to t paths P st and U on the graph G to the path P st ;

Initialize queue Q and set D, initial state
Join the queue Q;

Repeat the following steps when the queue Q is not empty:

A. The first element ((v, X), cost) in the pop-up queue Q; where v is the end point of the sub-path, X is a subset of Us that are included in the sub-path, and cost is the cost of the state (v, X).

B. If v=t and X=U, return cost;

C, adding the state (v, X) to the set D;

D, for all (v, u) edge loops in set E, update (Q, D, (v, X), cost + α × w (v, u));

w(v, u) is the weight of the edge (v, u);

E, for all x-point loops in the set U-X, update

(Q, D, (v, X ∪ {x}), cost + (1 - α) × dist (x, v)); where dist (x, v) is the distance from point x to point v.

The optimal path is obtained after the end of the loop.
The optimal multi-join point path searching method according to claim 1, wherein in the method, if an optimal solution has not been found at the end of the loop, ∞ is returned.
The optimal multi-join point path searching method according to claim 1, wherein in the method, the operation of updating (Q, D, (v, X), cost) is as follows:

When the state (v, X) ∈ D, return directly;

When state
When the state ((v, X), cost) is pushed into the queue Q;

When cost<Q.cost((v,X)), Q.update((v,X), cost).
An optimal multi-joining point path searching device for real-time multiplication is applicable to a mobile terminal, and the device includes:

Search information input unit: used to obtain path search preset information, including: graph G=(V, E, W), point set U, α, starting point s, destination point t; wherein, V, E, and W are points respectively a set of sets, edge sets, and weights;
a subset of vertices; the parameter α∈(0,1) is used to balance the distance and the proportion of the distance between the points P St and U to P st ;

a path searching unit: configured to search for preset information according to the path, and search for an optimal path from the starting point s to the destination point t in the graph G by using a best-priority dynamic programming strategy;

Search result output unit: for outputting an optimal path searched by the path search unit.
The optimal multi-join point path searching device according to claim 4, wherein the mobile terminal comprises: a mobile phone, a smart phone, a notebook computer, a personal digital assistant, and a tablet computer.