| Title: | Algorithms for Routing and Solving the Traffic Assignment Problem |
|---|---|
| Description: | Calculation of distances, shortest paths and isochrones on weighted graphs using several variants of Dijkstra algorithm. Proposed algorithms are unidirectional Dijkstra (Dijkstra, E. W. (1959) <doi:10.1007/BF01386390>), bidirectional Dijkstra (Goldberg, Andrew & Fonseca F. Werneck, Renato (2005) <https://archive.siam.org/meetings/alenex05/papers/03agoldberg.pdf>), A* search (P. E. Hart, N. J. Nilsson et B. Raphael (1968) <doi:10.1109/TSSC.1968.300136>), new bidirectional A* (Pijls & Post (2009) <https://repub.eur.nl/pub/16100/ei2009-10.pdf>), Contraction hierarchies (R. Geisberger, P. Sanders, D. Schultes and D. Delling (2008) <doi:10.1007/978-3-540-68552-4_24>), PHAST (D. Delling, A.Goldberg, A. Nowatzyk, R. Werneck (2011) <doi:10.1016/j.jpdc.2012.02.007>). Algorithms for solving the traffic assignment problem are All-or-Nothing assignment, Method of Successive Averages, Frank-Wolfe algorithm (M. Fukushima (1984) <doi:10.1016/0191-2615(84)90029-8>), Conjugate and Bi-Conjugate Frank-Wolfe algorithms (M. Mitradjieva, P. O. Lindberg (2012) <doi:10.1287/trsc.1120.0409>), Algorithm-B (R. B. Dial (2006) <doi:10.1016/j.trb.2006.02.008>). |
| Authors: | Vincent Larmet |
| Maintainer: | Vincent Larmet <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.1 |
| Built: | 2024-08-17 05:14:23 UTC |
| Source: | https://github.com/vlarmet/cppRouting |
Estimation of the User Equilibrium (UE)
assign_traffic( Graph, from, to, demand, algorithm = "bfw", max_gap = 0.001, max_it = .Machine$integer.max, aon_method = "bi", constant = 1, dial_params = NULL, verbose = TRUE )assign_traffic( Graph, from, to, demand, algorithm = "bfw", max_gap = 0.001, max_it = .Machine$integer.max, aon_method = "bi", constant = 1, dial_params = NULL, verbose = TRUE )
Graph |
An object generated by makegraph function. |
from |
A vector of origins |
to |
A vector of destinations. |
demand |
A vector describing the flow between each origin-destination pair. |
algorithm |
character. |
max_gap |
Numeric. Relative gap to achieve. Default to 0.001. |
max_it |
Numeric. Maximum number of iterations. Default to |
aon_method |
Character. |
constant |
numeric. Constant to maintain the heuristic function admissible in NBA* algorithm. Default to 1, when cost is expressed in the same unit than coordinates. See details |
dial_params |
List. Named list of hyperparameters for |
verbose |
Logical. If |
The most well-known assumptions in traffic assignment models are the ones following Wardrop's first principle. Traffic assignment models are used to estimate the traffic flows on a network. These models take as input a matrix of flows that indicate the volume of traffic between origin and destination (O-D) pairs. Unlike All-or-Nothing assignment (see get_aon), edge congestion is modeled through the Volume Decay Function (VDF). The Volume Decay Function used is the most popular in literature, from the Bureau of Public Roads :
t = t0 * (1 + a * (V/C)^b) with t = actual travel time (minutes), t0 = free-flow travel time (minutes), a = alpha parameter (unitless), b = beta parameter (unitless), V = volume or flow (veh/hour) C = edge capacity (veh/hour)
Traffic Assignment Problem is a convex problem and solving algorithms can be divided into two categories :
link-based : Method of Successive Average (msa) and Frank-Wolfe variants (normal : fw, conjugate : cfw and bi-conjugate : bfw).
These algorithms uses the descent direction given by AON assignment at each iteration, all links are updated at the same time.
bush-based : Algorithm-B (dial)
The problem is decomposed into sub-problems, corresponding to each origin of the OD matrix, that operate on acyclic sub-networks of the original transportation network, called bushes.
Link flows are shifted from the longest path to the shortest path recursively within each bush using Newton method.
Link-based algorithms are historically the first algorithms developed for solving the traffic assignment problem. It require low memory and are known to tail in the vicinity of the optimum and usually cannot be used to achieve highly precise solutions.
Algorithm B is more recent, and is better suited for achieve the highest precise solution. However, it require more memory and can be time-consuming according the network size and OD matrix size.
In cppRouting, the implementation of algorithm-B allow "batching", i.e. bushes are temporarily stored on disk if memory limit, defined by the user, is exceeded.
Please see the package website for practical example and deeper explanations about algorithms. (https://github.com/vlarmet/cppRouting/blob/master/README.md)
Convergence criterion can be set by the user using max_gap argument, it is the relative gap which can be written as : abs(TSTT/SPTT - 1) with TSTT (Total System Travel Time) = sum(flow * cost), SPTT (Shortest Path Travel Time) = sum(aon * cost)
Especially for link-based algorithms (msa, *fw), the larger part of computation time rely on AON assignment. So, choosing the right AON algorithm is crucial for fast execution time. Contracting the network on-the-fly before AON computing can be faster for large network and/or large OD matrix.
AON algorithms are :
bi : bidirectional Dijkstra algorithm
nba : bidirectional A* algorithm, nodes coordinates and constant parameter are needed
d : Dijkstra algorithm
cbi : contraction hierarchies + bidirectional search
cphast : contraction hierarchies + phast algorithm
These AON algorithm can be decomposed into two families, depending the sparsity of origin-destination matrix :
recursive pairwise : bi, nba and cbi. Optimal for high sparsity. One-to-one algorithm is called N times, with N being the length of from.
recursive one-to-many : d and cphast. Optimal for dense matrix. One-to-many algorithm is called N times, with N being the number of unique from (or to) nodes
For large instance, it may be appropriate to test different aon_method for few iterations and choose the fastest one for the final estimation.
Hyperparameters for algorithm-b are :
inneriter : number of time bushes are equilibrated within each iteration. Default to 20
max_tol : numerical tolerance. Flow is set to 0 if less than max_tol. Since flow shifting consist of iteratively adding or substracting double types, numerical error can occur and stop convergence.
Default to 1e-11.
tmp_path : Path for storing bushes during algorithm-B execution. Default using tempdir()
max_mem : Maximum amount of RAM used by algorithm-B in gigabytes. Default to 8.
In New Bidirectional A star algorithm, euclidean distance is used as heuristic function. To understand the importance of constant parameter, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md All algorithms are partly multithreaded (AON assignment).
A list containing :
The relative gap achieved
Number of iteration
A data.frame containing edges attributes, including equilibrated flows, new costs and free-flow travel times.
from, to and demand must be the same length.
alpha, beta and capacity must be filled in during network construction. See makegraph.
Wardrop, J. G. (1952). "Some Theoretical Aspects of Road Traffic Research".
M. Fukushima (1984). "A modified Frank-Wolfe algorithm for solving the traffic assignment problem".
R. B. Dial (2006). "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration".
M. Mitradjieva, P. O. Lindberg (2012). "The Stiff Is Moving — Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment".
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) # Origin-destination trips trips <- data.frame(from = c(0,0,0,0,1,1,1,1,2,2,2,3,3,4,5,5,5,5,5), to = c(1,2,5,3,2,5,2,4,2,5,2,3,5,2,0,0,3,5,1), flow = c(10,30,15,5,5,2,3,6,4,15,20,2,3,6,2,1,4,5,3)) #Construct graph graph <- makegraph(edges,directed=TRUE, alpha = 0.15, beta = 4, capacity = 5) # Solve traffic assignment problem ## using Bi-conjugate Frank-Wolfe algorithm traffic <- assign_traffic(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "bfw") print(traffic$data) ## using algorithm-B traffic2 <- assign_traffic(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "dial") print(traffic2$data)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) # Origin-destination trips trips <- data.frame(from = c(0,0,0,0,1,1,1,1,2,2,2,3,3,4,5,5,5,5,5), to = c(1,2,5,3,2,5,2,4,2,5,2,3,5,2,0,0,3,5,1), flow = c(10,30,15,5,5,2,3,6,4,15,20,2,3,6,2,1,4,5,3)) #Construct graph graph <- makegraph(edges,directed=TRUE, alpha = 0.15, beta = 4, capacity = 5) # Solve traffic assignment problem ## using Bi-conjugate Frank-Wolfe algorithm traffic <- assign_traffic(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "bfw") print(traffic$data) ## using algorithm-B traffic2 <- assign_traffic(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "dial") print(traffic2$data)
Contract a graph by using contraction hierarchies algorithm
cpp_contract(Graph, silent = FALSE)cpp_contract(Graph, silent = FALSE)
Graph |
An object generated by makegraph or cpp_simplify function. |
silent |
Logical. If |
Contraction hierarchies is a speed-up technique for finding shortest path in a graph.
It consist of two steps : preprocessing phase and query. cpp_contract() preprocess the input graph to later use special query algorithm implemented in get_distance_pair, get_distance_matrix, get_aon and get_path_pair functions.
To see the benefits of using contraction hierarchies, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md.
A contracted graph.
#Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Contract graph contracted_graph<-cpp_contract(graph,silent=TRUE)#Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Contract graph contracted_graph<-cpp_contract(graph,silent=TRUE)
Reduce the number of edges by removing non-intersection nodes, duplicated edges and isolated loops in the graph.
cpp_simplify( Graph, keep = NULL, rm_loop = TRUE, iterate = FALSE, silent = TRUE )cpp_simplify( Graph, keep = NULL, rm_loop = TRUE, iterate = FALSE, silent = TRUE )
Graph |
An object generated by makegraph function. |
keep |
Character or integer vector. Nodes of interest that will not be removed. Default to |
rm_loop |
Logical. if |
iterate |
Logical. If |
silent |
Logical. If |
To understand why process can be iterated, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md
The simplified cppRouting graph
Additional edge attributes like aux, alpha, beta and capacity will be removed.
The first iteration usually eliminates the majority of non-intersection nodes and is therefore faster.
#Simple directed graph edges<-data.frame(from=c(1,2,3,4,5,6,7,8), to=c(0,1,2,3,6,7,8,5), dist=c(1,1,1,1,1,1,1,1)) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(edges) plot(igr) } #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Simplify the graph, removing loop simp<-cpp_simplify(graph, rm_loop=TRUE) #Convert cppRouting graph to data frame simp<-to_df(simp) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(simp) plot(igr) } #Simplify the graph, keeping node 2 and keeping loop simp<-cpp_simplify(graph,keep=2 ,rm_loop=FALSE) #Convert cppRouting graph to data frame simp<-to_df(simp) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(simp) plot(igr) }#Simple directed graph edges<-data.frame(from=c(1,2,3,4,5,6,7,8), to=c(0,1,2,3,6,7,8,5), dist=c(1,1,1,1,1,1,1,1)) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(edges) plot(igr) } #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Simplify the graph, removing loop simp<-cpp_simplify(graph, rm_loop=TRUE) #Convert cppRouting graph to data frame simp<-to_df(simp) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(simp) plot(igr) } #Simplify the graph, keeping node 2 and keeping loop simp<-cpp_simplify(graph,keep=2 ,rm_loop=FALSE) #Convert cppRouting graph to data frame simp<-to_df(simp) #Plot if(requireNamespace("igraph",quietly = TRUE)){ igr<-igraph::graph_from_data_frame(simp) plot(igr) }
Given an origin-destination matrix, compute All-or-Nothing assignment.
get_aon(Graph, from, to, demand, algorithm = "bi", constant = 1)get_aon(Graph, from, to, demand, algorithm = "bi", constant = 1)
Graph |
An object generated by makegraph, or cpp_contract function. |
from |
A vector of origins |
to |
A vector of destinations. |
demand |
A vector describing the flow between each origin-destination pair. |
algorithm |
character. For contracted network : |
constant |
numeric. Constant to maintain the heuristic function admissible in NBA* algorithm. Default to 1, when cost is expressed in the same unit than coordinates. See details |
All-or-Nothing assignment (AON) is the simplest method to load flow on a network, since it assume there is no congestion effects.
The assignment algorithm itself is the procedure that loads the origin-destination matrix to the shortest path trees and produces the flows.
Origin-destination matrix is represented via 3 vectors : from, to and demand.
There is two variants of algorithms, depending the sparsity of origin-destination matrix :
recursive one-to-one : Bidirectional search (bi) and Bidirectional A* (nba). Optimal for high sparsity.
recursive one-to-many : Dijkstra (d) and PHAST (phast). Optimal for dense matrix.
For large network and/or large OD matrix, this function is a lot faster on a contracted network. In New Bidirectional A star algorithm, euclidean distance is used as heuristic function. To understand the importance of constant parameter, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md
All algorithms are multithreaded. Please use RcppParallel::setThreadOptions() to set the number of threads.
A data.frame containing edges attributes, including flow.
'from', 'to' and 'demand' must be the same length.
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) # Origin-destination trips trips <- data.frame(from = c(0,0,0,0,1,1,1,1,2,2,2,3,3,4,5,5,5,5,5), to = c(1,2,5,3,2,5,2,4,2,5,2,3,5,2,0,0,3,5,1), flow = c(10,30,15,5,5,2,3,6,4,15,20,2,3,6,2,1,4,5,3)) #Construct graph graph<-makegraph(edges,directed=TRUE) # Compute All-or-Nothing assignment aon <- get_aon(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "d") print(aon)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) # Origin-destination trips trips <- data.frame(from = c(0,0,0,0,1,1,1,1,2,2,2,3,3,4,5,5,5,5,5), to = c(1,2,5,3,2,5,2,4,2,5,2,3,5,2,0,0,3,5,1), flow = c(10,30,15,5,5,2,3,6,4,15,20,2,3,6,2,1,4,5,3)) #Construct graph graph<-makegraph(edges,directed=TRUE) # Compute All-or-Nothing assignment aon <- get_aon(Graph=graph, from=trips$from, to=trips$to, demand = trips$flow, algorithm = "d") print(aon)
Return the nodes that can be reached in a detour time set around the shortest path
get_detour(Graph, from, to, extra = NULL, keep = NULL, long = FALSE)get_detour(Graph, from, to, extra = NULL, keep = NULL, long = FALSE)
Graph |
An object generated by makegraph or cpp_simplify function. |
from |
A vector of one or more vertices from which shortest path are calculated (origin). |
to |
A vector of one or more vertices (destination). |
extra |
numeric. Additional cost |
keep |
numeric or character. Vertices of interest that will be returned. |
long |
logical. If |
Each returned nodes n meet the following condition :
SP(o,n) + SP(n,d) < SP(o,d) + t
with SP shortest distance/time, o the origin node, d the destination node and t the extra cost.
Modified bidirectional Dijkstra algorithm is ran for each path.
This algorithm is multithreaded. Please use RcppParallel::setThreadOptions() to set the number of threads.
list or a data.frame of nodes that can be reached
from and to must be the same length.
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) if(requireNamespace("igraph",quietly = TRUE)){ #Generate fully connected graph gf<- igraph::make_full_graph(400) igraph::V(gf)$names<-1:400 #Convert to data frame and add random weights df<-igraph::as_long_data_frame(gf) df$dist<-sample(1:100,nrow(df),replace = TRUE) #Construct cppRouting graph graph<-makegraph(df[,c(1,2,5)],directed = FALSE) #Pick up random origin and destination node origin<-sample(1:400,1) destination<-sample(1:400,1) #Compute distance from origin to all nodes or_to_all<-get_distance_matrix(graph,from=origin,to=1:400) #Compute distance from all nodes to destination all_to_dest<-get_distance_matrix(graph,from=1:400,to=destination,) #Get all shortest paths from origin to destination, passing by each node of the graph total_paths<-rowSums(cbind(t(or_to_all),all_to_dest)) #Compute shortest path between origin and destination distance<-get_distance_pair(graph,from=origin,to=destination) #Compute detour with an additional cost of 3 det<-get_detour(graph,from=origin,to=destination,extra=3) #Check result validity length(unlist(det)) length(total_paths[total_paths < distance + 3]) }#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) if(requireNamespace("igraph",quietly = TRUE)){ #Generate fully connected graph gf<- igraph::make_full_graph(400) igraph::V(gf)$names<-1:400 #Convert to data frame and add random weights df<-igraph::as_long_data_frame(gf) df$dist<-sample(1:100,nrow(df),replace = TRUE) #Construct cppRouting graph graph<-makegraph(df[,c(1,2,5)],directed = FALSE) #Pick up random origin and destination node origin<-sample(1:400,1) destination<-sample(1:400,1) #Compute distance from origin to all nodes or_to_all<-get_distance_matrix(graph,from=origin,to=1:400) #Compute distance from all nodes to destination all_to_dest<-get_distance_matrix(graph,from=1:400,to=destination,) #Get all shortest paths from origin to destination, passing by each node of the graph total_paths<-rowSums(cbind(t(or_to_all),all_to_dest)) #Compute shortest path between origin and destination distance<-get_distance_pair(graph,from=origin,to=destination) #Compute detour with an additional cost of 3 det<-get_detour(graph,from=origin,to=destination,extra=3) #Check result validity length(unlist(det)) length(total_paths[total_paths < distance + 3]) }
Compute all shortest distance between origin and destination nodes.
get_distance_matrix( Graph, from, to, algorithm = "phast", aggregate_aux = FALSE, allcores = FALSE )get_distance_matrix( Graph, from, to, algorithm = "phast", aggregate_aux = FALSE, allcores = FALSE )
Graph |
An object generated by makegraph, cpp_simplify or cpp_contract function. |
from |
A vector of one or more vertices from which distances are calculated (origin). |
to |
A vector of one or more vertices (destination). |
algorithm |
Character. Only for contracted graph, |
aggregate_aux |
Logical. If |
allcores |
Logical (deprecated). If |
If graph is not contracted, get_distance_matrix() recursively perform Dijkstra algorithm for each from nodes.
If graph is contracted, the user has the choice between :
many to many contraction hierarchies (mch) : optimal for square matrix.
PHAST (phast) : outperform mch on rectangular matrix
Shortest path is always computed according to the main edge weights, corresponding to the 3rd column of df argument in makegraph() function.
If aggregate_aux argument is TRUE, the values returned are the sum of auxiliary weights along shortest paths.
All algorithms are multithreaded. allcores argument is deprecated, please use RcppParallel::setThreadOptions() to set the number of threads.
See details in package website : https://github.com/vlarmet/cppRouting/blob/master/README.md
Matrix of shortest distances.
It is not possible to aggregate auxiliary weights on a Graph object coming from cpp_simplify function.
get_distance_pair, get_multi_paths
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges <- data.frame(from_vertex = c(0,0,1,1,2,2,3,4,4), to_vertex = c(1,3,2,4,4,5,1,3,5), time = c(9,2,11,3,5,12,4,1,6), dist = c(5,3,4,7,5,5,5,8,7)) #Construct directed graph with travel time as principal weight, and distance as secondary weight graph <- makegraph(edges[,1:3], directed=TRUE, aux = edges$dist) #Get all nodes IDs nodes <- graph$dict$ref # Get matrix of shortest times between all nodes : the result are in time unit time_mat <- get_distance_matrix(graph, from = nodes, to = nodes) # Get matrix of distance according shortest times : the result are in distance unit dist_mat <- get_distance_matrix(graph, from = nodes, to = nodes, aggregate_aux = TRUE) print(time_mat) print(dist_mat)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges <- data.frame(from_vertex = c(0,0,1,1,2,2,3,4,4), to_vertex = c(1,3,2,4,4,5,1,3,5), time = c(9,2,11,3,5,12,4,1,6), dist = c(5,3,4,7,5,5,5,8,7)) #Construct directed graph with travel time as principal weight, and distance as secondary weight graph <- makegraph(edges[,1:3], directed=TRUE, aux = edges$dist) #Get all nodes IDs nodes <- graph$dict$ref # Get matrix of shortest times between all nodes : the result are in time unit time_mat <- get_distance_matrix(graph, from = nodes, to = nodes) # Get matrix of distance according shortest times : the result are in distance unit dist_mat <- get_distance_matrix(graph, from = nodes, to = nodes, aggregate_aux = TRUE) print(time_mat) print(dist_mat)
Compute shortest distance between origin and destination nodes.
get_distance_pair( Graph, from, to, aggregate_aux = FALSE, algorithm = "bi", constant = 1, allcores = FALSE )get_distance_pair( Graph, from, to, aggregate_aux = FALSE, algorithm = "bi", constant = 1, allcores = FALSE )
Graph |
An object generated by makegraph, cpp_simplify or cpp_contract function. |
from |
A vector of one or more vertices from which distances are calculated (origin). |
to |
A vector of one or more vertices (destination). |
aggregate_aux |
Logical. If |
algorithm |
character. |
constant |
numeric. Constant to maintain the heuristic function admissible in |
allcores |
Logical (deprecated). If |
If graph is not contracted, the user has the choice between :
unidirectional Dijkstra (Dijkstra)
A star (A*) : projected coordinates should be provided
bidirectional Dijkstra (bi)
New bi-directional A star (NBA) : projected coordinates should be provided
If the input graph has been contracted by cpp_contract function, the algorithm is a modified bidirectional search.
Shortest path is always computed according to the main edge weights, corresponding to the 3rd column of df argument in makegraph function.
If aggregate_aux argument is TRUE, the values returned are the sum of auxiliary weights along shortest paths.
In A* and New Bidirectional A star algorithms, euclidean distance is used as heuristic function.
All algorithms are multithreaded. allcores argument is deprecated, please use RcppParallel::setThreadOptions() to set the number of threads.
To understand how A star algorithm work, see https://en.wikipedia.org/wiki/A*_search_algorithm. To understand the importance of constant parameter, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md
Vector of shortest distances.
from and to must be the same length.
It is not possible to aggregate auxiliary weights on a Graph object coming from cpp_simplify function.
get_distance_matrix, get_path_pair, cpp_contract
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6), dist = c(5,3,4,7,5,5,5,8,7)) #Construct directed graph with travel time as principal weight, and distance as secondary weight graph <- makegraph(edges[,1:3], directed=TRUE, aux = edges$dist) #Get all nodes IDs nodes <- graph$dict$ref # Get shortest times between all nodes : the result are in time unit time_mat <- get_distance_pair(graph, from = nodes, to = nodes) # Get distance according shortest times : the result are in distance unit dist_mat <- get_distance_pair(graph, from = nodes, to = nodes, aggregate_aux = TRUE) print(time_mat) print(dist_mat)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6), dist = c(5,3,4,7,5,5,5,8,7)) #Construct directed graph with travel time as principal weight, and distance as secondary weight graph <- makegraph(edges[,1:3], directed=TRUE, aux = edges$dist) #Get all nodes IDs nodes <- graph$dict$ref # Get shortest times between all nodes : the result are in time unit time_mat <- get_distance_pair(graph, from = nodes, to = nodes) # Get distance according shortest times : the result are in distance unit dist_mat <- get_distance_pair(graph, from = nodes, to = nodes, aggregate_aux = TRUE) print(time_mat) print(dist_mat)
Compute isochrones/isodistances from nodes.
get_isochrone(Graph, from, lim, setdif = FALSE, keep = NULL, long = FALSE)get_isochrone(Graph, from, lim, setdif = FALSE, keep = NULL, long = FALSE)
Graph |
An object generated by makegraph or cpp_simplify function. |
from |
numeric or character. A vector of one or more vertices from which isochrones/isodistances are calculated. |
lim |
numeric. A vector of one or multiple breaks. |
setdif |
logical. If |
keep |
numeric or character. Vertices of interest that will be returned. |
long |
logical. If |
If length(lim) > 1, value is a list of length(from), containing lists of length(lim).
All algorithms are multithreaded. Please use RcppParallel::setThreadOptions() to set the number of threads.
For large graph, keep argument can be used for saving memory.
list or a data.frame containing reachable nodes below cost limit(s).
get_isochrone() recursively perform Dijkstra algorithm for each from nodes and stop when cost limit is reached.
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct directed graph directed_graph<-makegraph(edges,directed=TRUE) #Get nodes reachable around node 4 with maximum distances of 1 and 2 iso<-get_isochrone(Graph=directed_graph,from = "4",lim=c(1,2)) #With setdif set to TRUE iso2<-get_isochrone(Graph=directed_graph,from = "4",lim=c(1,2),setdif=TRUE) print(iso) print(iso2)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct directed graph directed_graph<-makegraph(edges,directed=TRUE) #Get nodes reachable around node 4 with maximum distances of 1 and 2 iso<-get_isochrone(Graph=directed_graph,from = "4",lim=c(1,2)) #With setdif set to TRUE iso2<-get_isochrone(Graph=directed_graph,from = "4",lim=c(1,2),setdif=TRUE) print(iso) print(iso2)
Compute all shortest paths between origin and destination nodes.
get_multi_paths(Graph, from, to, keep = NULL, long = FALSE)get_multi_paths(Graph, from, to, keep = NULL, long = FALSE)
Graph |
An object generated by makegraph or cpp_simplify function. |
from |
A vector of one or more vertices from which shortest paths are calculated (origin). |
to |
A vector of one or more vertices (destination). |
keep |
numeric or character. Vertices of interest that will be returned. |
long |
logical. If |
get_multi_paths() recursively perform Dijkstra algorithm for each 'from' nodes. It is the equivalent of get_distance_matrix, but it return the shortest path node sequence instead of the distance.
This algorithm is multithreaded. Please use RcppParallel::setThreadOptions() to set the number of threads.
List or a data.frame containing shortest paths.
Be aware that if 'from' and 'to' have consequent size, output will require much memory space.
get_path_pair, get_isochrone, get_detour
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Get all nodes nodes<-unique(c(edges$from_vertex,edges$to_vertex)) #Construct directed graph directed_graph<-makegraph(edges,directed=TRUE) #Get all shortest paths (node sequences) between all nodes dir_paths<-get_multi_paths(Graph=directed_graph, from=nodes, to=nodes) print(dir_paths) #Get the same result in data.frame format dir_paths_df<-get_multi_paths(Graph=directed_graph, from=nodes, to=nodes, long = TRUE) print(dir_paths_df)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Get all nodes nodes<-unique(c(edges$from_vertex,edges$to_vertex)) #Construct directed graph directed_graph<-makegraph(edges,directed=TRUE) #Get all shortest paths (node sequences) between all nodes dir_paths<-get_multi_paths(Graph=directed_graph, from=nodes, to=nodes) print(dir_paths) #Get the same result in data.frame format dir_paths_df<-get_multi_paths(Graph=directed_graph, from=nodes, to=nodes, long = TRUE) print(dir_paths_df)
Compute shortest path between origin and destination nodes.
get_path_pair( Graph, from, to, algorithm = "bi", constant = 1, keep = NULL, long = FALSE )get_path_pair( Graph, from, to, algorithm = "bi", constant = 1, keep = NULL, long = FALSE )
Graph |
An object generated by makegraph, cpp_simplify or cpp_contract function. |
from |
A vector of one or more vertices from which shortest paths are calculated (origin). |
to |
A vector of one or more vertices (destination). |
algorithm |
character. |
constant |
numeric. Constant to maintain the heuristic function admissible in A* and NBA algorithms. |
keep |
numeric or character. Vertices of interest that will be returned. |
long |
logical. If |
If graph is not contracted, the user has the choice between :
unidirectional Dijkstra (Dijkstra)
A star (A*) : projected coordinates should be provided
bidirectional Dijkstra (bi)
New bi-directional A star (NBA) : projected coordinates should be provided
If the input graph has been contracted by cpp_contract function, the algorithm is a modified bidirectional search.
In A* and NBA algorithms, euclidean distance is used as heuristic function.
All algorithms are multithreaded. Please use RcppParallel::setThreadOptions() to set the number of threads.
To understand the importance of constant parameter, see the package description : https://github.com/vlarmet/cppRouting/blob/master/README.md
list or a data.frame containing shortest path nodes between from and to.
from and from must be the same length.
get_multi_paths, get_isochrone, get_detour
#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Get all nodes nodes<-unique(c(edges$from_vertex,edges$to_vertex)) #Construct directed and undirected graph directed_graph<-makegraph(edges,directed=TRUE) non_directed<-makegraph(edges,directed=FALSE) #Sampling origin and destination nodes origin<-sample(nodes,10,replace=TRUE) destination<-sample(nodes,10,replace=TRUE) #Get distance between origin and destination in the two graphs dir_paths<-get_path_pair(Graph=directed_graph, from=origin, to=destination) non_dir_paths<-get_path_pair(Graph=non_directed, from=origin, to=destination) print(dir_paths) print(non_dir_paths)#Choose number of cores used by cppRouting RcppParallel::setThreadOptions(numThreads = 1) #Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Get all nodes nodes<-unique(c(edges$from_vertex,edges$to_vertex)) #Construct directed and undirected graph directed_graph<-makegraph(edges,directed=TRUE) non_directed<-makegraph(edges,directed=FALSE) #Sampling origin and destination nodes origin<-sample(nodes,10,replace=TRUE) destination<-sample(nodes,10,replace=TRUE) #Get distance between origin and destination in the two graphs dir_paths<-get_path_pair(Graph=directed_graph, from=origin, to=destination) non_dir_paths<-get_path_pair(Graph=non_directed, from=origin, to=destination) print(dir_paths) print(non_dir_paths)
Construct graph
makegraph( df, directed = TRUE, coords = NULL, aux = NULL, capacity = NULL, alpha = NULL, beta = NULL )makegraph( df, directed = TRUE, coords = NULL, aux = NULL, capacity = NULL, alpha = NULL, beta = NULL )
df |
A data.frame or matrix containing 3 columns: from, to, cost. See details. |
directed |
logical. If |
coords |
Optional. A data.frame or matrix containing all nodes coordinates. Columns order should be 'node_ID', 'X', 'Y'. |
aux |
Optional. A vector or a single value describing an additional edge weight. |
capacity |
Optional. A vector or a single value describing edge capacity. Used for traffic assignment. |
alpha |
Optional. A vector or a single value describing alpha parameter. Used for traffic assignment. |
beta |
Optional. A vector or a single value describing beta parameter. Used for traffic assignment. |
'from' and 'to' are character or numeric vector containing nodes IDs.
'cost' is a non-negative numeric vector describing the cost (e.g time, distance) between each 'from' and 'to' nodes.
coords should not be angles (e.g latitude and longitude), but expressed in a projection system.
aux is an additional weight describing each edge. Shortest paths are always computed using 'cost' but aux can be summed over shortest paths.
capacity, alpha and beta are parameters used in the Volume Delay Function (VDF) to equilibrate traffic in the network. See assign_traffic.
capacity, alpha, beta and aux must have a length equal to nrow(df). If a single value is provided, this value is replicated for each edge.
alpha must be different from 0 and alpha must be greater or equal to 1.
For more details and examples about traffic assignment, please see the package website : https://github.com/vlarmet/cppRouting/blob/master/README.md
Named list with two useful attributes for the user :
nbnode : total number of vertices
dict$ref : vertices IDs
#Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct directed and undirected graph directed_graph<-makegraph(edges,directed=TRUE) non_directed<-makegraph(edges,directed=FALSE) #Visualizing directed and undirected graphs if(requireNamespace("igraph",quietly = TRUE)){ plot(igraph::graph_from_data_frame(edges)) plot(igraph::graph_from_data_frame(edges,directed=FALSE)) } #Coordinates of each nodes coord<-data.frame(node=c(0,1,2,3,4,5),X=c(2,2,2,0,0,0),Y=c(0,2,2,0,2,4)) #Construct graph with coordinates directed_graph2<-makegraph(edges, directed=TRUE, coords=coord)#Data describing edges of the graph edges<-data.frame(from_vertex=c(0,0,1,1,2,2,3,4,4), to_vertex=c(1,3,2,4,4,5,1,3,5), cost=c(9,2,11,3,5,12,4,1,6)) #Construct directed and undirected graph directed_graph<-makegraph(edges,directed=TRUE) non_directed<-makegraph(edges,directed=FALSE) #Visualizing directed and undirected graphs if(requireNamespace("igraph",quietly = TRUE)){ plot(igraph::graph_from_data_frame(edges)) plot(igraph::graph_from_data_frame(edges,directed=FALSE)) } #Coordinates of each nodes coord<-data.frame(node=c(0,1,2,3,4,5),X=c(2,2,2,0,0,0),Y=c(0,2,2,0,2,4)) #Construct graph with coordinates directed_graph2<-makegraph(edges, directed=TRUE, coords=coord)
Convert cppRouting graph to data.frame
to_df(Graph)to_df(Graph)
Graph |
An object generated by cppRouting::makegraph() or cpp_simplify() function. |
Data.frame with from, to and dist column
#Simple directed graph edges<-data.frame(from=c(1,2,3,4,5,6,7,8), to=c(0,1,2,3,6,7,8,5), dist=c(1,1,1,1,1,1,1,1)) #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Convert cppRouting graph to data.frame df<-to_df(graph)#Simple directed graph edges<-data.frame(from=c(1,2,3,4,5,6,7,8), to=c(0,1,2,3,6,7,8,5), dist=c(1,1,1,1,1,1,1,1)) #Construct cppRouting graph graph<-makegraph(edges,directed=TRUE) #Convert cppRouting graph to data.frame df<-to_df(graph)