The Shortest Path Problem with Time Windows

The shortest path problem with turn restrictions (SPPTR) aims to find the shortest path on a network with turn restrictions. Five different algorithms and the 0-1 programming model for the SPPTR.

Reference: Gutiérrez E, Medaglia A L. Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks[J]. Annals of Operations Research, 2008, 157(1): 169-182. (labeling_v1)

Reference: Li Qingquan, et al. A hybrid link-node approach for finding shortest paths in road networks with turn restrictions[J]. Transactions in GIS, 2015. (labeling_v2)

Referenece: Kirby R F, Potts R B. The minimum route problem for networks with turn penalties and prohibitions[J]. Transportation Research, 1969, 3(3): 397-408. (node_spliting)

Reference: Winter S. Modeling costs of turns in route planning[J]. GeoInformatica, 2002, 6(4): 363-380. (line_graph)

labeling_v3 is the labeling algorithm for the SPPTR with improved labeling strategies.

SPPTR_01 is a 0-1 mathematical programmimg model for the SPPTR.

Variables	Meaning
network	Dictionary, {node1: {node2: [cost1, time1], node3: [cost2, time2] ...}, ...}
source	The source node
destination	The destination node
tr	Turn restrictions
nn	The number of nodes
neighbor	Dictionary, {node1: {node2: length, node3: length, ...}, ...}
p_list	List, the path label associated to each label
queue	The priority queue, which outputs the label that has the minimum value of the summation of objectives at each iteration
omega	List, the ever explored labels
label_in	The number of labels added into the priority queue
label_out	The number of labels extracted from the priority queue

Example

if __name__ == '__main__':
    test_network = {
        0: {2: 1},
        1: {2: 1},
        2: {0: 1, 1: 1, 3: 2, 5: 1},
        3: {4: 1},
        4: {5: 2},
        5: {2: 1},
    }
    tr = [[0, 2, 5]]
    print(main(test_network, 0, 5, tr))

Output (labeling_v1):

({'path': [0, 2, 1, 2, 5], 'length': 4}, 8, 7)

Output (labeling_v2):

({'path': [0, 2, 1, 2, 5], 'length': 4}, 6, 6)

The results indicate that labeling_v2 is more efficient than labeling_v1, as it adds and extracts less labels from the priority queue.