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vrp_nodes_indices

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/constraint_solver/vrp_nodes_indices.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/vrp_nodes_indices.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

Sample to better understand Node/Index relation.

This script generate few markdown tables to better understand the relation between nodes and indices.

Things to notice:

Since we have two duplicates (node 5 and node 4) solver need 2 extra indices to have an unique index for each vehicle start/stop and locations.
Solver needs to "create" an index for a vehicle 1 start since solver need an unique start index per vehicle.
All end nodes are moved to the end of the index list aka [15, 16, 17, 18].
routing.Size() return the number of node which are not end nodes (here 15 aka [0-14]) note: using the two properties above, we know that any index in range(routing.Size()) is not a vehicle end node.
Since end nodes are moved to the end, their respective "empty" node index are reused so all locations indices are "shifted" e.g. node 9 is mapped to index 6
Same for start nodes which are moved to "empty" space e.g. start node 7 mapped to index 4

Takeaway:

Allways use routing.Start(), routing.End(), manager.IndexToNode() or manager.NodeToIndex().
Location node is not necessarily equal to its index.
To loop through ALL indices use manager.GetNumberOfIndices() (Python) or manager::num_indices() (C++)

python

from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp


def main():
    """Entry point of the program."""
    locations = 17
    starts = [5, 5, 7, 8]
    ends = [1, 2, 4, 4]
    vehicles = len(starts)
    assert len(starts) == len(ends)

    manager = pywrapcp.RoutingIndexManager(locations, vehicles, starts, ends)
    routing = pywrapcp.RoutingModel(manager)

    print("Starts/Ends:")
    header = "| |"
    separator = "|---|"
    v_starts = "| start |"
    v_ends = "| end |"
    for v in range(manager.GetNumberOfVehicles()):
        header += f" vehicle {v} |"
        separator += "---|"
        v_starts += f" {starts[v]} |"
        v_ends += f" {ends[v]} |"
    print(header)
    print(separator)
    print(v_starts)
    print(v_ends)

    print("\nNodes:")
    print(
        "| locations | manager.GetNumberOfNodes | manager.GetNumberOfIndices |"
        " routing.nodes | routing.Size |"
    )
    print("|---|---|---|---|---|")
    print(
        f"| {locations} | {manager.GetNumberOfNodes()} |"
        f" {manager.GetNumberOfIndices()} | {routing.nodes()} |"
        f" {routing.Size()} |"
    )

    print("\nLocations:")
    print("| node | index | routing.IsStart | routing.IsEnd |")
    print("|---|---|---|---|")
    for node in range(manager.GetNumberOfNodes()):
        if node in starts or node in ends:
            continue
        index = manager.NodeToIndex(node)
        print(
            f"| {node} | {index} | {routing.IsStart(index)} |"
            f" {routing.IsEnd(index)} |"
        )

    print("\nStart/End:")
    print("| vehicle | Start/end | node | index | routing.IsStart | routing.IsEnd |")
    print("|---|---|---|---|---|---|")
    for v in range(manager.GetNumberOfVehicles()):
        start_index = routing.Start(v)
        start_node = manager.IndexToNode(start_index)
        print(
            f"| {v} | start | {start_node} | {start_index} |"
            f" {routing.IsStart(start_index)} | {routing.IsEnd(start_index)} |"
        )
    for v in range(manager.GetNumberOfVehicles()):
        end_index = routing.End(v)
        end_node = manager.IndexToNode(end_index)
        print(
            f"| {v} | end  | {end_node} | {end_index} |"
            f" {routing.IsStart(end_index)} | {routing.IsEnd(end_index)} |"
        )


main()