I have been using Google OR-Tools to optimize routing of a single vehicle over the span of a single day. I have included the code below, which runs in Python 3.
The time matrix I have included represents 42 locations; the first two locations are the depot where the vehicle will begin and end the day (these won't necessarily always be the same location). The remaining forty locations all represent McDonald's restaurants in the Minneapolis area. The vehicle cannot leave the depot until 6:00am (21600 seconds), and must return to the depot by 6:00pm (64800 seconds). I do have time windows enforced for visits to the locations, but for the sake of brevity and simplicity in my question, I've allowed the locations to be visited at any time (while still meeting the condition of beginning and ending the day at 6:00am and 6:00pm, respectively). Additionally, every location must be visited for a duration of 30 minutes (1800 seconds).
When I run my implementation (I have included the results below the code), there are a lot of locations that are not visited, due to the constraints I have placed. I want to modify my solution to allow for schedules to be created across multiple days. For example, I would like my implementation to explore solutions where the locations are schedule to be visited the following day as well, starting at 6:00am (21600 seconds + 86400 seconds) and ending at 6:00pm (64800 seconds + 86400 seconds). I also want to allow for disjointed time windows, though I'm afraid that may be too much to ask for someone to help me with at once. I have attempted this on my own, but my efforts have been fruitless and yielded only errors. I thought sharing my working solution and my constraints would be a good place to start when asking for help, but I'd be more than happy to provide any additional context and information I may have omitted.
I have already referenced the following resources:
- Multiple time windows for vehicle routing problem instance #167
- VRP with Time Windows - More than 1 time window per location #456
- Multiple Time Windows per Location, and Vehicle Specialties & Replenishment
- Multiple time windows vrp [or-tools]
I warmly welcome any suggestions, guidance, or support. Thank you!
Source:
from ortools.constraint_solver import pywrapcp
from ortools.constraint_solver import routing_enums_pb2
Matrix = 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Windows = [[21600, 21600], [64800, 64800], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400], [0, 86400]]
Durations = [0, 0, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800]
Penalties = [576460752303423487, 576460752303423487, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]
Slack_Max = 86400
Capacity = 86400
# The inputs to RoutingIndexManager are:
# 1. The number of rows of the time matrix, which is the number of locations (including the depot).
# 2. The number of vehicles in the problem.
# 3. The node corresponding to the depot.
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(Matrix), 1, [0], [1])
# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)
# Create and register a transit callback.
def time_callback(from_index, to_index):
# Returns the travel time between the two nodes.
# Convert from routing variable Index to time matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return Matrix[from_node][to_node] + Durations[from_node]
transit_callback_index = routing.RegisterTransitCallback(time_callback)
# Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# Add Time Windows constraint.
routing.AddDimension(
transit_callback_index,
Slack_Max, # An upper bound for slack (the wait times at the locations).
Capacity, # An upper bound for the total time over each vehicle's route.
False, # Determine whether the cumulative variable is set to zero at the start of the vehicle's route.
'Time')
time_dimension = routing.GetDimensionOrDie('Time')
# Allow all locations except the first two to be droppable.
for node in range(2, len(Matrix)):
routing.AddDisjunction([manager.NodeToIndex(node)], Penalties[node])
# Add time window constraints for each location except depot.
for location_idx, time_window in enumerate(Windows):
if location_idx == 0 or location_idx == 1:
continue
index = manager.NodeToIndex(location_idx)
time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
# Add time window constraints for each vehicle start node.
index = routing.Start(0)
time_dimension.CumulVar(index).SetRange(Windows[0][0],Windows[0][1])
index = routing.End(0)
time_dimension.CumulVar(index).SetRange(Windows[1][0],Windows[1][1])
# Instantiate route start and end times to produce feasible times.
routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.Start(0)))
routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.End(0)))
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
# Setting local search metaheuristics:
search_parameters.local_search_metaheuristic = (routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
search_parameters.time_limit.seconds = 5
search_parameters.log_search = False
# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)
# Print the results
result = {
'Dropped': [],
'Scheduled': []
}
# Return the dropped locations
for node in range(routing.Size()):
if routing.IsStart(node) or routing.IsEnd(node):
continue
if solution.Value(routing.NextVar(node)) == node:
result['Dropped'].append(manager.IndexToNode(node))
# Return the scheduled locations
time = 0
index = routing.Start(0)
while not routing.IsEnd(index):
time = time_dimension.CumulVar(index)
result['Scheduled'].append([manager.IndexToNode(index), solution.Min(time),solution.Max(time)])
index = solution.Value(routing.NextVar(index))
time = time_dimension.CumulVar(index)
result['Scheduled'].append([manager.IndexToNode(index), solution.Min(time),solution.Max(time)])
print(result)
Output:
{'Dropped': [5, 8, 9, 20, 21, 22, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41], 'Scheduled': [[0, 21600, 21600], [14, 21964, 21982], [15, 24235, 24253], [10, 26468, 26486], [12, 28494, 28512], [11, 30568, 30586], [13, 32677, 32695], [23, 34869, 34887], [29, 37037, 37055], [24, 39103, 39121], [7, 41413, 41431], [3, 43898, 43916], [2, 46266, 46284], [4, 48674, 48692], [6, 51672, 51690], [17, 53921, 53939], [19, 56163, 56181], [18, 58543, 58561], [26, 60553, 60571], [16, 62703, 62721], [1, 64800, 64800]]}
from Google OR-Tools TSP spanning multiple days with start/stop times
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