如何解决OR-Tools：我怎么不能从仓库到第一个退出时刻的等待时间？
我正在解决日程安排问题，我有 N 名员工驾驶车辆以一致的日期访问 M 客户的家。
我看到的问题是，每辆车的总时间包括从仓库到下车到达的时间，再到第一个访问地点的第一个一致日期。例如，如果车辆 0 个工作日的时间窗口是（上午 8 点，晚上 19 点），第一个日期是 3（上午 9 点 15 点）：
Route for vehicle 0:
0 Time(09:10,09:10) -> 3 Time(09:15,09:15) -> 7 Time(12:00,12:00) -> 11 Time(16:35,16:35) -> 0 Time(17:31,17:31)
Time of the route: 571min
我的预期路线时间为 501 分钟，我不想将早上 8 点到 9.10 的 70 分钟等待时间相加。我怎么能做到这一点？
先谢谢你！我希望@Mizux 可以帮助我 :)
使用当前解决方案进行编辑：跟踪总路线分钟数和仅行驶时间以便可以比较两者：
# Data
time_matrix=[
[0,350.8,556.1,272.5,401.7,319.4,306.1,521.2,569.4,502.4,722.5,742.1],[275.4,243.5,200.9,404.8,436.4,139.7,279.3,256.8,189.8,409.9,468.6],[419.6,182.4,338,541.9,573.5,283.9,239.4,177.2,73.6,250.2,308.9],[115.4,245.3,442.8,372.4,291.5,289.8,370,446.1,388.2,608.3,614.7],[391.3,443.9,608.6,410.2,292.9,527.5,539.6,615.7,586.8,782.9,747.8],[248.9,412.8,609.2,351.8,300.1,415,478.5,554.6,774.7,686.7],[207.7,115.5,320.8,268.1,462.2,378.6,356.6,334.1,267.1,487.2,545.9],[419.5,220.6,199.4,304.1,449.2,507.6,322.1,76.1,257.6,306.3,309.9],[478.8,241.6,135.1,379.5,524.6,583,343.1,75.4,208.7,242,245.6],[346,108.8,134.9,264.4,468.3,499.9,210.3,170.7,148.2,309.2,367.9],[576.8,330.9,229.1,495.2,699.1,730.7,404.2,374.4,299,230.8,333.9],[681.4,444.2,277.6,586.3,706.6,765,545.7,302.8,238.6,335.4,207.8,0]
]
ttw = [(0,660),(0,(60,75),\
(120,135),(90,105),(180,195),(240,255),(285,300),\
(480,495),(510,525),525)]
services_duration = [0,90,45,60,30,150,45]
NUM_VEHICLES = 3
MIN_ORDERS_BY_VEHICLE = 3 # minimum 2 orders by vehicle
RELATIVE_START_TIME = 8 # 8AM start work day
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def create_data_model():
"""Stores the data for the problem."""
data = {}
data['time_matrix'] = time_matrix
data['time_windows'] = ttw # time windows with concerted dates
data['time_service'] = services_duration # service time for each order
data['num_vehicles'] = NUM_VEHICLES
# we start from initial routes for trying to optimize them
data['initial_routes'] = [
[3,7,11],# order vehicle 0
[4,6,10],# order vehicle 1
[5,8,9] # # order vehicle 2
]
# vehicles starts and ends from/to same location
data['starts'] = [0,1,2]
data['ends'] = [0,2]
data['breaks'] = [(360,360,120),(360,120)]
return data
def print_solution(data,manager,routing,solution):
time_dimension = routing.GetDimensionorDie('Time')
count_dimension = routing.GetDimensionorDie('count')
travel_dimension = routing.GetDimensionorDie('travel')
total_time = 0
driving_time = 0
for vehicle_id in range(data['num_vehicles']):
index = routing.Start(vehicle_id)
plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
i = 0
while not routing.IsEnd(index):
time_var = time_dimension.CumulVar(index)
travel_var = travel_dimension.CumulVar(index)
if i == 0: # store wait time until first exit moment in order can substract it from total route time later
first_wait_time_depot = solution.Min(time_var)
count_var = count_dimension.CumulVar(index)
plan_output += '{0} Time({1},{2}) -> '.format(manager.IndexToNode(index),"{:02d}:{:02d}".format(*divmod((RELATIVE_START_TIME*60)+solution.Min(time_var),60)),"{:02d}:{:02d}".format(*divmod((RELATIVE_START_TIME*60)+solution.Max(time_var),60))
)
index = solution.Value(routing.Nextvar(index))
i+=1
time_var = time_dimension.CumulVar(index)
travel_var = travel_dimension.CumulVar(index)
count_var = count_dimension.CumulVar(index)
plan_output += '{0} Time({1},{2})\n'.format(manager.IndexToNode(index),60)))
print('Orders by vehicle: {}'.format(solution.Min(count_var)-1))
plan_output += 'Time of the route (with waiting and service times): {}min\n'.format(
solution.Min(time_var)-first_wait_time_depot)
plan_output += 'Time of the route (only driving time): {}min\n'.format(
solution.Min(travel_var))
print(plan_output)
total_time += solution.Min(time_var)-first_wait_time_depot
driving_time += solution.Min(travel_var)
print('Total time of all routes: {}min'.format(total_time))
print('Total driving time of all routes: {}min'.format(driving_time))
return {'driving_time': driving_time,'total_time':total_time}
def main():
"""Entry point of the program."""
data = create_data_model()
# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['time_matrix']),data['num_vehicles'],data['starts'],data['ends'])
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 data['time_service'][from_node]+(int(round(data['time_matrix'][from_node][to_node]/60.)))
def travel_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 int(round(data['time_matrix'][from_node][to_node]/60.))
transit_callback_index = routing.RegisterTransitCallback(time_callback)
travel_callback_index = routing.RegisterTransitCallback(travel_callback)
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# Add Time dimension.
time = 'Time'
routing.AddDimension(
transit_callback_index,660,# allow waiting time
660,# maximum time per vehicle
False,# Don't force start cumul to zero. Vehicles don't have to start to exactly start hour
time)
time_dimension = routing.GetDimensionorDie(time)
# Add only travel time dimension.
routing.AddDimension(
travel_callback_index,# maximum time per vehicle
True,# Don't force start cumul to zero. Vehicles don't have to start to exactly start hour
'travel')
travel_dimension = routing.GetDimensionorDie('travel')
# Add time window constraints for each location except depots.
for location_idx,time_window in enumerate(data['time_windows']):
if location_idx in data['starts']:
continue # except depots
index = manager.NodetoIndex(location_idx)
time_dimension.CumulVar(index).SetRange(time_window[0],time_window[1])
# Set allowed vehicles for order
routing.SetAllowedVehiclesForIndex([],index) # for the moment,all vehicles can visit any node
# Add COUNT dimension constraint.
count_dimension_name = 'count'
routing.AddConstantDimension(
1,# increment by one every time
len(data['time_matrix'])+1,# make sure the return to depot node can be counted
True,# set count to zero
count_dimension_name)
count_dimension = routing.GetDimensionorDie(count_dimension_name)
# enable empty route cost
# https://github.com/google/or-tools/issues/2067
# https://github.com/google/or-tools/issues/2161
for vehicle_id in range(data['num_vehicles']):
routing.ConsiderEmptyRouteCostsForVehicle(True,vehicle_id)
# Add time window constraints for each vehicle start node.
for vehicle_id in range(data['num_vehicles']):
# force depot waiting time to zero
time_dimension.SlackVar(routing.Start(vehicle_id)).SetValue(0)
index = routing.Start(vehicle_id)
time_dimension.CumulVar(index).SetRange(data['time_windows'][vehicle_id][0],data['time_windows'][vehicle_id][1])
# https://activimetrics.com/blog/ortools/counting_dimension/
for vehicle_id in range(data['num_vehicles']):
index_end = routing.End(vehicle_id)
count_dimension.SetCumulVarSoftLowerBound(index_end,MIN_ORDERS_BY_VEHICLE + 1,100000)
# set break time for vehicles
node_visit_transit = {}
for n in range(routing.Size()):
if n >= len(data['time_service']):
node_visit_transit[n] = 0
else:
node_visit_transit[n] = 1
break_intervals = {}
for v in range(data['num_vehicles']):
vehicle_break = data['breaks'][v]
break_intervals[v] = [
routing.solver().FixedDurationIntervalVar(vehicle_break[0],vehicle_break[1],vehicle_break[2],False,'Break for vehicle {}'.format(v))
]
time_dimension.SetBreakIntervalsOfVehicle(
break_intervals[v],v,node_visit_transit
)
# Instantiate route start and end times to produce feasible times.
# to start the later and finish the earliest possible
for i in range(manager.GetNumberOfVehicles()):
routing.AddVariableMaximizedByFinalizer(
time_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.End(i)))
for i in range(manager.GetNumberOfVehicles()):
routing.AddVariableMaximizedByFinalizer(
travel_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(
travel_dimension.CumulVar(routing.End(i)))
initial_solution = routing.ReadAssignmentFromroutes(data['initial_routes'],True)
print("Initial sol:\n")
ini_times = print_solution(data,initial_solution)
# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEApest_ARC)
search_parameters.local_search_Metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
search_parameters.time_limit.FromSeconds(100)
solution = routing.solveFromAssignmentWithParameters(initial_solution,search_parameters)
if solution:
print("\nSolved sol:\n")
end_times = print_solution(data,solution)
print("\nTotal route minutes saved: {} min".format(ini_times['total_time'] - end_times['total_time']))
print("Only driving minutes saved: {} min".format(ini_times['driving_time'] - end_times['driving_time']))
if __name__ == '__main__':
main()
解决方法
一些事情：
- 创建维度时不要“强制累积量开始为零”，即将其设置为
false，这样车辆就不必在早上 8 点准时出发。 - 您可以将仓库等待时间强制为零：
time_dimension.SlackVar(routing.Start(vehicle)).SetValue(0) - 您可以使用 Finalizer 开始较晚并尽可能早地完成
for i in range(manager.GetNumberOfVehicles()):
routing.AddVariableMaximizedByFinalizer(
time_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.End(i)))
编辑：
也许你的总时间计算是错误的：
17:30 = 17*60 + 30 = 1051 min (from 0:00AM)
9:10 = 9*60+10 = 550 min (from 0:00AM)
和 1051 - 550 = 501 min 所以看起来你的总时间（持续时间）计算是错误的......
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