利用Google的OR-Tools解决智能调度问题
解决智能调度问题可以利用Google的OR-Tools库来实现。以下是一个详细的解决思路及解决方案：
一、定义问题
货物信息：包括重量、体积、提货坐标位置、提货时间范围、送货坐标位置、送货时间范围。
车辆信息：包括载重、车厢容积、每公里费用。
目标：最小化总成本，同时满足所有约束条件。
二、建模
使用VRP（Vehicle Routing Problem）模型，扩展为带时间窗的VRP（VRPTW）。
定义决策变量：每个货物由哪辆车运输，以及运输顺序。
定义约束条件：车辆载重和容积限制、时间窗限制、路径长度限制等。
定义目标函数：最小化总成本。
三、求解
使用OR-Tools中的路由库（Routing Library）来求解问题。
设置初始解和搜索策略，以提高求解效率。
四、解决方案
1. 导入必要的库
python
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
import math
2. 定义数据结构
python
class Cargo:
def __init__(self, weight, volume, pickup_location, pickup_time_window, delivery_location, delivery_time_window):
self.weight = weight
self.volume = volume
self.pickup_location = pickup_location
self.pickup_time_window = pickup_time_window
self.delivery_location = delivery_location
self.delivery_time_window = delivery_time_window
class Vehicle:
def __init__(self, capacity_weight, capacity_volume, cost_per_km):
self.capacity_weight = capacity_weight
self.capacity_volume = capacity_volume
self.cost_per_km = cost_per_km
3. 计算距离和时间
python
def distance(location1, location2):
# 假设location是一个(x, y)坐标
x1, y1 = location1
x2, y2 = location2
return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
def time_to_travel(distance, speed=1.0):
# 假设速度为1.0单位距离/单位时间
return distance / speed
4. 创建数据模型
python
def create_data_model():
data = {}
data['cargo'] = [
Cargo(10, 2, (0, 0), (0, 10), (1, 1), (10, 20)),
Cargo(20, 3, (2, 2), (5, 15), (3, 3), (15, 25)),
# 添加更多货物信息
]
data['vehicles'] = [
Vehicle(50, 10, 1.0),
Vehicle(30, 8, 1.2),
# 添加更多车辆信息
]
data['distance_matrix'] = []
for i in range(len(data['cargo']) + 1):
row = []
for j in range(len(data['cargo']) + 1):
if i == 0:
loc1 = (0, 0) # 假设起点为(0, 0)
else:
loc1 = data['cargo'][i-1].pickup_location
if j == 0:
loc2 = (0, 0) # 假设起点为(0, 0)
else:
loc2 = data['cargo'][j-1].pickup_location
row.append(distance(loc1, loc2))
data['distance_matrix'].append(row)
return data
5. 创建路由模型
python
def create_routing_model(data):
manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']), len(data['vehicles']), 0)
routing = pywrapcp.RoutingModel(manager)
def distance_callback(from_index, to_index):
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['distance_matrix'][from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(distance_callback)
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
def demand_callback(index):
node = manager.IndexToNode(index)
if node == 0:
return 0
return data['cargo'][node-1].weight
demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback)
routing.AddDimensionWithVehicleCapacity(
demand_callback_index,
0, # 车辆容量下限
[v.capacity_weight for v in data['vehicles']], # 每辆车的容量
True, # 是否强制从0开始
'Capacity'
)
def time_callback(from_index, to_index):
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
if from_node == 0:
loc1 = (0, 0)
else:
loc1 = data['cargo'][from_node-1].pickup_location
if to_node == 0:
loc2 = (0, 0)
else:
loc2 = data['cargo'][to_node-1].pickup_location
travel_time = time_to_travel(distance(loc1, loc2))
if to_node == 0:
return travel_time
return travel_time + data['cargo'][to_node-1].pickup_time_window[0]
time_callback_index = routing.RegisterTransitCallback(time_callback)
routing.AddDimension(
time_callback_index,
0, # 允许的最大等待时间
3000, # 最大时间窗口
False, # 不强制从0开始
'Time'
)
time_dimension = routing.GetDimensionOrDie('Time')
for location_idx, cargo in enumerate(data['cargo']):
index = manager.NodeToIndex(location_idx + 1)
time_dimension.CumulVar(index).SetRange(cargo.pickup_time_window[0], cargo.pickup_time_window[1])
for vehicle_id in range(len(data['vehicles'])):
index = routing.Start(vehicle_id)
time_dimension.CumulVar(index).SetRange(data['vehicles'][vehicle_id].pickup_time_window[0], data['vehicles'][vehicle_id].pickup_time_window[1])
for i in range(len(data['vehicles'])):
routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(time_dimension.CumulVar(routing.End(i)))
return routing, manager
6. 求解并输出结果
python
def solve_and_print_solution(data, routing, manager):
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
solution = routing.SolveWithParameters(search_parameters)
if solution:
total_distance = 0
total_cost = 0
for vehicle_id in range(len(data['vehicles'])):
index = routing.Start(vehicle_id)
plan_output = f'Route for vehicle {vehicle_id}:\n'
route_distance = 0
while not routing.IsEnd(index):
plan_output += f' {manager.IndexToNode(index)} -> '
previous_index = index
index = solution.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(previous_index, index, vehicle_id)
plan_output += f' {manager.IndexToNode(index)}\n'
plan_output += f'Distance of the route: {route_distance}m\n'
print(plan_output)
total_distance += route_distance
total_cost += route_distance * data['vehicles'][vehicle_id].cost_per_km
print(f'Total Distance of all routes: {total_distance}m')
print(f'Total Cost of all routes: {total_cost}')
else:
print('No solution found.')
7. 主函数
python
def main():
data = create_data_model()
routing, manager = create_routing_model(data)
solve_and_print_solution(data, routing, manager)
if __name__ == '__main__':
main()五、总结
以上代码展示了如何使用Google OR-Tools解决带时间窗的车辆路径问题（VRPTW）。通过定义货物和车辆的信息，计算距离和时间，创建路由模型，并求解最优路径，最终输出满足要求的最低成本方案。可以根据实际需求调整数据模型和参数，以适应不同的应用场景。