当前运筹优化领域的研究者在使用 branch-cut-and-price (BCP) 算法求解车辆路径问题 (VRP)的最优解方面取得了重大进展。BCP算法是VRPSolver中常用的算法，在许多 VRP变体的求解中表现优异。然而，其复杂的底层数学模型使其对于路径规划从业者（入门者）而言难以理解。为了解决这个问题，Najib Errami等人开发了VRPSolverEasy这个python工具包（Najib Errami, Eduardo Queiroga, Ruslan Sadykov, Eduardo Uchoa (2023) VRPSolverEasy: A Python Library for the Exact Solution of a Rich Vehicle Routing Problem. INFORMS Journal on Computing），VRPSolverEasy 提供了一个 Python 接口，无需任何混合整数规划建模知识即可使用的VRPSolver。在使用时，可以直接以VRP问题常用元素定义，例如仓库、客户、链接和车辆类型。VRPSolverEasy 可以处理多种流行的 VRP 变体及其任意组合。
目录
1. VRPSolverEasy安装
VRPSolverEasy包提供了两种使用模式，一种是免费版本，该版本中使用了开源线性规划求解器COIN-OR CLP（果然开源才是王道，COIN-OR还有其它的开源求解器，具体可参考文章开源建模框架+开源求解器 | 使用pyomo建模框架实现交通物流优化问题的求解 (shortest path p），直接使用pip安装就可获取免费版本。
python3 -m pip install VRPSolverEasy
另一个版本是学术版本（其实是使用商业版本的CPLEX求解器），该版本提供了一些基于MIP的启发式方法，在求解性能上更强，更容易获取可行解，但是安装起来稍微有点麻烦，需要以下四个步骤：
- 将VRPSolverEasy python包克隆到本地
- 安装CPLEX
- 下载并安装Bapcod，Bapcod是基于C++写的branch-and-price包，也是VRPSolverEasy python包的求解内核，一直在保持持续更新，可能也是感觉使用C++怕别人觉得困难，也推出了python接口
4. 安装完后使用cmake进行编译
cmake --build build --config Release --target bapcod-shared
编译后会生成对应不同系统的三个库文件：
"Bapcod-path/build/Bapcod/libbapcod-shared.so" // Linux
"Bapcod-path/build/Bapcod/libbapcod-shared.dylib" // MacOs
"Bapcod-path/build/Bapcod/Release/bapcod-shared.dll" // Windows
用新生成的库文件替换VRPSolverEasy中旧的库文件（lib/）,然后再重新安装VRPSolverEasy包：
python -m pip install
在使用VRPSolverEasy时，需进行参数设置solver_name=‘CPLEX’，如果使用的是Windows系统，参数设置时还需要明确CPLEX的路径，cplex_path=‘
2. VRPSolverEasy模块介绍
在安装完成后就可以使用VRPSolverEasy模块进行建模了
import VRPSolverEasy
model=VRPSolverRasy.Model()
VRPSolverEasy模型主要通过车场节点（depot points）、客户节点（customer points）、弧（link）和车辆类型（vehicle types）来进行定义。
2.1 添加车场节点（depot points）
model.add_depot(id=<id>,name='',service_time=0.0,
tw_begin=0.0,tw_end=0.0))
depot点的属性及解释如下
2.2 添加客户节点（customer points）
每个客户与一个或多个节点关联，每个节点（车场或客户）都应该有唯一的标识
model.add_customer(id=<id>,id_customer=<id>,name='',
demand=0,penalty=0.0,service_time=0.0,tw_begin=0.0,
tw_end=0.0,incompatible_vehicles=[])
此外，VRPSolverEasy还设置了添加额外节点的功能，用于表示可替代的时间窗和/或客户位置（实现一个客户对应多个节点，以便处理不同VRP问题变体的复杂情形），以及可能具有不同兼容车辆集的情况。
model.add_point(id=<id>,id_customer=<id>,name='',
demand=0,penalty=0.0,service_time=0.0,tw_begin=0.0,
tw_end=0.0,incompatible_vehicles=[])
customer点的属性及解释如下
2.3 添加弧（link）
这里link既可以是有向的arc(is_directed=True),也可以是无向的edge(is_directed=False)，link的属性及解释如下
2.4 添加车辆类型（vehicle type）
model.add_vehicle_type(id=<id>,start_point_id=-1,end_point_id=-1,
name='',capacity=0,fixed_cost=0.0,var_cost_dist=0.0,
var_cost_time=0.0,max_number=1,tw_begin=0.0,tw_end=0.0)
vehicle type的属性及解释如下
此外，模型设置了总的最大车辆数（所以类型），默认取值为10000，可通过如下方式进行修改
model.set_max_total_vehicles_number(<value>)
路径成本的计算通过link成本的加和得到，link成本包括三部分：（1）link上的固定成本；（2）根据link的旅行时间和不同车型换算得到的成本；（3）根据link的距离和不同车型换算得到的成本。路径包含的属性及解释如下
在求解机制上，VRPSolverEasy首先将现有模型转化为VRPSolver可求解的模型（Pessoa et al.2020）,然后再调用Bapcod包（Sadykov et al.2021）进行求解,求解时可设置的参数如下：
model.set_parameters(time_limit=300,upper_bound=1000000,heuristic_used=False,
time_limit_heuristic=20,solver_name='CLP',print_level=-1)
VRPSolverEasy求解的速度取决于upper_bound的取值，upper_bound越接近最优解，求解就越快，所以VRPSolverEasy实际上是先通过CLP或者CPLEX得到一个启发式的可行解作为上界，然后再进行求解，VRPSolverEasy求解参数设置的一些属性及解释如下：
在模型求解结束后，如果求到了解（model.solution.is_defined()==True）,那么目标值可通过model.solution.value得到，路径信息可通过model.solution.routes得到。
3. VRPTW算例
设置若干客户点和车场节点构造vrptw的算例如下
# data
cost_per_distance = 10
begin_time = 0
end_time = 5000
nb_point = 7
# map with names and coordinates
coordinates = {"Wisconsin, USA": (44.50, -89.50), # depot
"West Virginia, USA": (39.000000, -80.500000),
"Vermont, USA": (44.000000, -72.699997),
"Texas, the USA": (31.000000, -100.000000),
"South Dakota, the US": (44.500000, -100.000000),
"Rhode Island, the US": (41.742325, -71.742332),
"Oregon, the US": (44.000000, -120.500000)
}
# demands of points
demands = [0, 500, 300, 600, 658, 741, 436]
模型构建
# Initialisation
model = solver.Model()
# Add vehicle type
model.add_vehicle_type(
id=1,
start_point_id=0,
end_point_id=0,
name="VEH1",
capacity=1100,
max_number=6,
var_cost_dist=cost_per_distance,
tw_end=5000)
# Add depot
model.add_depot(id=0, name="D1", tw_begin=0, tw_end=5000)
coordinates_keys = list(coordinates.keys())
# Add Customers
for i in range(1, nb_point):
model.add_customer(
id=i,
name=coordinates_keys[i],
demand=demands[i],
tw_begin=begin_time,
tw_end=end_time)
# Add links
coordinates_values = list(coordinates.values())
for i in range(0, 7):
for j in range(i + 1, 7):
dist = compute_euclidean_distance(coordinates_values[i][0],
coordinates_values[j][0],
coordinates_values[i][1],
coordinates_values[j][1])
model.add_link(
start_point_id=i,
end_point_id=j,
distance=dist,
time=dist)
求解
model.solve()
结果输出
if model.solution.is_defined():
print(model.solution)
Route for vehicle 1:
ID : 0 --> 2 --> 5 --> 0
Name : DEPOT --> Vermont, USA --> Rhode Island, the US --> DEPOT
End time : 0.0 --> 16.807 --> 19.259 --> 37.230000000000004
Load : 0.0 --> 300.0 --> 1041.0 --> 1041.0
Total cost : 372.29999999999995
Route for vehicle 1:
ID : 0 --> 1 --> 3 --> 0
Name : DEPOT --> West Virginia, USA --> Texas, the USA --> DEPOT
End time : 0.0 --> 10.548 --> 31.625 --> 48.728
Load : 0.0 --> 500.0 --> 1100.0 --> 1100.0
Total cost : 487.2800000000001
Route for vehicle 1:
ID : 0 --> 4 --> 6 --> 0
Name : DEPOT --> South Dakota, the US --> Oregon, the US --> DEPOT
End time : 0.0 --> 10.5 --> 31.006 --> 62.010000000000005
Load : 0.0 --> 658.0 --> 1094.0 --> 1094.0
Total cost : 620.1
4. VRPSolverEasy可求解的其它类型VRP部分算例
4.1 CVRP
容量限制车辆路径问题（CVRP）是最基础的 VRP，是指满足不同区域里的顾客需求的有容量限制的车辆路径规划问题。该问题的目标是最大限度降低总路径成本，即车辆行驶的总距离。
from VRPSolverEasy.src import solver
import os,sys,getopt
import math
import numpy as np
def read_instance(name : str):
""" Read an instance in the folder data from a given name """
path_project = os.path.abspath(os.getcwd())
with open (name,
"r",encoding="UTF-8" )as file:
elements = [str(element) for element in file.read().split()]
file.close()
return elements
def compute_euclidean_distance(x_i, y_i, x_j, y_j,number_digit=3):
"""Compute the euclidean distance between 2 points from graph"""
return round(math.sqrt((x_i - x_j)**2 +
(y_i - y_j)**2), number_digit)
def solve_demo(instance_path,
solver_name="CLP",
solver_path="",
time_resolution=30,
disableBuiltInHeur=False,
upper_bound=-1):
"""return a solution from modelisation"""
# read instance
data = read_cvrp_instances(instance_path)
# get data
vehicle_type = data["VehicleTypes"]
depot = data["Points"][0]
customers = data["Points"][1:]
links = data["Links"]
# modelisation of problem
model = solver.Model()
# add vehicle type
model.add_vehicle_type(id=vehicle_type["id"],
start_point_id=vehicle_type["start_point_id"],
end_point_id=vehicle_type["end_point_id"],
max_number=vehicle_type["max_number"],
capacity=vehicle_type["capacity"],
var_cost_dist=vehicle_type["var_cost_dist"]
)
# add depot
model.add_depot(id=depot["id"])
# add all customers
for customer in customers:
model.add_customer(id=customer["id"],
demand=customer["demand"]
)
# add all links
for link in links:
model.add_link(start_point_id=link["start_point_id"],
end_point_id=link["end_point_id"],
distance=link["distance"]
)
# set parameters
if disableBuiltInHeur:
model.set_parameters(time_limit=time_resolution, solver_name=solver_name,
heuristic_used=False)
print('Built-in heuristic is disabled')
else:
model.set_parameters(time_limit=time_resolution, solver_name=solver_name,
heuristic_used=True)
print('Built-in heuristic is enabled')
if upper_bound != -1:
model.parameters.upper_bound = upper_bound
''' If you have cplex 22.1 installed on your laptop windows you have to specify
solver path'''
if (solver_name == "CPLEX" and solver_path != ""):
model.parameters.cplex_path = solver_path
# solve model
model.solve()
if model.solution.is_defined :
path_instance_name = instance_path.split(".")[0]
name_instance = path_instance_name.split("\\")[
len(path_instance_name.split("\\"))-1]
print('{0} {1} {2} {3} {4} {5} {6} {7} {8} {9}\n'.format(
"instance_name","solver_name","ext_heuristic",
"solution_value",
"solution_time",
"best_lb",
"root_lb",
"root_time",
"nb_branch_and_bound_nodes",
"status"
), end='')
print('{0} {1} {2} {3} {4} {5} {6} {7} {8} {9}\n'.format(
instance_path,solver_name,False if upper_bound == -1 else True,
model.solution.value,
model.statistics.solution_time,
model.statistics.best_lb,
model.statistics.root_lb,
model.statistics.root_time,
model.statistics.nb_branch_and_bound_nodes,
model.status
))
# export the result
# model.solution.export(instance_name.split(".")[0] + "_result")
return model.solution
def read_cvrp_instances(instance_name):
"""Read literature instances from CVRPLIB by giving the name of instance
and returns dictionary containing all elements of model"""
instance_iter = iter(read_instance(instance_name))
points = []
id_point = 0
dimension_input = -1
capacity_input = -1
# Instantiate the data problem.
data = {}
while True:
element = next(instance_iter)
if element == "DIMENSION":
next(instance_iter) # pass ":"
dimension_input = int(next(instance_iter))
elif element == "CAPACITY":
next(instance_iter) # pass ":"
capacity_input = int(next(instance_iter))
elif element == "EDGE_WEIGHT_TYPE":
next(instance_iter) # pass ":"
element = next(instance_iter)
if element != "EUC_2D":
raise Exception("EDGE_WEIGHT_TYPE : " + element + """
is not supported (only EUC_2D)""")
elif element == "NODE_COORD_SECTION":
break
# Initialize vehicle type
vehicle_type = {"id": 1, # we cannot have an id less than 1
"start_point_id": id_point,
"end_point_id": id_point,
"capacity": capacity_input,
"max_number": dimension_input,
"var_cost_dist": 1
}
vehicles = []
index = 0
for i in range(dimension_input):
vehicles.append(capacity_input)
data['vehicle_capacities'] = vehicles
data['vehicle_capacity'] = capacity_input
data['num_vehicles'] = dimension_input
data['depot'] = 0
# Create points
for current_id in range(dimension_input):
point_id = int(next(instance_iter))
if point_id != current_id + 1:
raise Exception("Unexpected index")
x_coord = float(next(instance_iter))
y_coord = float(next(instance_iter))
points.append({"x": x_coord,
"y": y_coord,
"demand": -1,
"id": id_point})
id_point += 1
element = next(instance_iter)
if element != "DEMAND_SECTION":
raise Exception("Expected line DEMAND_SECTION")
jobs = []
# Get the demands
for current_id in range(dimension_input):
point_id = int(next(instance_iter))
if point_id != current_id + 1:
raise Exception("Unexpected index")
demand = int(next(instance_iter))
points[current_id]["demand"] = demand
jobs.append(demand)
data['demands'] = jobs
element = next(instance_iter)
if element != "DEPOT_SECTION":
raise Exception("Expected line DEPOT_SECTION")
next(instance_iter) # pass id depot
end_depot_section = int(next(instance_iter))
if end_depot_section != -1:
raise Exception("Expected only one depot.")
# Compute the links of graph
links = []
nb_link = 0
matrix = [[0 for i in range((len(points)))] for i in range(len(points))]
for i, point in enumerate(points):
for j in range(i + 1, len(points)):
dist = compute_euclidean_distance(point["x"],
point["y"],
points[j]["x"],
points[j]["y"],
0)
links.append({"name": "L" + str(nb_link),
"start_point_id": point["id"],
"end_point_id": points[j]["id"],
"distance": dist
})
matrix[i][j] = dist
matrix[j][i] = dist
nb_link += 1
data['distance_matrix'] = matrix
return {"Points": points,
"VehicleTypes": vehicle_type,
"Links": links}
def main(argv):
instance_path = ''
solver_name = ''
solver_path = ''
disableBuiltInHeur = False
time_resolution = 30
upper_bound = -1
opts, args = getopt.getopt(argv,"i:s:u:b:e:p:")
for opt, arg in opts:
if opt == "-i":
instance_path = arg
elif opt == "-s":
solver_name = arg
elif opt == "-u":
upper_bound = float(arg)
elif opt == "-b":
disableBuiltInHeur = arg == "yes"
elif opt == "-e":
time_resolution = float(arg)
if opt in ["-p"]:
solver_path = arg
solve_demo(instance_path, solver_name, solver_path, time_resolution, disableBuiltInHeur, upper_bound)
if __name__ == "__main__":
if len(sys.argv) > 1:
main(sys.argv[1:])
4.2 MDVRP
多车场路径规划问题（MDVRP）是 CVRP 的一种变体，其中车辆来自于不同车场。
import os
import math
import sys
import getopt
from VRPSolverEasy.src import solver
class DataMdvrp:
"""Contains all data for MDVRP problem
"""
def __init__(
self,
nb_customers: int,
nb_depots: int,
vehicle_capacity: int,
cust_demands=None,
cust_coordinates=None,
depot_coordinates=None):
self.nb_customers = nb_customers
self.nb_depots = nb_depots
self.vehicle_capacity = vehicle_capacity
self.cust_demands = cust_demands
self.cust_coordinates = cust_coordinates
self.depot_coordinates = depot_coordinates
def compute_euclidean_distance(x_i, y_i, x_j, y_j, number_digit=3):
"""Compute the euclidean distance between 2 points from graph"""
return round(math.sqrt((x_i - x_j)**2 +
(y_i - y_j)**2), number_digit)
def read_instance(name: str):
""" Read an instance in the folder data from a given name """
with open(
os.path.normpath(name),
"r", encoding="UTF-8") as file:
return [str(element) for element in file.read().split()]
def solve_demo(instance_name,
time_resolution=30,
solver_name_input="CLP",
solver_path=""):
"""return a solution from modelisation"""
# read parameters given in command line
type_instance = "MDVRP/"
if len(sys.argv) > 1:
print(instance_name)
opts = getopt.getopt(instance_name, "i:t:s:p:")
for opt, arg in opts[0]:
if opt in ["-i"]:
instance_name = arg
folder_data = ""
type_instance = ""
if opt in ["-t"]:
time_resolution = float(arg)
if opt in ["-s"]:
solver_name_input = arg
if opt in ["-p"]:
solver_path = arg
# read instance
data = read_mdvrp_instances(instance_name)
# modelisation of problem
model = solver.Model()
# add vehicle types
for i in range(data.nb_depots):
model.add_vehicle_type(id=data.nb_customers + i,
start_point_id=data.nb_customers + i,
end_point_id=data.nb_customers + i,
capacity=data.vehicle_capacity,
max_number=data.nb_customers,
var_cost_dist=1
)
# add all customers
for i in range(data.nb_customers):
model.add_customer(id=i,
id_customer=i+1,
demand=data.cust_demands[i]
)
# add depots
for i in range(data.nb_customers,data.nb_customers + data.nb_depots):
model.add_depot(id=i)
nb_link = 0
# Compute the links between depots and other points
for index,coord_depot in enumerate(data.depot_coordinates):
for i, cust_i in enumerate(data.cust_coordinates):
dist = compute_euclidean_distance(
cust_i[0],
cust_i[1],
coord_depot[0],
coord_depot[1])
model.add_link(start_point_id=index+data.nb_customers,
end_point_id=i,
distance=dist
)
# Compute the links between points
for i,cust_i in enumerate(data.cust_coordinates):
for j in range(i + 1, len(data.cust_coordinates)):
dist = compute_euclidean_distance(cust_i[0],
cust_i[1],
data.cust_coordinates[j][0],
data.cust_coordinates[j][1])
model.add_link(start_point_id=i,
end_point_id=j,
distance=dist
)
# set parameters
model.set_parameters(time_limit=time_resolution,
solver_name=solver_name_input)
''' If you have cplex 22.1 installed on your laptop windows you have to specify
solver path'''
if (solver_name_input == "CPLEX" and solver_path != ""):
model.parameters.cplex_path = solver_path
#model.export(instance_name,all_elements=True)
# solve model
model.solve()
# export the result
# model.solution.export(instance_name.split(".")[0] + "_result")
return model.solution.value
def read_mdvrp_instances(instance_full_path):
"""Read literature instances of MDVRP by giving the name of instance
and returns dictionary containing all elements of model"""
instance_iter = iter(
read_instance(instance_full_path))
# pass type instance
next(instance_iter)
next(instance_iter)
nb_customers = int(next(instance_iter))
nb_depots = int(next(instance_iter))
vehicle_capacities = []
for _ in range(nb_depots):
# pass max duration
next(instance_iter)
vehicle_capacities.append(int(next(instance_iter)))
cust_demands = []
cust_coordinates = []
for _ in range(nb_customers):
next(instance_iter)
cust_x = int(next(instance_iter))
cust_y = int(next(instance_iter))
cust_coordinates.append([cust_x, cust_y])
# pass duration
next(instance_iter)
cust_demand = int(next(instance_iter))
cust_demands.append(cust_demand)
for _ in range(6):
next(instance_iter)
depot_coordinates = []
# add depots and vehicle types
for _ in range(nb_depots):
next(instance_iter)
cust_x = int(next(instance_iter))
cust_y = int(next(instance_iter))
depot_coordinates.append([cust_x, cust_y])
for _ in range(4):
next(instance_iter)
return DataMdvrp(nb_customers,
nb_depots,
vehicle_capacities[0],
cust_demands,
cust_coordinates,
depot_coordinates
)
if __name__ == "__main__":
if len(sys.argv) > 1:
solve_demo(sys.argv[1:])
else:
print("""Please indicates the parameters of your model like this : \n
python MDVRP.py -i INSTANCE_PATH/NAME_INSTANCE \n
-t TIME_RESOLUTION -s SOLVER_NAME (-p PATH_SOLVER (WINDOWS only))
""")
4.3 RICHVRP
RichVRP 是 VRPSolverEasy 解决的特色问题之一，这里给出一个示例。它包括开放路线、多个仓库、多个时间窗口、两种类型的车辆（小型和大型）、可选客户和不兼容车辆（有些客户只可由小型车辆提供服务）。
import os
import math
import sys
import getopt
from VRPSolverEasy.src import solver
class Depot:
def __init__(self, id, x, y, tw_begin, tw_end):
self.id = id
self.x = x
self.y = y
self.tw_begin = tw_begin
self.tw_end = tw_end
def __str__(self):
return (f"Depot(id: {self.id}, x: {self.x}, y: {self.y}, "
f"tw_begin: {self.tw_begin}, tw_end: {self.tw_end})")
class Vehicle:
def __init__(self, capacity, fixed_cost, var_cost, max_number):
self.capacity = capacity
self.fixed_cost = fixed_cost
self.var_cost = var_cost
self.max_number = max_number
def __str__(self):
return (f"Vehicle(capacity: {self.capacity}, "
f"fixed_cost: {self.fixed_cost}, var_cost: {self.var_cost}, "
f"max_number: {self.max_number})")
class Customer:
def __init__(self, id, x, y, demand, service_time, optional, only_small_veh, time_windows):
self.id = id
self.x = x
self.y = y
self.demand = demand
self.service_time = service_time
self.optional = optional # Is the customer optional?
self.only_small_veh = only_small_veh # Can the customer served only by small vehicles?
self.time_windows = time_windows # List of time windows (list of pairs)
def __str__(self):
tw_str = ', '.join([f"({start}, {end})" for start, end in self.time_windows])
return (f"Customer(id: {self.id}, x: {self.x}, y: {self.y}, "
f"demand: {self.demand}, service_time: {self.service_time}, "
f"optional: {self.optional}, only_small_veh: {self.only_small_veh}, "
f"time_windows: [{tw_str}])")
class DataRichVrp:
"""Contains all data for RichVRP
"""
def __init__(
self,
depots : None,
big_vehicle : None,
small_vehicle : None,
customers : None):
self.depots = depots
self.big_vehicle = big_vehicle
self.small_vehicle = small_vehicle
self.customers = customers
def __str__(self):
depots_str = '\n'.join([str(depot) for depot in self.depots])
big_vehicle_str = str(self.big_vehicle)
small_vehicle_str = str(self.small_vehicle)
customers_str = '\n'.join([str(customer) for customer in self.customers])
return (f"DataRichVrp:\n\nDepots:\n{depots_str}\n\nBig Vehicle:\n{big_vehicle_str}"
f"\n\nSmall Vehicle:\n{small_vehicle_str}\n\nCustomers:\n{customers_str}")
def compute_euclidean_distance(x_i, y_i, x_j, y_j, number_digit=3):
"""Compute the euclidean distance between 2 points from graph"""
return round(math.sqrt((x_i - x_j)**2 +
(y_i - y_j)**2), number_digit)
def read_instance(name: str):
""" Read an instance in the folder data from a given name """
with open(
os.path.normpath(name),
"r", encoding="UTF-8") as file:
return [str(element) for element in file.read().split()]
def solve_demo(instance_name,
time_resolution=30,
solver_name_input="CLP",
solver_path=""):
"""return a solution from modelisation"""
# read parameters given in command line
if len(sys.argv) > 1:
print(instance_name)
opts = getopt.getopt(instance_name, "i:t:s:p:")
for opt, arg in opts[0]:
if opt in ["-i"]:
instance_name = arg
if opt in ["-t"]:
time_resolution = float(arg)
if opt in ["-s"]:
solver_name_input = arg
if opt in ["-p"]:
solver_path = arg
# read instance
data = read_richvrp_instance(instance_name)
print(data)
# modelisation of problem
model = solver.Model()
big_vehicle_id = 1 # Big vehicles have odd ids
big_vehicle_ids = [] # Store all the ids for big vehicles
small_vehicle_id = 2 # Small vehicles have even ids
# Add depots and vehicles
for depot in data.depots:
# Add the depot
model.add_depot(id = depot.id,
tw_begin = depot.tw_begin,
tw_end = depot.tw_end)
# Add the big vehicle to this depot
model.add_vehicle_type(id = big_vehicle_id,
start_point_id = depot.id,
end_point_id = -1, # A vehicle may end anywhere
capacity = data.big_vehicle.capacity,
max_number = data.big_vehicle.max_number,
fixed_cost = data.big_vehicle.fixed_cost,
var_cost_dist = data.big_vehicle.var_cost,
tw_begin = depot.tw_begin,
tw_end = depot.tw_end)
# Add the small vehicle to this depot
model.add_vehicle_type(id = small_vehicle_id,
start_point_id = depot.id,
end_point_id = -1, # A vehicle may end anywhere
capacity = data.small_vehicle.capacity,
max_number = data.small_vehicle.max_number,
fixed_cost = data.small_vehicle.fixed_cost,
var_cost_dist = data.small_vehicle.var_cost,
tw_begin = depot.tw_begin,
tw_end = depot.tw_end)
big_vehicle_ids.append(big_vehicle_id)
big_vehicle_id += 2
small_vehicle_id += 2
# ID for alternative points of a customer with multiple time windows
next_id = max([customer.id for customer in data.customers]) + 1
# IDs of a customer, including the alternative ones
customer_ids = {customer.id : [customer.id] for customer in data.customers}
# Add customers
for customer in data.customers:
# Add a point for each time window of a customer
for i, tw in enumerate(customer.time_windows):
point_id = customer.id
if i > 0: # Is it an alternative point?
point_id = next_id
customer_ids[customer.id].append(next_id)
next_id += 1 # Get the next alternative ID
model.add_customer(id = point_id,
id_customer = customer.id,
demand = customer.demand,
service_time = customer.service_time,
tw_begin = tw[0],
tw_end = tw[1],
penalty = 1.0 if customer.optional else 0.0,
incompatible_vehicles = big_vehicle_ids if customer.only_small_veh else [])
# Compute the links between depots and other points
for depot in data.depots:
for customer in data.customers:
dist = compute_euclidean_distance(customer.x, customer.y, depot.x, depot.y)
for point_id in customer_ids[customer.id]:
model.add_link(start_point_id = depot.id,
end_point_id = point_id,
distance = dist,
time = dist)
# Compute the links between customer points
for i, c1 in enumerate(data.customers):
for j, c2 in enumerate(data.customers):
if j <= i:
continue
dist = compute_euclidean_distance(c1.x, c1.y, c2.x, c2.y)
# Add a link for each pair of points from c1 to c2
for point_id_c1 in customer_ids[c1.id]:
for point_id_c2 in customer_ids[c2.id]:
model.add_link(start_point_id = point_id_c1,
end_point_id = point_id_c2,
distance = dist,
time = dist)
# set parameters
model.set_parameters(time_limit=time_resolution,
solver_name=solver_name_input)
''' If you have cplex 22.1 installed on your laptop windows you have to specify
solver path'''
if (solver_name_input == "CPLEX" and solver_path != ""):
model.parameters.cplex_path = solver_path
# model.export(instance_name)
# Solve model
model.solve()
print("\nCustomer IDs and time windows:")
for customer in data.customers:
ids_and_tws = []
for i, point_id in enumerate(customer_ids[customer.id]):
ids_and_tws.append(f"(id: {point_id}, tw: {list(customer.time_windows[i])})")
print(f"Customer {customer.id}: {', '.join(ids_and_tws)}")
if model.solution.is_defined():
print(model.solution)
# export the result
# model.solution.export(instance_name.split(".")[0] + "_result")
return model.solution.value
def read_richvrp_instance(instance_full_path):
"""Read instance of RichVRP by giving the name of instance
and returns dictionary containing all elements of model"""
instance_iter = iter(
read_instance(instance_full_path))
nb_depots = int(next(instance_iter))
# Read depots
depots = []
for _ in range(nb_depots):
id = int(next(instance_iter))
x = int(next(instance_iter))
y = int(next(instance_iter))
tw_begin = int(next(instance_iter))
tw_end = int(next(instance_iter))
depots.append(Depot(id, x, y, tw_begin, tw_end))
# Read big vehicle
capacity_big_veh = int(next(instance_iter))
fixed_cost_big_veh = int(next(instance_iter))
var_cost_big_veh = float(next(instance_iter))
max_numb_big_veh = int(next(instance_iter))
big_vehicle = Vehicle(capacity_big_veh, fixed_cost_big_veh, var_cost_big_veh, max_numb_big_veh)
# Read small vehicle
capacity_small_veh = int(next(instance_iter))
fixed_cost_small_veh = int(next(instance_iter))
var_cost_small_veh = float(next(instance_iter))
max_numb_small_veh = int(next(instance_iter))
small_vehicle = Vehicle(capacity_small_veh, fixed_cost_small_veh, var_cost_small_veh, max_numb_small_veh)
# Read customers
nb_customers = int(next(instance_iter))
customers = []
for _ in range(nb_customers):
id = int(next(instance_iter))
x = int(next(instance_iter))
y = int(next(instance_iter))
demand = int(next(instance_iter))
service_time = int(next(instance_iter))
optional = int(next(instance_iter)) == 1 if True else False
small_vehicle_flag = int(next(instance_iter)) == 1 if True else False
nb_time_windows = int(next(instance_iter))
time_windows = []
for _ in range(nb_time_windows):
tw_begin = int(next(instance_iter))
tw_end = int(next(instance_iter))
time_windows.append((tw_begin, tw_end))
customers.append(Customer(id, x, y, demand, service_time, optional, small_vehicle_flag, time_windows))
return DataRichVrp(depots, big_vehicle, small_vehicle, customers)
if __name__ == "__main__":
if len(sys.argv) > 1:
solve_demo(sys.argv[1:])
else:
print("""Please indicates the parameters of your model like this : \n
python RichVRP.py -i INSTANCE_PATH/NAME_INSTANCE \n
-t TIME_RESOLUTION -s SOLVER_NAME (-p PATH_SOLVER (WINDOWS only))
""")
5. 性能
毕竟是精确算法求解器，在大规模问题上还是拼不过启发式算法，对于200 个以上客户的算例得到最优解可能需要很长时间（数小时或数天），但少于 100 个客户的算例一般可以在几分钟内得到解决。
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