【进阶二】Python实现(MD)VRPTW常见求解算法——遗传算法（GA）
基于python语言，实现经典遗传算法（GA）对（多车场）带有时间窗的车辆路径规划问题（（MD）VRPTW）进行求解。
目录
- 往期优质资源
- 1. 适用场景
- 2. 求解效果
- 3. 代码分析
- 4. 数据格式
- 5. 分步实现
- 6. 完整代码
- 参考
往期优质资源
- python实现6种智能算法求解CVRP问题
- python实现7种智能算法求解MDVRP问题
- python实现7种智能算法求解MDVRPTW问题
- Python版MDHFVRPTW问题智能求解算法代码【TS算法】
- Python版MDHFVRPTW问题智能求解算法代码【SA算法】
- Python版MDHFVRPTW问题智能求解算法代码【GA算法】
- Python版MDHFVRPTW问题智能求解算法代码【DPSO算法】
- Python版MDHFVRPTW问题智能求解算法代码【DE算法】
- Python版MDHFVRPTW问题智能求解算法代码【ACO算法】
- Python版HVRP问题智能求解算法代码【GA算法】
- Python版HVRP问题智能求解算法代码【DPSO算法】
1. 适用场景
- 求解MDVRPTW或VRPTW
- 车辆类型单一
- 车辆容量不小于需求节点最大需求
- 车辆路径长度或运行时间无限制
- 需求节点服务成本满足三角不等式
- 节点时间窗至少满足车辆路径只包含一个需求节点的情况
- 多车辆基地或单一
- 各车场车辆总数满足实际需求
2. 求解效果
（1）收敛曲线
（2）车辆路径
3. 代码分析
应用GA算法求解MDVRPTW时保留了已有代码的架构与思路，为能够求解带有时间窗的（多车场）车辆路径规划问题，这里参考既有文献对路径分割算法进行了改进（"splitRoutes"函数），在分割车辆路径时不仅考虑了车辆容量限制，还考虑了节点的时间窗约束，以此使得分割后的路径可行。在此改进下继承了大量原有代码，降低了代码改进量。
4. 数据格式
以csv文件储存数据，其中demand.csv文件记录需求节点数据，共包含需求节点id，需求节点横坐标，需求节点纵坐标，需求量；depot.csv文件记录车场节点数据，共包含车场id，车场横坐标，车场纵坐标，车队数量。需要注意的是：需求节点id应为整数，车场节点id任意，但不可与需求节点id重复。 可参考github主页相关文件。
5. 分步实现
（1）数据结构
定义Sol()类，Node()类，Model()类，其属性如下表：
- Sol()类，表示一个可行解
| 属性 | 描述 |
|---|---|
| node_id_list | 需求节点id有序排列集合 |
| obj | 优化目标值 |
| fitness | 解的适应度 |
| route_list | 车辆路径集合，对应MDVRPTW的解 |
| timetable_list | 车辆节点访问时间集合，对应MDVRPTW的解 |
| cost_of_distance | 距离成本 |
| cost_of_time | 时间成本 |
- Node()类，表示一个网络节点
| 属性 | 描述 |
|---|---|
| id | 物理节点id，需唯一 |
| x_coord | 物理节点x坐标 |
| y_coord | 物理节点y坐标 |
| demand | 物理节点需求 |
| depot_capacity | 车辆基地车队规模 |
| start_time | 最早开始服务（被服务）时间 |
| end_time | 最晚结束服务（被服务）时间 |
| service_time | 需求节点服务时间 |
- Model()类，存储算法参数
| 属性 | 描述 |
|---|---|
| best_sol | 全局最优解，值类型为Sol() |
| demand_dict | 需求节点集合（字典），值类型为Node() |
| depot_dict | 车场节点集合（字典），值类型为Node() |
| depot_id_list | 车场节点id集合 |
| demand_id_list | 需求节点id集合 |
| sol_list | 种群，值类型为Sol() |
| distance_matrix | 节点距离矩阵 |
| time_matrix | 节点旅行时间矩阵 |
| opt_type | 优化目标类型，0：最小旅行距离，1：最小时间成本 |
| vehicle_cap | 车辆容量 |
| vehicle_speed | 车辆行驶速度，用于计算旅行时间 |
| pc | 交叉概率 |
| pm | 突变概率 |
| n_select | 优良个体选择数量 |
| popsize | 种群规模 |
（2）文件读取
def readCSVFile(demand_file,depot_file,model):
with open(demand_file,'r') as f:
demand_reader=csv.DictReader(f)
for row in demand_reader:
node = Node()
node.id = int(row['id'])
node.x_coord = float(row['x_coord'])
node.y_coord = float(row['y_coord'])
node.demand = float(row['demand'])
node.start_time=float(row['start_time'])
node.end_time=float(row['end_time'])
node.service_time=float(row['service_time'])
model.demand_dict[node.id] = node
model.demand_id_list.append(node.id)
model.number_of_demands=len(model.demand_id_list)
with open(depot_file, 'r') as f:
depot_reader = csv.DictReader(f)
for row in depot_reader:
node = Node()
node.id = row['id']
node.x_coord = float(row['x_coord'])
node.y_coord = float(row['y_coord'])
node.depot_capacity = float(row['capacity'])
node.start_time=float(row['start_time'])
node.end_time=float(row['end_time'])
model.depot_dict[node.id] = node
model.depot_id_list.append(node.id)
（3）计算距离&时间矩阵
def calDistanceTimeMatrix(model):
for i in range(len(model.demand_id_list)):
from_node_id = model.demand_id_list[i]
for j in range(i + 1, len(model.demand_id_list)):
to_node_id = model.demand_id_list[j]
dist = math.sqrt((model.demand_dict[from_node_id].x_coord - model.demand_dict[to_node_id].x_coord) ** 2
+ (model.demand_dict[from_node_id].y_coord - model.demand_dict[to_node_id].y_coord) ** 2)
model.distance_matrix[from_node_id, to_node_id] = dist
model.distance_matrix[to_node_id, from_node_id] = dist
model.time_matrix[from_node_id,to_node_id] = math.ceil(dist/model.vehicle_speed)
model.time_matrix[to_node_id,from_node_id] = math.ceil(dist/model.vehicle_speed)
for _, depot in model.depot_dict.items():
dist = math.sqrt((model.demand_dict[from_node_id].x_coord - depot.x_coord) ** 2
+ (model.demand_dict[from_node_id].y_coord - depot.y_coord) ** 2)
model.distance_matrix[from_node_id, depot.id] = dist
model.distance_matrix[depot.id, from_node_id] = dist
model.time_matrix[from_node_id,depot.id] = math.ceil(dist/model.vehicle_speed)
model.time_matrix[depot.id,from_node_id] = math.ceil(dist/model.vehicle_speed)
（4）适应度计算
适应度计算依赖" splitRoutes "函数对有序节点序列行解分割得到车辆行驶路线，同时在得到各车辆形式路线后在满足车场车队规模条件下分配最近车场，之后调用 " calTravelCost "函数确定车辆访问各路径节点的到达和离开时间点，并计算旅行距离成本和旅行时间成本。
def selectDepot(route,depot_dict,model):
min_in_out_distance=float('inf')
index=None
for _,depot in depot_dict.items():
if depot.depot_capacity>0:
in_out_distance=model.distance_matrix[depot.id,route[0]]+model.distance_matrix[route[-1],depot.id]
if in_out_distance<min_in_out_distance:
index=depot.id
min_in_out_distance=in_out_distance
if index is None:
print("there is no vehicle to dispatch")
sys.exit(0)
route.insert(0,index)
route.append(index)
depot_dict[index].depot_capacity=depot_dict[index].depot_capacity-1
return route,depot_dict
def calTravelCost(route_list,model):
timetable_list=[]
cost_of_distance=0
cost_of_time=0
for route in route_list:
timetable=[]
for i in range(len(route)):
if i == 0:
depot_id=route[i]
next_node_id=route[i+1]
travel_time=model.time_matrix[depot_id,next_node_id]
departure=max(0,model.demand_dict[next_node_id].start_time-travel_time)
timetable.append((departure,departure))
elif 1<= i <= len(route)-2:
last_node_id=route[i-1]
current_node_id=route[i]
current_node = model.demand_dict[current_node_id]
travel_time=model.time_matrix[last_node_id,current_node_id]
arrival=max(timetable[-1][1]+travel_time,current_node.start_time)
departure=arrival+current_node.service_time
timetable.append((arrival,departure))
cost_of_distance = cost_of_distance + model.distance_matrix[last_node_id,current_node_id]
cost_of_time += model.time_matrix[last_node_id,current_node_id] + current_node.service_time\
+max(current_node.start_time-timetable[-1][1]+travel_time,0)
else:
last_node_id = route[i - 1]
depot_id=route[i]
travel_time = model.time_matrix[last_node_id,depot_id]
departure = timetable[-1][1]+travel_time
timetable.append((departure,departure))
cost_of_distance +=model.distance_matrix[last_node_id,depot_id]
cost_of_time+=model.time_matrix[last_node_id,depot_id]
timetable_list.append(timetable)
return timetable_list,cost_of_time,cost_of_distance
def extractRoutes(node_id_list,Pred,model):
depot_dict=copy.deepcopy(model.depot_dict)
route_list = []
route = []
label = Pred[node_id_list[0]]
for node_id in node_id_list:
if Pred[node_id] == label:
route.append(node_id)
else:
route, depot_dict=selectDepot(route,depot_dict,model)
route_list.append(route)
route = [node_id]
label = Pred[node_id]
route, depot_dict = selectDepot(route, depot_dict, model)
route_list.append(route)
return route_list
def splitRoutes(node_id_list,model):
depot=model.depot_id_list[0]
V={id:float('inf') for id in model.demand_id_list}
V[depot]=0
Pred={id:depot for id in model.demand_id_list}
for i in range(len(node_id_list)):
n_1=node_id_list[i]
demand=0
departure=0
j=i
cost=0
while True:
n_2 = node_id_list[j]
demand = demand + model.demand_dict[n_2].demand
if n_1 == n_2:
arrival= max(model.demand_dict[n_2].start_time,model.depot_dict[depot].start_time+model.time_matrix[depot,n_2])
departure=arrival+model.demand_dict[n_2].service_time+model.time_matrix[n_2,depot]
if model.opt_type == 0:
cost=model.distance_matrix[depot,n_2]*2
else:
cost=model.time_matrix[depot,n_2]*2
else:
n_3=node_id_list[j-1]
arrival= max(departure-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2],model.demand_dict[n_2].start_time)
departure=arrival+model.demand_dict[n_2].service_time+model.time_matrix[n_2,depot]
if model.opt_type == 0:
cost=cost-model.distance_matrix[n_3,depot]+model.distance_matrix[n_3,n_2]+model.distance_matrix[n_2,depot]
else:
cost=cost-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2]\
+model.demand_dict[n_2].start_time-departure-model.time_matrix[n_3,depot]+model.time_matrix[n_3,n_2]\
+model.time_matrix[n_2,depot]
if demand<=model.vehicle_cap and departure-model.time_matrix[n_2,depot] <= model.demand_dict[n_2].end_time:
if departure <= model.depot_dict[depot].end_time:
n_4=node_id_list[i-1] if i-1>=0 else depot
if V[n_4]+cost <= V[n_2]:
V[n_2]=V[n_4]+cost
Pred[n_2]=i-1
j=j+1
else:
break
if j==len(node_id_list):
break
route_list= extractRoutes(node_id_list,Pred,model)
return len(route_list),route_list
def calFitness(model):
max_obj=-float('inf')
best_sol=Sol()
best_sol.obj=float('inf')
# calculate travel distance and travel time
for sol in model.sol_list:
node_id_list=copy.deepcopy(sol.node_id_list)
num_vehicle, route_list = splitRoutes(node_id_list, model)
# travel cost
timetable_list,cost_of_time,cost_of_distance =calTravelCost(route_list,model)
if model.opt_type == 0:
sol.obj=cost_of_distance
else:
sol.obj=cost_of_time
sol.route_list = route_list
sol.timetable_list = timetable_list
sol.cost_of_distance=cost_of_distance
sol.cost_of_time=cost_of_time
if sol.obj > max_obj:
max_obj=sol.obj
if sol.obj < best_sol.obj:
best_sol=copy.deepcopy(sol)
# calculate fitness
for sol in model.sol_list:
sol.fitness=max_obj-sol.obj
if best_sol.obj<model.best_sol.obj:
model.best_sol=copy.deepcopy(best_sol)
（5）初始解生成
def generateInitialSol(model):
demand_id_list=copy.deepcopy(model.demand_id_list)
for i in range(model.popsize):
seed=int(random.randint(0,10))
random.seed(seed)
random.shuffle(demand_id_list)
sol=Sol()
sol.node_id_list=copy.deepcopy(demand_id_list)
model.sol_list.append(sol)
（6）优良个体选择
def selectSol(model):
sol_list=copy.deepcopy(model.sol_list)
model.sol_list=[]
for i in range(model.n_select):
f1_index=random.randint(0,len(sol_list)-1)
f2_index=random.randint(0,len(sol_list)-1)
f1_fit=sol_list[f1_index].fitness
f2_fit=sol_list[f2_index].fitness
if f1_fit<f2_fit:
model.sol_list.append(sol_list[f2_index])
else:
model.sol_list.append(sol_list[f1_index])
（7）交叉
def crossSol(model):
sol_list=copy.deepcopy(model.sol_list)
model.sol_list=[]
while True:
f1_index = random.randint(0, len(sol_list) - 1)
f2_index = random.randint(0, len(sol_list) - 1)
if f1_index!=f2_index:
f1 = copy.deepcopy(sol_list[f1_index])
f2 = copy.deepcopy(sol_list[f2_index])
if random.random() <= model.pc:
cro1_index=int(random.randint(0,len(model.demand_id_list)-1))
cro2_index=int(random.randint(cro1_index,len(model.demand_id_list)-1))
new_c1_f = []
new_c1_m=f1.node_id_list[cro1_index:cro2_index+1]
new_c1_b = []
new_c2_f = []
new_c2_m=f2.node_id_list[cro1_index:cro2_index+1]
new_c2_b = []
for index in range(len(model.demand_id_list)):
if len(new_c1_f)<cro1_index:
if f2.node_id_list[index] not in new_c1_m:
new_c1_f.append(f2.node_id_list[index])
else:
if f2.node_id_list[index] not in new_c1_m:
new_c1_b.append(f2.node_id_list[index])
for index in range(len(model.demand_id_list)):
if len(new_c2_f)<cro1_index:
if f1.node_id_list[index] not in new_c2_m:
new_c2_f.append(f1.node_id_list[index])
else:
if f1.node_id_list[index] not in new_c2_m:
new_c2_b.append(f1.node_id_list[index])
new_c1=copy.deepcopy(new_c1_f)
new_c1.extend(new_c1_m)
new_c1.extend(new_c1_b)
f1.nodes_seq=new_c1
new_c2=copy.deepcopy(new_c2_f)
new_c2.extend(new_c2_m)
new_c2.extend(new_c2_b)
f2.nodes_seq=new_c2
model.sol_list.append(copy.deepcopy(f1))
model.sol_list.append(copy.deepcopy(f2))
else:
model.sol_list.append(copy.deepcopy(f1))
model.sol_list.append(copy.deepcopy(f2))
if len(model.sol_list)>model.popsize:
break
（8）突变
def muSol(model):
sol_list=copy.deepcopy(model.sol_list)
model.sol_list=[]
while True:
f1_index = int(random.randint(0, len(sol_list) - 1))
f1 = copy.deepcopy(sol_list[f1_index])
m1_index=random.randint(0,len(model.demand_id_list)-1)
m2_index=random.randint(0,len(model.demand_id_list)-1)
if m1_index!=m2_index:
if random.random() <= model.pm:
node1=f1.node_id_list[m1_index]
f1.node_id_list[m1_index]=f1.node_id_list[m2_index]
f1.node_id_list[m2_index]=node1
model.sol_list.append(copy.deepcopy(f1))
else:
model.sol_list.append(copy.deepcopy(f1))
if len(model.sol_list)>model.popsize:
break
（9）绘制收敛曲线
def plotObj(obj_list):
plt.rcParams['font.sans-serif'] = ['SimHei'] #show chinese
plt.rcParams['axes.unicode_minus'] = False # Show minus sign
plt.plot(np.arange(1,len(obj_list)+1),obj_list)
plt.xlabel('Iterations')
plt.ylabel('Obj Value')
plt.grid()
plt.xlim(1,len(obj_list)+1)
plt.show()
（10）绘制车辆路线
def plotRoutes(model):
for route in model.best_sol.route_list:
x_coord=[model.depot_dict[route[0]].x_coord]
y_coord=[model.depot_dict[route[0]].y_coord]
for node_id in route[1:-1]:
x_coord.append(model.demand_dict[node_id].x_coord)
y_coord.append(model.demand_dict[node_id].y_coord)
x_coord.append(model.depot_dict[route[-1]].x_coord)
y_coord.append(model.depot_dict[route[-1]].y_coord)
plt.grid()
if route[0]=='d1':
plt.plot(x_coord,y_coord,marker='o',color='black',linewidth=0.5,markersize=5)
elif route[0]=='d2':
plt.plot(x_coord,y_coord,marker='o',color='orange',linewidth=0.5,markersize=5)
else:
plt.plot(x_coord,y_coord,marker='o',color='b',linewidth=0.5,markersize=5)
plt.xlabel('x_coord')
plt.ylabel('y_coord')
plt.show()
（11）输出结果
def outPut(model):
work=xlsxwriter.Workbook('result.xlsx')
worksheet=work.add_worksheet()
worksheet.write(0, 0, 'cost_of_time')
worksheet.write(0, 1, 'cost_of_distance')
worksheet.write(0, 2, 'opt_type')
worksheet.write(0, 3, 'obj')
worksheet.write(1,0,model.best_sol.cost_of_time)
worksheet.write(1,1,model.best_sol.cost_of_distance)
worksheet.write(1,2,model.opt_type)
worksheet.write(1,3,model.best_sol.obj)
worksheet.write(2,0,'vehicleID')
worksheet.write(2,1,'route')
worksheet.write(2,2,'timetable')
for row,route in enumerate(model.best_sol.route_list):
worksheet.write(row+3,0,'v'+str(row+1))
r=[str(i)for i in route]
worksheet.write(row+3,1, '-'.join(r))
r=[str(i)for i in model.best_sol.timetable_list[row]]
worksheet.write(row+3,2, '-'.join(r))
work.close()
（12）主函数
def run(demand_file,depot_file,epochs,pc,pm,popsize,n_select,v_cap,v_speed,opt_type):
"""
:param demand_file: demand file path
:param depot_file: depot file path
:param epochs: Iterations
:param pc: Crossover probability
:param pm: Mutation probability
:param popsize: Population size
:param n_select: Number of excellent individuals selected
:param v_cap: Vehicle capacity
:param v_speed: Vehicle free speed
:param opt_type: Optimization type:0:Minimize the cost of travel distance;1:Minimize the cost of travel time
:return:
"""
model=Model()
model.vehicle_cap=v_cap
model.pc=pc
model.pm=pm
model.popsize=popsize
model.n_select=n_select
model.opt_type=opt_type
readCSVFile(demand_file,depot_file,model)
calDistanceTimeMatrix(model)
generateInitialSol(model)
history_best_obj = []
best_sol=Sol()
best_sol.obj=float('inf')
model.best_sol=best_sol
for ep in range(epochs):
calFitness(model)
selectSol(model)
crossSol(model)
muSol(model)
history_best_obj.append(model.best_sol.obj)
print("%s/%s， best obj: %s" % (ep,epochs,model.best_sol.obj))
plotObj(history_best_obj)
plotRoutes(model)
outPut(model)
6. 完整代码
代码和数据文件可获取：
https://download.csdn.net/download/python_n/56114085
参考
- Prins C . A simple and e ective evolutionary algorithm for the vehicle routing problem[J]. Computers & operations research, 2004, 31(12):p.1985-2002.
- Cheng, L., A Genetic Algorithm for The Vehicle Routing Problem with Time Windows. 2005.