#车辆路径问题 提示：这里可以添加系列文章的所有文章的目录，目录需要自己手动添加 利用Python和Gurobi求解VRPSPDTW
考虑需求动态变化的共享单车调度问题研究
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文章目录
- 一、模型的建立
- 二、使用步骤
- 1.Gurobi代码
- 2.遗传算法代码
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一、模型的建立
二、使用步骤
1.Gurobi代码
代码如下（示例）：
import sys
import math
import os
import json
import random
from itertools import permutations
import gurobipy as gp
from gurobipy import GRB
import itertools
import pandas as pd
# 定义基本数据
data = {}
data['distance_matrix'] = [[0, 548, 776, 696, 582, 274, 502, 194, 308, 194],
[548, 0, 684, 308, 194, 502, 730, 354, 696, 742],
[776, 684, 0, 992, 878, 502, 274, 810, 468, 742],
[696, 308, 992, 0, 114, 650, 878, 502, 844, 890],
[582, 194, 878, 114, 0, 536, 764, 388, 730, 776],
[274, 502, 502, 650, 536, 0, 228, 308, 194, 240],
[502, 730, 274, 878, 764, 228, 0, 536, 194, 468],
[194, 354, 810, 502, 388, 308, 536, 0, 342, 388],
[308, 696, 468, 844, 730, 194, 194, 342, 0, 274],
[194, 742, 742, 890, 776, 240, 468, 388, 274, 0],]
data['depot'] = 0
data['demands'] = [0, 5, -5, 10, -20, -10, -20, 40, -40, 5]
data['vehicle_capacities'] = [15,]
T = 3
distList = data['distance_matrix']
Q = data['demands']
capacities = data['vehicle_capacities']
capacity = capacities[0]
n = len(distList)
dist = {(i, j): distList[i][j] for i in range(n) for j in range(n)}
# 建立模型和添加变量
m = gp.Model()
x = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='e') u = m.addVars(n, ub=capacity, name='u')
t = m.addVars(n, ub=T, name='t')
# 添加约束条件
# 装载量
pairs = [(i, j) for i in range(n) for j in range(1, n) if i != j]
for (i,j) in pairs:
if Q[j]>0:
m.addConstr(u[j]*x[i,j] == x[i,j]*((Q[j]/T)*t[j] + u[i]))
else:
m.addConstr(u[j]*x[i,j] == x[i,j]*(Q[j]-(Q[j]/T)*t[j] + u[i]))
u[0].LB = 0
u[0].UB = 0
# 时间窗
for (i,j) in pairs:
m.addConstr(t[j] >= (dist[i,j]/750)+t[i]-(1-x[i, j])*T)
t[0].LB = 0
t[0].UB = 0
# 进出平衡
m.addConstrs(x.sum(i, '*') == x.sum('*',i) for i in range(n))
# 不出现自己到自己的情况
m.addConstrs(x[i,i] == 0 for i in range(n))
# 所有点最多被访问一次
m.addConstrs(x.sum(i, '*') <= 1 for i in range(1, n))
m.addConstrs(x.sum('*', i) <= 1 for i in range(1, n))
AllNodesVisited={i: gp.quicksum(x[j,i] for j in range(n) if i!=j) for i in range(1,n)} # (2.2)
m.addConstrs(AllNodesVisited[i]<=1 for i in range(1,n))
# 至少有1辆调度车进行调度
m.addConstr(x.sum(0, '*') >= 1)
m.addConstr(x.sum('*', 0) >= 1)
# 设置目标函数
total_satisfied = gp.quicksum((u[i]-u[j])*x[i,j] for j in [2,4,5,6,8] for i in range(n))
total_unzero = gp.quicksum(Q[i] for i in [2,4,5,6,8])
total_distri = gp.quicksum(u[i] for i in range(n))
total_time = gp.quicksum(t[i] for i in range(n))
totaldist = gp.quicksum(x[i,j]*dist[i,j] for i in range(n) for j in range(n))
m.setObjective(totaldist*0.01+(x.sum(0,'*')*40)+(-total_satisfied-total_unzero)*15,GRB.MINIMIZ
E)
# 结果计算
m.optimize()2.遗传算法代码
代码如下（示例）：
附录 C
89
distance.append(calDist(dataDict['NodeCoor'][eachRoute[j-1]],dataDict['NodeCoor'][eachRoute[j]]))
#distance_of_all_point.append(distance(y[len(y)-1],start_point_0))
all_route_distance.append(distance)
for z in range(len(distance)):
route_time.append(distance[z]/dataDict['Velocity'])
arrive_time = list(np.cumsum(route_time))
for m in range(len(arrive_time)):
if arrive_time[m] > dataDict['TimeWindow']:
arrive_time[m] = np.nan
all_arrive_time.append(arrive_time)
for p in range(len(arrive_time)-1):
if np.isnan(arrive_time[p]):
scheduling_requirements.append(np.nan)
else:
if
dataDict['InitialValue'][eachRoute[p+1]]+dataDict['DemandRate'][eachRoute[p+1]]*arrive_time[p]>
0:
if dataDict['DemandRate'][eachRoute[p+1]]>0:
scheduling_requirements.append(dataDict['InitialValue'][eachRoute[p+1]]+dataDict['DemandRate'][
eachRoute[p+1]]*arrive_time[p])
else:
scheduling_requirements.append(dataDict['InitialValue'][eachRoute[p+1]]+dataDict['DemandRate'][
eachRoute[p+1]]*arrive_time[p]+(1-arrive_time[p])*dataDict['DemandRate'][eachRoute[p+1]])
else:
scheduling_requirements.append((1-arrive_time[p])*dataDict['DemandRate'][eachRoute[p+1]])
for t in range(len(scheduling_requirements)):
if not np.isnan(scheduling_requirements[t]):
scheduling_requirements[t] = round(scheduling_requirements[t])
#scheduling_requirements = [round(u) for u in scheduling_requirements]
all_route_scheduling_quantity.append(scheduling_requirements)
return all_route_distance,all_arrive_time,all_route_scheduling_quantity
# 调度车离开各区域时的装载量
def all_truck_loading_leave(routes,dataDict=dataDict):
all_truck_loading_leave = []
arriveTime = quantityDistanceArriveTime(routes)[2]
for t in range(len(arriveTime)):
truck_loading = []
if np.isnan(arriveTime[t][0]): 87
import numpy as np
import matplotlib.pyplot as plt
from deap import base, tools, creator, algorithms
import random
import pandas as pd
params = {
'font.family': 'serif',
'figure.dpi': 300,
'savefig.dpi': 300,
'font.size': 12,
'legend.fontsize': 'small'
}
plt.rcParams.update(params)
from copy import deepcopy
# 问题定义
creator.create('FitnessMin', base.Fitness, weights=(-1.0,)) # 最小化问题
# 给个体一个routes属性用来记录其表示的路线
creator.create('Individual', list, fitness=creator.FitnessMin)
# 用字典存储参数
dataDict = {}
# 节点坐标，节点0是配送中心的坐标
dataDict['NodeCoor']=pd.read_excel('cluster_center_2hour.xlsx',sheet_name='Sheet1')['number'].toli
st()
# 将配送中心的需求设置为0
dataDict['Demand'] = pd.read_excel('cluster_center_2hour.xlsx',sheet_name='Sheet1')['需求'].tolist()
dataDict['MaxLoad'] = 20
#dataDict['ServiceTime'] = 1/150
dataDict['DemandRate']=[x/2 for x in
pd.read_excel('cluster_center_2hour.xlsx',sheet_name='Sheet1')['需求'].tolist()]
dataDict['Velocity'] = 20
dataDict['InitialValue'] = pd.read_excel('cluster_center_2hour.xlsx',sheet_name='Sheet1')['初始车辆
（round）'].tolist()
dataDict['TimeWindow'] = 2
dataDict['SetUpCost'] = 80
dataDict['RunningCost'] = 2
for m in range(len(begin)):
real_number_of_dispatch = list(map(lambda x: x[0]-x[1], zip(leave[m], begin[m])))
all_real_number_of_dispatch.append(real_number_of_dispatch)
return all_real_number_of_dispatch
# 实际调入量的总数
def all_real_number_of_dispatch_sum(routes):
a = all_real_number_of_dispatch(routes)
for i in a:
for z in range(len(i)):
if np.isnan(i[z]):
i[z] = 0
else:
if i[z] > 0:
i[z] = 0
all_real_number_of_dispatch_sum = [sum(i) for i in a]
return all_real_number_of_dispatch_sum
# 未满足的单车需求量
def all_unsatisfied(routes):
allUnsatisfied = []
a = all_real_number_of_dispatch(routes)
routesNum = []
for _ in routes:
x = []
for b in _:
if b != 0:
x.append(b)
routesNum.append(x)
routesDemand = []
for c in routesNum:
y = []
for d in c:
y.append(total_demand[d])
routesDemand.append(y)
for i in range(len(a)):
for k in range(len(a[i])):
if np.isnan(a[i][k]):
a[i][k] = 0
truck_loading.append(np.nan)
else:
if arriveTime[t][0]<0:
truck_loading.append(0)
else:
if arriveTime[t][0]>dataDict['MaxLoad']:
truck_loading.append(dataDict['MaxLoad'])
else:
truck_loading.append(arriveTime[t][0])
if len(arriveTime[t]) == 1:
all_truck_loading_leave.append(truck_loading)
else:
for i in range(len(arriveTime[t])-1):
if np.isnan(arriveTime[t][i+1]):
truck_loading.append(np.nan)
else:
if truck_loading[i]+arriveTime[t][i+1]<0:
truck_loading.append(0)
else:
if truck_loading[i]+arriveTime[t][i+1]<dataDict['MaxLoad']:
truck_loading.append(truck_loading[i]+arriveTime[t][i+1])
else:
truck_loading.append(dataDict['MaxLoad'])
all_truck_loading_leave.append(truck_loading)
return all_truck_loading_leave
# 调度车到达各区域时的装载量
def all_truck_loading_begin(routes):
all_truck_loading_begin = []
leave = all_truck_loading_leave(routes)
for r in leave:
v = r[:]
v.insert(0,0)
f = v[0:-1]
all_truck_loading_begin.append(f)
return all_truck_loading_begin
# 实际各区域的调度量
def all_real_number_of_dispatch(routes):
all_real_number_of_dispatch = []
leave = all_truck_loading_leave(routes)
begin = all_truck_loading_begin(routes)
dataDict['PenaltyCost'] = 4
line = pd.read_csv('distance.csv')['line'].tolist()
distance_km = pd.read_csv('distance.csv')['distance(km)'].tolist()
distance_value = dict(zip(line,distance_km))
#生成个体
def genInd(dataDict = dataDict):
n Customer = len(dataDict['NodeCoor']) - 1 # 顾客数量
perm = np.random.permutation(nCustomer) + 1 # 生成顾客的随机排列,注意顾客编号为1--n
permSlice = []
a = random.sample([i+1 for i in range(len(perm)-1)],np.random.randint(1,len(perm)))
a.sort()
routePoint = [0]+a+[len(perm)]
for i,j in zip(routePoint[0::], routePoint[1::]):
permSlice.append(perm[i:j].tolist())
# 将路线片段合并为染色体
ind = [0]
for eachRoute in permSlice:
ind = ind + eachRoute + [0]
return ind
# 染色体解码
def decodeInd(ind):
indCopy = np.array(deepcopy(ind))
idxList = list(range(len(indCopy)))
zeroIdx = np.asarray(idxList)[indCopy == 0]
routes = []
for i,j in zip(zeroIdx[0::], zeroIdx[1::]):
routes.append(ind[i:j]+[0])
return routes
# 求得路径长度，到达区域时间和到达每个区域的调度需求
def quantityDistanceArriveTime(routes,dataDict=dataDict):
all_route_scheduling_quantity = []
all_route_distance = []
all_arrive_time = []
for eachRoute in routes:
distance = []
route_time = []
scheduling_requirements = []
for j in range(1,len(eachRoute)):
totalDistance = 0
if np.nan in quantityDistanceArriveTime([eachRoute])[1][0]:
eachRoute =
eachRoute[0:quantityDistanceArriveTime([eachRoute])[1][0].index(np.nan)+1]+[0]
else:
eachRoute = eachRoute
for i,j in zip(eachRoute[0::], eachRoute[1::]):
totalDistance += calDist(dataDict['NodeCoor'][i], dataDict['NodeCoor'][j])
AllDistance.append(totalDistance)
return sum(AllDistance),np.var(AllDistance)
# 评价函数
def evaluate(ind):
routes = decodeInd(ind)
totalDistanceCost = calRouteLen(routes)[0]*dataDict['RunningCost']
totalSetUpCost = len(routes)*dataDict['SetUpCost']
return (totalDistanceCost +
loadPenalty(routes)*dataDict['PenaltyCost']+totalSetUpCost),#+calRouteLen(routes)[1]*5),
# 交叉
def genChild(ind1, ind2, nTrail=5,dataDict=dataDict):
routes1 = decodeInd(ind1)
numSubroute1 = len(routes1)
subroute1 = routes1[np.random.randint(0, numSubroute1)]
unvisited = set(ind1) - set(subroute1)
unvisitedPerm = [digit for digit in ind2 if digit in unvisited]
bestRoute = None
bestFit = np.inf
if numSubroute1 < 3:
breakSubroute = []
breakSubroute.append([0]+unvisitedPerm+[0])
breakSubroute.append(subroute1)
routesFit =
cal RouteLen(breakSubroute)[0]*dataDict['RunningCost']+loadPenalty(breakSubroute)*dataDict['Pe
naltyCost']+len(breakSubroute)*dataDict['SetUpCost']#+calRouteLen(breakSubroute)[1]*5
if routesFit < bestFit:
bestRoute = breakSubroute
bestFit = routesFit
else:
for _ in range(nTrail):
breakPos = [0]+random.sample(range(1,len(unvisitedPerm)),numSubroute1-2)
breakPos.sort()
not_satisfied = list(map(lambda x: x[0]-x[1], zip(routesDemand[i], a[i])))
for j in range(len(not_satisfied)):
if not_satisfied[j] > 0:
not_satisfied[j] = 0
cost = sum(not_satisfied)
allUnsatisfied.append(cost)
return allUnsatisfied
# 各区域的总调度需求
def total_demand(dataDict=dataDict):
totalDemand = []
for i in range(len(dataDict['Demand'])):
totalDemand.append(dataDict['InitialValue'][i]+dataDict['Demand'][i])
return totalDemand
# 各需求点之间的距离
def calDist(pos1, pos2):
num1 = dataDict['NodeCoor'].index(pos1)
num2 = dataDict['NodeCoor'].index(pos2)
distance = distance_value.get("({}, {})".format(num1,num2))
return distance
# 各区域未满足量
def loadPenalty(routes):
penalty = 0
penalty = abs(sum(all_unsatisfied(routes)))
return penalty
# 到达各区域的时间
def calArriveTime(route, dataDict = dataDict):
arrivalTime = 0
arrivalTimeList = []
for i in range(0, len(route)-2):
arrivalTime += calDist(dataDict['NodeCoor'][route[i]],
dataDict['NodeCoor'][route[i+1]])/dataDict['Velocity']
arrivalTimeList.append(arrivalTime)
return arrivalTime,arrivalTimeList
# 路径总距离计算
def calRouteLen(routes,dataDict=dataDict):
AllDistance = []
for eachRoute in routes:
breakSubroute = []
for u,v in zip(breakPos[0::], breakPos[1::]):
breakSubroute.append([0]+unvisitedPerm[u:v]+[0])
breakSubroute.append([0]+unvisitedPerm[v:]+[0])
breakSubroute.append(subroute1)
routesFit =
calRouteLen(breakSubroute)[0]*dataDict['RunningCost']+loadPenalty(breakSubroute)*dataDict['Pe
naltyCost']+len(breakSubroute)*dataDict['SetUpCost']#+calRouteLen(breakSubroute)[1]*5
if routesFit < bestFit:
bestRoute = breakSubroute
bestFit = routesFit
child = []
for eachRoute in bestRoute:
child += eachRoute[:-1]
return child+[0]
def crossover(ind1, ind2):
''交叉操作'''
ind1[:], ind2[:] = genChild(ind1, ind2), genChild(ind2, ind1)
return ind1, ind2
# 变异
def opt(route,dataDict=dataDict, k=2):
n Cities = len(route)
optimizedRoute = route
min Distance =
calRouteLen([route])[0]*dataDict['RunningCost']+loadPenalty([route])*dataDict['PenaltyCost']
for i in range(1,nCities-2):
for j in range(i+k, nCities):
if j-i == 1:
continue
reversedRoute = route[:i]+route[i:j][::-1]+route[j:]
reversedRouteDist =
calRouteLen([reversedRoute])[0]*dataDict['RunningCost']+loadPenalty([reversedRoute])*dataDict['
PenaltyCost']
if reversedRouteDist < minDistance:
min Distance = reversedRouteDist
optimizedRoute = reversedRoute
return optimizedRoute
def mutate(ind):
routes = decodeInd(ind)
optimizedAssembly = []
for eachRoute in routes: 附录 C
95
optimizedRoute = opt(eachRoute)
optimizedAssembly.append(optimizedRoute)
child = []
for eachRoute in optimizedAssembly:
child += eachRoute[:-1]
ind[:] = child+[0]
return ind,
total_demand = total_demand()
# 注册遗传算法操作
toolbox = base.Toolbox()
toolbox.register('individual', tools.initIterate, creator.Individual, genInd)
toolbox.register('population', tools.initRepeat, list, toolbox.individual)
toolbox.register('evaluate', evaluate)
toolbox.register('select', tools.selTournament, tournsize=2)
toolbox.register('mate', crossover)
toolbox.register('mutate', mutate)
# 生成初始族群
toolbox.popSize = 200
pop = toolbox.population(toolbox.popSize)
# 记录迭代数据
stats=tools.Statistics(key=lambda ind: ind.fitness.values)
stats.register('min', np.min)
stats.register('avg', np.mean)
stats.register('std', np.std)
hallOfFame = tools.HallOfFame(maxsize=1)
# 遗传算法参数
toolbox.ngen = 200
toolbox.cxpb = 0.8
toolbox.mutpb = 0.1
# 算法主程序
pop,logbook=algorithms.eaMuPlusLambda(pop, toolbox, mu=toolbox.popSize,
lambda_=toolbox.popSize,cxpb=toolbox.cxpb,
mutpb=toolbox.mutpb, ngen=toolbox.ngen ,stats=stats, halloffame=hallOfFame, verbose=True)
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