模拟退火解 深圳杯2020C题
简介
第二问的公式
\[\frac{x_{i}-f}{v_{i}} \geq T+\sum_{j=0(j !=i)}^{29} \frac{x_{j}-f}{r}
\]
\]
T 路径上一周消耗的时间
f 最低电量
r 充电速度
v 每个sensor的消耗速度
x 每个sensor的电池电量
code
主要使用了模拟退火
main.py
#coding=utf-8
from solution import solution
from draw import draw
import time
import winsound
def main1():
solve = solution(salesNumber = 1)
# 因为 xlsx2 文件可以用来解决问题1,2,3所以直接都读取了
myNodes = solve.readFromFile('B题附件2.xlsx')
start = time.clock()
xmin, x, y = solve.solutionForSubjectOne()
elapsed = (time.clock() - start)
drawObj = draw()
drawObj.drawY(x, y)
drawObj.drawRoute1(xmin, myNodes)
print("Time used:", elapsed)
def main2():
# 问题2 要赋值
xmin = [16, 27, 15, 12, 8, 11, 14, 6, 7, 9, 1, 2, 0, 17, 20, 19, 18, 25, 26, 29, 21, 23, 24, 28, 22, 4, 3, 5, 10, 13]
solve = solution(salesNumber=1)
# 因为 xlsx2 文件可以用来解决问题1,2,3所以直接都读取了
myNodes = solve.readFromFile(
'XXX')
start = time.clock()
drawObj = draw()
solve.setScheme(minEnergy=15, moveSpeed=10, chargeRate=20)
re = solve.solutionForSubjectTwo(xmin)
elapsed = (time.clock() - start)
drawObj.drawRect2(re, myNodes, 15) # 15是最小电量
print("Time used:", elapsed)
def main3():
# 问题3解决方案
solve = solution(salesNumber=4)
solve.setScheme(minEnergy=15, moveSpeed=10, chargeRate=20)
solve.setCoef(consumeOneMeter = 0.001, consumeOneMa = 1)
# 因为 xlsx2 文件可以用来解决问题1,2,3所以直接都读取了
myNodes = solve.readFromFile(
'XXX')
start = time.clock()
drawObj = draw()
xmin, ymin, drawX, drawY = solve.monituihuo()
elapsed = (time.clock() - start)
drawObj.drawY(drawX, drawY)
drawObj.drawRoute3(xmin, myNodes, ymin)
# 将 xmin 拆分为4 个
travelingSalesman = []
allDistance = []
for i in range(4):
tmp = [0]
allDistance.append(0)
travelingSalesman.append(tmp)
j = 0
for i in range(len(xmin)):
if (xmin[i] != 0):
travelingSalesman[j].append(xmin[i])
else:
j += 1
re = []
for i in range(4):
tmp = solve.solveFor3(travelingSalesman[i])
re.append(tmp)
# for i in range(4):
# print(re[i])
# print(travelingSalesman[i])
newRE = []
for i in range(30):
newRE.append(0)
for i in range(4):
for j in range(len(travelingSalesman[i])):
newRE[travelingSalesman[i][j]] = re[i][j]
drawObj.drawRect2(newRE, myNodes, 15) # 15是最小电量
for i in range(len(newRE)):
print(newRE[i])
# 对每一个节点进行绘图
# drawObj.drawRect3(re, travelingSalesman, myNodes)
# 根据得到的路径图 计算 传感器节点所需要的的电池电量
print("Time used:", elapsed)
def test():
solve = solution(salesNumber=4)
solve.setScheme(minEnergy=15, moveSpeed=10, chargeRate=20)
solve.setCoef(consumeOneMeter=0.001, consumeOneMa=1)
# 因为 xlsx2 文件可以用来解决问题1,2,3所以直接都读取了
myNodes = solve.readFromFile('XXX')
start = time.clock()
drawObj = draw()
newRE = [
15.0,
16.75801,
17.53926,
16.46503,
16.79056,
16.17204,
16.46503,
17.08354,
16.49758,
16.46503,
16.79056,
16.46503,
17.40906,
17.11609,
16.46503,
16.23715,
16.46503,
16.79056,
17.44161,
16.79056,
16.46503,
16.13948,
16.79056,
17.44161,
16.13948,
16.79056,
16.39992,
16.17204,
17.08354,
16.75801
]
drawObj.drawRect2(newRE, myNodes, 15) # 15是最小电量
if __name__ == "__main__":
test()
winsound.Beep(300, 2000)
utils.py
#coding=utf-8
from math import radians, cos, sin, asin, sqrt
def haversine(lon1, lat1, lon2, lat2): # 经度1，纬度1，经度2，纬度2 （十进制度数）
"""
https://blog.csdn.net/vernice/article/details/46581361
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# 将十进制度数转化为弧度
lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
# haversine公式
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat / 2) ** 2 + cos(lat1) * cos(lat2) * sin(dlon / 2) ** 2
c = 2 * asin(sqrt(a))
r = 6371 # 地球平均半径，单位为公里
return c * r * 1000
node.py
#coding=utf-8
class node:
def __init__(self):
self.name = ''
self.x = 0
self.y = 0
self.energyConsumptionRate = 0 # ma/s
self.batteryCapacity = 0 # ma 存储总值
self.lastAct = 0 # 默认为0 如果上次是减去数值那么就是 -1 如果上次是加上数值那么就是1
self.plusOrMinus = 0.01 # 默认是每次增加100
self.id = 0
self.curBatteryCap = 0
self.button = False
self.numberPlus = 0
def mySet(self, name, x, y, energyConsumptionRate, batteryCapacity, id):
self.name = name
self.x = x
self.y = y
self.energyConsumptionRate = energyConsumptionRate
self.batteryCapacity = batteryCapacity
self.curBatteryCap = batteryCapacity
self.oldBatteryCapacity = batteryCapacity
self.id = id
def getName(self):
return self.name
def reSet(self):
self.batteryCapacity = self.oldBatteryCapacity
self.curBatteryCap = self.oldBatteryCapacity
def getX(self):
return self.x
def getY(self):
return self.y
def pp(self):
print(self.name, self.id, '电池容量', self.batteryCapacity, '最初电量', self.oldBatteryCapacity, '加了', self.numberPlus, '次')
def getV(self):
return self.energyConsumptionRate
def plus(self):
self.numberPlus += 1
if(self.lastAct == -1):
self.batteryCapacity += self.plusOrMinus
self.lastAct = 1
# self.plusOrMinus = 1
elif(self.lastAct == 1):
self.batteryCapacity += self.plusOrMinus
self.lastAct = 1
elif(self.lastAct == 0):
self.batteryCapacity += self.plusOrMinus
self.lastAct = 1
def turnOn(self):
self.button = True
def consume(self, time, minEnergy):
self.curBatteryCap -= time * self.energyConsumptionRate
# 校验是否符合标准只要不符合标准返回一个 -1
if(not self.button):
return 0
if(self.curBatteryCap >= minEnergy):
return 1
else:
self.plus()
return -1
def charge(self, r): # r 充电速率
delt = self.batteryCapacity - self.curBatteryCap
time = delt / r
self.curBatteryCap = self.batteryCapacity
return time
def setCharge(self):
self.curBatteryCap = self.batteryCapacity
self.button = False
if __name__ == '__main__':
n = node()
draw.py
#coding=utf-8
import matplotlib.pyplot as plt
from utils import haversine
import numpy as np
import xlwt
plt.rcParams['font.sans-serif'] = ['SimHei'] # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False # 用来正常显示负号
class draw:
def __init__(self):
pass
def drawRoute1(self, res, myNodes):
for i in range(len(myNodes)):
plt.figure(num=2)
plt.scatter(myNodes[i].getX(), myNodes[i].getY())
plt.annotate(myNodes[i].getName(), (myNodes[i].getX(), myNodes[i].getY()))
sumDistance = self.calcSumDistance(res, myNodes)
plt.xlabel('总路程 = ' + str(sumDistance))
self.cmdRoute(res)
plt.show()
def drawRoute3(self, res, myNodes, energy):
for i in range(len(myNodes)):
plt.figure(num=2)
plt.scatter(myNodes[i].getX(), myNodes[i].getY())
plt.annotate(myNodes[i].getName(), (myNodes[i].getX(), myNodes[i].getY()))
# 绘制线条
# 首先将一个单纯的解化成四个解
travelingSalesman = []
allDistance = []
for i in range(4):
tmp = [0]
allDistance.append(0)
travelingSalesman.append(tmp)
j = 0
for i in range(len(res)):
if (res[i] != 0):
travelingSalesman[j].append(res[i])
else:
j += 1
# 得到每一个旅行商行驶的距离
sumDistance = 0
for i in range(4):
for j in range(len(travelingSalesman[i])):
lastPoint = travelingSalesman[i][j]
if (j + 1 >= len(travelingSalesman[i])):
nextPoint = travelingSalesman[i][0]
else:
nextPoint = travelingSalesman[i][j + 1]
x1 = myNodes[lastPoint].getX()
y1 = myNodes[lastPoint].getY()
x2 = myNodes[nextPoint].getX()
y2 = myNodes[nextPoint].getY()
distance = haversine(x1, y1, x2, y2)
plt.plot([x1, x2], [y1, y2])
allDistance[i] += distance
sumDistance += distance
plt.xlabel('sumDistance=' + str(sumDistance) + 'energy=' + str(energy))
plt.show()
def calcSumDistance(self, res, myNodes):
sumDistance = 0
for i in range(len(res)):
lastPoint = res[i]
if (i + 1 >= len(res)):
nextPoint = res[0]
else:
nextPoint = res[i + 1]
x1 = myNodes[lastPoint].getX()
y1 = myNodes[lastPoint].getY()
x2 = myNodes[nextPoint].getX()
y2 = myNodes[nextPoint].getY()
plt.plot([x1, x2], [y1, y2])
sumDistance += haversine(x1, y1, x2, y2)
return sumDistance
def cmdRoute(self, result):
result2 = []
check = False
for i in range(len(result)):
if (result[i] == 0):
check = True
if (check):
result2.append(result[i])
for i in range(len(result)):
if (result[i] == 0):
check = False
if (check):
result2.append(result[i])
for i in range(len(result2)):
print(str(result2[i]) + ' -> ', end='')
print(str(result2[0])) # 一个循环
def drawY(self, drawX, drawY):
plt.figure(num=1)
plt.title('模拟退火求TSP问题收敛图')
plt.xlabel('次数')
plt.ylabel('y')
plt.plot(drawX, drawY)
plt.show()
def drawRect2(self, re, myNodes, minB):
plt.figure(num=3)
N = len(re) - 1
re = re[1:] # 去掉数据中心
index = np.arange(N)
width = 0.45
plt.bar(index, re, width, label="每个传感器的电池容量 单位(ma)", color="#90EE90")
plt.xlabel('传感器')
plt.ylabel('电池容量')
plt.title('电池容量分布图')
plt.ylim(13,18)
name = []
for i in range(1, len(myNodes)):
name.append(str(i))
plt.xticks(index, name)
plt.legend(loc="upper right")
plt.axhline(minB)
self.wr2(re, myNodes)
plt.show()
def wr2(self, re, myNodes):
# 将电池电量输入到excel文件
workbook = xlwt.Workbook(encoding='utf-8')
# 创建一个worksheet
worksheet = workbook.add_sheet('My Worksheet')
# 写入excel
# 参数对应 行, 列, 值
for i in range(len(re)):
worksheet.write(i, 0, myNodes[i+1].getName())
worksheet.write(i, 1, re[i])
# 保存
workbook.save('问题二电池电量.xls')
solution.py
#coding=utf-8
import xlrd
from node import node
from utils import haversine
import numpy as np
import math
import matplotlib.pyplot as plt
import random
class solution:
'''
暂时先不考虑约束吧
'''
def __init__(self, salesNumber):
self.minEnergy = 40
self.moveSpeed = 5 # 15000 / 3600
self.sumDistance = 0
self.myNodes = []
self.SalesManNum = salesNumber
self.minDistance = 0
self.chargeRate = 0.1 # r 0.5
self.consumeOneMeter = 0.0001
self.consumeOneMa = 1
def readFromFile(self, filename):
data = xlrd.open_workbook(filename)
table = data.sheet_by_name('Sheet1')
name = table.name
rowNum = table.nrows
colNum = table.ncols
print(name, rowNum, colNum)
for i in range(31):
if (i == 0):
continue
tmp = []
tmp.append(i)
for j in range(4):
tmp.append(table.cell(i, j).value)
if(i == 1):
tmp[4] = 0.000000001
tmp[4] = tmp[4] / 3600 # ma/s
minBatteryCapacity = self.minEnergy
n = node()
n.mySet(id = tmp[0], name = tmp[1], x = tmp[2], y = tmp[3], energyConsumptionRate = tmp[4], batteryCapacity = minBatteryCapacity ) # 每个电池的默认初始容量是100ma 容忍度是3
self.myNodes.append(n)
for i in range(len(self.myNodes)):
self.myNodes[i].pp()
return self.myNodes
def aimFunction1(self, res):
'''
res 是一个 节点序列带上 3 个 0 的序列 list
'''
# 得到每一个旅行商走过的道路
allDistance = 0
for i in range(len(res)):
lastPoint = res[i]
if (i + 1 >= len(res)):
nextPoint = res[0]
else:
nextPoint = res[i + 1]
x1 = self.myNodes[lastPoint].getX()
y1 = self.myNodes[lastPoint].getY()
x2 = self.myNodes[nextPoint].getX()
y2 = self.myNodes[nextPoint].getY()
distance = haversine(x1, y1, x2, y2)
allDistance += distance
return allDistance
def aimFunction5(self, res):
# 将res分解为4段res
result = []
tmp = [0]
for i in range(len(res)):
if(res[i] == 0):
result.append(tmp)
tmp = [0]
else:
tmp.append(res[i])
result.append(tmp)
# 计算每一个路程 消耗的时间 和 能量均衡的时候消耗的充电时间
subTime = []
subDistance = 0
for i in range(self.SalesManNum):
subTime.append(0)
for i in range(len(self.myNodes)):
self.myNodes[i].reSet()
# 从0开始的一个字符串
subTime[0]= self.solve(result[0])
subTime[1]= self.solve(result[1])
subTime[2]= self.solve(result[2])
subTime[3]= self.solve(result[3])
subTime.sort()
# 最大花瓣的时间最短 每条路径 所耗费时间 也尽可能短
return subTime[3] + subTime[0] + subTime[1] + subTime[2]
def solve(self, res):
# 计算此字符串总距离
# 新增定义行走
sumDistance = 0
for i in range(len(res)):
lastPoint = res[i]
if (i + 1 >= len(res)):
nextPoint = res[0]
else:
nextPoint = res[i + 1]
x1 = self.myNodes[lastPoint].getX()
y1 = self.myNodes[lastPoint].getY()
x2 = self.myNodes[nextPoint].getX()
y2 = self.myNodes[nextPoint].getY()
sumDistance += haversine(x1, y1, x2, y2)
T = sumDistance / self.moveSpeed
f = self.minEnergy
r = self.chargeRate
mA = []
mb = []
# 去除 DC 的影响
resul = []
for i in range(0, len(res)): # 默认res[0] = 0 的时候才能去除 影响
resul.append(res[i])
if len(resul) != 0:
for i in range(len(resul)):
tmp = []
for j in range(len(resul)):
if (i == j):
tmp.append(r / self.myNodes[resul[j]].getV())
else:
tmp.append(-1)
mA.append(tmp)
mb.append(T*r - (len(resul) - 1)*f + r / self.myNodes[resul[i]].getV() * f)
A = np.array(mA)
b = np.array(mb).T
re = np.linalg.solve(A,b) # 得到每一个的电池容量
allEnergy = sumDistance * self.consumeOneMeter
for i in range(len(resul)):
allEnergy += (re[i] - f) * self.consumeOneMa
return allEnergy
def solveFor3(self, res):
sumDistance = 0
for i in range(len(res)):
lastPoint = res[i]
if (i + 1 >= len(res)):
nextPoint = res[0]
else:
nextPoint = res[i + 1]
x1 = self.myNodes[lastPoint].getX()
y1 = self.myNodes[lastPoint].getY()
x2 = self.myNodes[nextPoint].getX()
y2 = self.myNodes[nextPoint].getY()
sumDistance += haversine(x1, y1, x2, y2)
T = sumDistance / self.moveSpeed
f = self.minEnergy
r = self.chargeRate
mA = []
mb = []
# 去除 DC 的影响 不去了
resul = []
for i in range(0, len(res)): # 默认res[0] = 0 的时候才能去除 影响
resul.append(res[i])
if len(resul) != 0:
for i in range(len(resul)):
tmp = []
for j in range(len(resul)):
if (i == j):
tmp.append(r / self.myNodes[resul[j]].getV())
else:
tmp.append(-1)
mA.append(tmp)
mb.append(T*r - (len(resul) - 1)*f + r / self.myNodes[resul[i]].getV() * f)
A = np.array(mA)
b = np.array(mb).T
re = np.linalg.solve(A,b) # 得到每一个的电池容量
return re # 对应res 的电池电量
def monituihuo(self): # 解决问题三
T = 100 # initiate temperature
oldT = 100
Tmin = 1e-8 # mininum value of temperature
# 初始化所有分布
x = self.initX()
k = 500
y = 1000000 # 初始y值
xmin = [] # 记录数据值
ymin = 1000000
# 温度衰减系数
a = 0.95
n = 500
drawX = [i for i in range(500)]
drawY = []
while n > 0 and T > 0:
n-=1
for i in range(k):
y = self.aimFunction5(x)
xNew = self.genNewResult(x)
yNew = self.aimFunction5(xNew)
if(yNew <= y):
x = xNew.copy()
y = yNew
if(yNew < ymin):
xmin = x.copy()
ymin = yNew
else:
# p = 1 / (1 + math.exp(-(yNew - y) / T))
p = math.exp(-(yNew - y) / (T))
r = np.random.uniform(low=0, high = 1)
if (r < p):
x = xNew.copy()
y = yNew
drawY.append(y)
T = T * a
print('直接输出', x, self.aimFunction5(x))
print('记录最小数值', xmin, ymin)
return xmin, ymin, drawX, drawY
def initX(self):
city_num = 29 # 不包括起始城市的序列
x = [i for i in range(1, city_num+1)]
random.shuffle(x)
if (self.SalesManNum == 1):
x.insert(random.randint(0, len(x)), 0)
elif(self.SalesManNum == 4):
x.insert(random.randint(0, len(x)), 0)
x.insert(random.randint(0, len(x)), 0)
x.insert(random.randint(0, len(x)), 0)
print('初始路线', x)
return x
def genNewResult(self, res):
'''
res 就是 X 的值 T 温度越高产生翻转的概率越大 oldT 原本最大温度
'''
r = res.copy()
x = np.random.uniform(low= 0 , high= 1)
if x >= 0 and x < 0.4: # 使用交换法生成新的路径
# print('交换')
c1 = random.randint(0, len(r)-1)
c2 = random.randint(0, len(r)-1)
tmp = r[c1]
r[c1] = r[c2]
r[c2] = tmp
elif x >= 0.4 and x < 0.7: # 使用移动序列产生新路径
# print('移动')
c1 = random.randint(0, len(r) - 1)
c2 = random.randint(0, len(r) - 1)
c3 = random.randint(0, len(r) - 1)
tmp = [c1, c2, c3]
tmp.sort()
c1 = tmp[0]
c2 = tmp[1]
c3 = tmp[2]
tmp1 = r[0:c1]
tmp2 = r[c1:c2]
tmp3 = r[c2:c3]
tmp4 = r[c3:]
r = tmp1 + tmp3 + tmp2 + tmp4
else:
# print('倒置')
c1 = random.randint(0, len(r) - 1)
c2 = random.randint(0, len(r) - 1)
if c1 > c2:
tmp = c1
c1 = c2
c2 = tmp
tmp1 = r[0:c1]
tmp2 = r[c1:c2]
tmp3 = r[c2:]
tmp2.reverse()
r = tmp1 + tmp2 + tmp3
return r
def solutionForSubjectOne(self):
T = 100 # initiate temperature
# 初始化所有分布
x = self.initX()
k = 500
y = 1000000 # 初始y值
xmin = [] # 记录数据值
ymin = 1000000
# 温度衰减系数
a = 0.95
# 绘图
drawX = [i for i in range(500)]
drawY = []
n = 500
while n > 0:
n-=1
for i in range(k):
y = self.aimFunction1(x)
# generate a new x in the neighboorhood of x by transform function （）
xNew = self.genNewResult(x)
yNew = self.aimFunction1(xNew)
if (yNew <= y):
x = xNew.copy()
y = yNew
if (yNew < ymin):
xmin = x.copy()
ymin = yNew
else:
p = math.exp(-(yNew - y) / T)
r = np.random.uniform(low=0, high=1)
if (r < p):
x = xNew.copy()
y = yNew
drawY.append(y)
T = T * a
print('直接输出', x, self.aimFunction1(x))
print('记录最小数值', xmin, ymin)
return xmin, drawX, drawY
def solutionForSubjectTwo(self, res):
# 计算此字符串总距离
# 新增定义行走
sumDistance = 0
for i in range(len(res)):
lastPoint = res[i]
if (i + 1 >= len(res)):
nextPoint = res[0]
else:
nextPoint = res[i + 1]
x1 = self.myNodes[lastPoint].getX()
y1 = self.myNodes[lastPoint].getY()
x2 = self.myNodes[nextPoint].getX()
y2 = self.myNodes[nextPoint].getY()
sumDistance += haversine(x1, y1, x2, y2)
T = sumDistance / self.moveSpeed
res.sort() # 当这个正序 生成的结果电量也是正序的
f = self.minEnergy
r = self.chargeRate
mA = []
mb = []
# 去除 DC 的影响
resul = []
for i in range(0, len(res)): # 默认res[0] = 0 的时候才能去除 不去除了
resul.append(res[i])
if len(resul) != 0:
for i in range(len(resul)):
tmp = []
for j in range(len(resul)):
if (i == j):
tmp.append(r / self.myNodes[resul[j]].getV())
else:
tmp.append(-1)
mA.append(tmp)
mb.append(T*r - (len(resul) - 1)*f + r / self.myNodes[resul[i]].getV() * f)
A = np.array(mA)
b = np.array(mb).T
re = np.linalg.solve(A,b) # 得到每一个的电池容量
return re
def setScheme(self, minEnergy = 15, moveSpeed = 10, chargeRate = 20):
self.minEnergy = minEnergy
self.moveSpeed = moveSpeed
self.chargeRate = chargeRate
def setCoef(self, consumeOneMeter = 0.0001, consumeOneMa = 1):
self.consumeOneMeter = consumeOneMeter
self.consumeOneMa = consumeOneMa
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