技术标签: 算法 python 机器学习 TSP+python
旅行商人要拜访n个城市,并最终回到出发城市,要求每个城市只能拜访一次,优化目标是最小化路程之和。
20个城市坐标:(88, 16),(42, 76),(5, 76),(69, 13),(73, 56),(100, 100),(22, 92),(48, 74),(73, 46),(39, 1),(51, 75),(92, 2),(101, 44),(55, 26),(71, 27),(42, 81),(51, 91),(89, 54),(33, 18),(40, 78)
结果路径图如下:
粒子群算法模仿鸟群觅食行为,核心思想是通过向距离食物最近的鸟集聚,不断更新速度和位置以达到最优解,即表现不好的个体通过向表现好的个体学习使得自身往好的方向转变,这里存在一个前提:所有鸟知道距离食物的远近,距离食物最近包含两部分:当前最近和历史最近。标准粒子群算法适合求解函数极值问题,在TSP、背包问题上多用混合型粒子群算法。详细介绍可参考[粒子群算法研究]
算法设计的关键在于如何向表现较好的个体学习,标准粒子群算法引入惯性因子w、自我认知因子c1、社会认知因子c2分别作为自身、当代最优解和历史最优解的权重,指导粒子速度和位置的更新,这在求解函数极值问题时比较容易实现,而在TSP问题上,速度位置的更新则难以直接采用加权的方式进行,一个常见的方法是采用基于遗传算法交叉算子的混合型粒子群算法进行求解,这里采用顺序交叉算子,对惯性因子w、自我认知因子c1、社会认知因子c2则以w/(w+c1+c2),c1/(w+c1+c2),c2/(w+c1+c2)的概率接受粒子本身、当前最优解、全局最优解交叉的父代之一(即按概率选择其中一个作为父代,不加权),具体算法实现如下。
# -*- coding: utf-8 -*-
"""
粒子群算法求解TSP问题
随机在(0,101)二维平面生成20个点
距离最小化
"""
import math
import random
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.pylab import mpl
mpl.rcParams['font.sans-serif'] = ['SimHei'] # 添加这条可以让图形显示中文
def calDistance(CityCoordinates):
‘’’
计算城市间距离
输入:CityCoordinates-城市坐标;
输出:城市间距离矩阵-dis_matrix
‘’'
dis_matrix = pd.DataFrame(data=None,columns=range(len(CityCoordinates)),index=range(len(CityCoordinates)))
for i in range(len(CityCoordinates)):
xi,yi = CityCoordinates[i][0],CityCoordinates[i][1]
for j in range(len(CityCoordinates)):
xj,yj = CityCoordinates[j][0],CityCoordinates[j][1]
if (xixj) & (yiyj):
dis_matrix.iloc[i,j] = round(math.pow(10,10))
else:
dis_matrix.iloc[i,j] = round(math.sqrt((xi-xj)2+(yi-yj)2),2)
return dis_matrix
def calFitness(line,dis_matrix):
‘’’
计算路径距离,即评价函数
输入:line-路径,dis_matrix-城市间距离矩阵;
输出:路径距离-dis_sum
‘’'
dis_sum = 0
dis = 0
for i in range(len(line)-1):
dis = dis_matrix.loc[line[i],line[i+1]]#计算距离
dis_sum = dis_sum+dis
dis = dis_matrix.loc[line[-1],line[0]]
dis_sum = dis_sum+dis
return round(dis_sum,1)
def draw_path(line,CityCoordinates):
‘’’
#画路径图
输入:line-路径,CityCoordinates-城市坐标;
输出:路径图
‘’‘
x,y= [],[]
for i in line:
Coordinate = CityCoordinates[i]
x.append(Coordinate[0])
y.append(Coordinate[1])
x.append(x[0])
y.append(y[0])
plt.plot(x, y,‘r-’, color=’#4169E1’, alpha=0.8, linewidth=0.8)
plt.xlabel(‘x’)
plt.ylabel(‘y’)
plt.show()
def crossover(bird,pLine,gLine,w,c1,c2):
‘’’
采用顺序交叉方式;交叉的parent1为粒子本身,分别以w/(w+c1+c2),c1/(w+c1+c2),c2/(w+c1+c2)
的概率接受粒子本身逆序、当前最优解、全局最优解作为parent2,只选择其中一个作为parent2;
输入:bird-粒子,pLine-当前最优解,gLine-全局最优解,w-惯性因子,c1-自我认知因子,c2-社会认知因子;
输出:交叉后的粒子-croBird;
‘’'
croBird = [None]*len(bird)#初始化
parent1 = bird#选择parent1
#选择parent2(轮盘赌操作)
randNum = random.uniform(0, sum([w,c1,c2]))
if randNum <= w:
parent2 = [bird[i] for i in range(len(bird)-1,-1,-1)]#bird的逆序
elif randNum <= w+c1:
parent2 = pLine
else:
parent2 = gLine
<span class="token comment">#parent1-> croBird</span>
start_pos <span class="token operator">=</span> random<span class="token punctuation">.</span>randint<span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token builtin">len</span><span class="token punctuation">(</span>parent1<span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span>
end_pos <span class="token operator">=</span> random<span class="token punctuation">.</span>randint<span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token builtin">len</span><span class="token punctuation">(</span>parent1<span class="token punctuation">)</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span>
<span class="token keyword">if</span> start_pos<span class="token operator">></span>end_pos<span class="token punctuation">:</span>start_pos<span class="token punctuation">,</span>end_pos <span class="token operator">=</span> end_pos<span class="token punctuation">,</span>start_pos
croBird<span class="token punctuation">[</span>start_pos<span class="token punctuation">:</span>end_pos<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span> <span class="token operator">=</span> parent1<span class="token punctuation">[</span>start_pos<span class="token punctuation">:</span>end_pos<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">.</span>copy<span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token comment"># parent2 -> croBird</span>
list1 <span class="token operator">=</span> <span class="token builtin">list</span><span class="token punctuation">(</span><span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">0</span><span class="token punctuation">,</span>start_pos<span class="token punctuation">)</span><span class="token punctuation">)</span>
list2 <span class="token operator">=</span> <span class="token builtin">list</span><span class="token punctuation">(</span><span class="token builtin">range</span><span class="token punctuation">(</span>end_pos<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token builtin">len</span><span class="token punctuation">(</span>parent2<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
list_index <span class="token operator">=</span> list1<span class="token operator">+</span>list2<span class="token comment">#croBird从后往前填充</span>
j <span class="token operator">=</span> <span class="token operator">-</span><span class="token number">1</span>
<span class="token keyword">for</span> i <span class="token keyword">in</span> list_index<span class="token punctuation">:</span>
<span class="token keyword">for</span> j <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span>j<span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token builtin">len</span><span class="token punctuation">(</span>parent2<span class="token punctuation">)</span><span class="token operator">+</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">:</span>
<span class="token keyword">if</span> parent2<span class="token punctuation">[</span>j<span class="token punctuation">]</span> <span class="token operator">not</span> <span class="token keyword">in</span> croBird<span class="token punctuation">:</span>
croBird<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> parent2<span class="token punctuation">[</span>j<span class="token punctuation">]</span>
<span class="token keyword">break</span>
<span class="token keyword">return</span> croBird
if name == ‘main’:
#参数
CityNum = 20#城市数量
MinCoordinate = 0#二维坐标最小值
MaxCoordinate = 101#二维坐标最大值
iterMax = 200#迭代次数
iterI = 1#当前迭代次数
<span class="token comment">#PSO参数</span>
birdNum <span class="token operator">=</span> <span class="token number">50</span><span class="token comment">#粒子数量</span>
w <span class="token operator">=</span> <span class="token number">0.2</span><span class="token comment">#惯性因子</span>
c1 <span class="token operator">=</span> <span class="token number">0.4</span><span class="token comment">#自我认知因子</span>
c2 <span class="token operator">=</span> <span class="token number">0.4</span><span class="token comment">#社会认知因子</span>
pBest<span class="token punctuation">,</span>pLine <span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">,</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token comment">#当前最优值、当前最优解,(自我认知部分)</span>
gBest<span class="token punctuation">,</span>gLine <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">,</span><span class="token punctuation">[</span><span class="token punctuation">]</span><span class="token comment">#全局最优值、全局最优解,(社会认知部分)</span>
<span class="token comment">#随机生成城市数据,城市序号为0,1,2,3...</span>
<span class="token comment"># CityCoordinates = [(random.randint(MinCoordinate,MaxCoordinate),random.randint(MinCoordinate,MaxCoordinate)) for i in range(CityNum)]</span>
CityCoordinates <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">(</span><span class="token number">88</span><span class="token punctuation">,</span> <span class="token number">16</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">42</span><span class="token punctuation">,</span> <span class="token number">76</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">5</span><span class="token punctuation">,</span> <span class="token number">76</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">69</span><span class="token punctuation">,</span> <span class="token number">13</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">73</span><span class="token punctuation">,</span> <span class="token number">56</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">100</span><span class="token punctuation">,</span> <span class="token number">100</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">22</span><span class="token punctuation">,</span> <span class="token number">92</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">48</span><span class="token punctuation">,</span> <span class="token number">74</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">73</span><span class="token punctuation">,</span> <span class="token number">46</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">39</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">51</span><span class="token punctuation">,</span> <span class="token number">75</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">92</span><span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">101</span><span class="token punctuation">,</span> <span class="token number">44</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">55</span><span class="token punctuation">,</span> <span class="token number">26</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">71</span><span class="token punctuation">,</span> <span class="token number">27</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">42</span><span class="token punctuation">,</span> <span class="token number">81</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">51</span><span class="token punctuation">,</span> <span class="token number">91</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">89</span><span class="token punctuation">,</span> <span class="token number">54</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">33</span><span class="token punctuation">,</span> <span class="token number">18</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token punctuation">(</span><span class="token number">40</span><span class="token punctuation">,</span> <span class="token number">78</span><span class="token punctuation">)</span><span class="token punctuation">]</span>
dis_matrix <span class="token operator">=</span> calDistance<span class="token punctuation">(</span>CityCoordinates<span class="token punctuation">)</span><span class="token comment">#计算城市间距离,生成矩阵</span>
birdPop <span class="token operator">=</span> <span class="token punctuation">[</span>random<span class="token punctuation">.</span>sample<span class="token punctuation">(</span><span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>CityCoordinates<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">,</span><span class="token builtin">len</span><span class="token punctuation">(</span>CityCoordinates<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span>birdNum<span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token comment">#初始化种群,随机生成</span>
fits <span class="token operator">=</span> <span class="token punctuation">[</span>calFitness<span class="token punctuation">(</span>birdPop<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span>dis_matrix<span class="token punctuation">)</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span>birdNum<span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token comment">#计算种群适应度</span>
gBest <span class="token operator">=</span> pBest <span class="token operator">=</span> <span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token comment">#全局最优值、当前最优值</span>
gLine <span class="token operator">=</span> pLine <span class="token operator">=</span> birdPop<span class="token punctuation">[</span>fits<span class="token punctuation">.</span>index<span class="token punctuation">(</span><span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token comment">#全局最优解、当前最优解</span>
<span class="token keyword">while</span> iterI <span class="token operator"><=</span> iterMax<span class="token punctuation">:</span><span class="token comment">#迭代开始</span>
<span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>birdPop<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">:</span>
birdPop<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> crossover<span class="token punctuation">(</span>birdPop<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span>pLine<span class="token punctuation">,</span>gLine<span class="token punctuation">,</span>w<span class="token punctuation">,</span>c1<span class="token punctuation">,</span>c2<span class="token punctuation">)</span>
fits<span class="token punctuation">[</span>i<span class="token punctuation">]</span> <span class="token operator">=</span> calFitness<span class="token punctuation">(</span>birdPop<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">,</span>dis_matrix<span class="token punctuation">)</span>
pBest<span class="token punctuation">,</span>pLine <span class="token operator">=</span> <span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token punctuation">,</span>birdPop<span class="token punctuation">[</span>fits<span class="token punctuation">.</span>index<span class="token punctuation">(</span><span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span>
<span class="token keyword">if</span> <span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span> <span class="token operator"><=</span> gBest<span class="token punctuation">:</span>
gBest<span class="token punctuation">,</span>gLine <span class="token operator">=</span> <span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token punctuation">,</span>birdPop<span class="token punctuation">[</span>fits<span class="token punctuation">.</span>index<span class="token punctuation">(</span><span class="token builtin">min</span><span class="token punctuation">(</span>fits<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>iterI<span class="token punctuation">,</span>gBest<span class="token punctuation">)</span><span class="token comment">#打印当前代数和最佳适应度值</span>
iterI <span class="token operator">+=</span> <span class="token number">1</span><span class="token comment">#迭代计数加一</span>
<span class="token keyword">print</span><span class="token punctuation">(</span>gLine<span class="token punctuation">)</span><span class="token comment">#路径顺序</span>
draw_path<span class="token punctuation">(</span>gLine<span class="token punctuation">,</span>CityCoordinates<span class="token punctuation">)</span><span class="token comment">#画路径图</span>
智能优化算法类别 | 启发式算法求解TSP问题系列博文 |
---|---|
进化算法 | 遗传算法求解TSP问题 |
仿人智能优化算法 | 禁忌搜索算法求解TSP问题 |
仿自然优化算法 | 模拟退火算法求解TSP问题 |
群智能优化算法 | 蚁群算法求解TSP问题 |
群智能优化算法 | 粒子群算法求解TSP问题 |
总结篇 | 五种常见启发式算法求解TSP问题 |
改进篇 | 遗传-粒子群算法&遗传-禁忌搜索算法求解TSP问题 |
记录学习过程,欢迎指正
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文章浏览阅读4.5k次,点赞5次,收藏18次。阅读测试程序,设计一个Book类。函数接口定义:class Book{}该类有 四个私有属性 分别是 书籍名称、 价格、 作者、 出版年份,以及相应的set 与get方法;该类有一个含有四个参数的构造方法,这四个参数依次是 书籍名称、 价格、 作者、 出版年份 。裁判测试程序样例:import java.util.*;public class Main { public static void main(String[] args) { List <Book>_6-1 book类的设计java
文章浏览阅读613次,点赞28次,收藏27次。相比于以前的传统手工管理方式,智能化的管理方式可以大幅降低学校的运营人员成本,实现了校园导航的标准化、制度化、程序化的管理,有效地防止了校园导航的随意管理,提高了信息的处理速度和精确度,能够及时、准确地查询和修正建筑速看等信息。课题主要采用微信小程序、SpringBoot架构技术,前端以小程序页面呈现给学生,结合后台java语言使页面更加完善,后台使用MySQL数据库进行数据存储。微信小程序主要包括学生信息、校园简介、建筑速看、系统信息等功能,从而实现智能化的管理方式,提高工作效率。
传统上用户登陆状态会以 Session 的形式保存在服务器上,而 Session ID 则保存在前端的 Cookie 中;而使用 JWT 以后,用户的认证信息将会以 Token 的形式保存在前端,服务器不需要保存任何的用户状态,这也就是为什么 JWT 被称为无状态登陆的原因,无状态登陆最大的优势就是完美支持分布式部署,可以使用一个 Token 发送给不同的服务器,而所有的服务器都会返回同样的结果。有状态和无状态最大的区别就是服务端会不会保存客户端的信息。
文章浏览阅读9.8k次,点赞260次,收藏442次。前几天在知乎上看到这么一个问题,一位在读学生,自己非常想自学编程,但是很怕走一些弯路,于是提问「自学编程需要注意什么?」,我看了一圈回答,看起来都不是自学过来的,很多回答抓不到重点。我的读者都知道,我是非科班 0 基础自学过来的,我很清楚一个人自学编程有哪些误区,有哪些需要注意的地方,以及哪些可以提升效率的地方,所以,我从我的自学经历给一些自学编程的后来者总结了一些建议,希望给正在自学编程或者打算走_自学编程哪些注意
文章浏览阅读1.9k次。21.等值线图(Counter Plot)21.1.Contour Demo21.2.Creating a “meshgrid”21.3.Calculation of the Values21.4.Changing the Colours and the Line Style21.5.Filled Contours21.6.Individual Colours21.等值线图(Counter Plot)两个变量函数的等值线(或等高线)是函数具有常数值的曲线。它是平行于x,y平面的函数f(x,y_counter图
文章浏览阅读1.1k次。Vue刷新当前页面并url带参_vue刷新页面并传递参数
文章浏览阅读1.3k次。目录Pktgen入门系统要求设置巨大的TLB /巨大页面支持BIOS设置终端显示获取源代码编译DPDK和Pktgen设置环境运行应用程序Pktgen入门本节包含有关如何启动和运行DPDK和pktgen流量生成器应用程序的说明。这些说明与pktgen在Ubuntu桌面系统上设置DPDK有关。但是,该版本应该可以在任何最新的Linux系统上使用,这些系统对kernel支持巨大的TLB /巨大页面。系统要求主要的系统要求是支持DPDK数据包处理框架。._pktgen-dpdk:22.04.1
文章浏览阅读774次。判断URL中是否包含中文汉字- (BOOL)df_isContainChinese{ NSUInteger length = [self length]; for (NSUInteger i = 0; i < length; i++) { NSRange range = NSMakeRange(i, 1); NSString *subString = [self substringWithRange:range]; const cha_检测url中是否有中文
文章浏览阅读72次。查询语言的格式查询语言必须包括SELECT操作以及可选择性的包含FROM, WHERE, AND, ORDER BY, and OR.查询语言的基本格式query Q1{ description: "Select all drivers older than 65." statement: SELECT org.example.Driver WHERE..._composer access control language