前言

提示：这里可以添加本文要记录的大概内容：

模拟算法（SA）来求解VRP问题

VRP拆解为TSP问题后，对TSP问题进行算子改变，从而实现可行解之间的改变。

TSP算子改变：可以分为两两元素改变，两两片段改变

提示：以下是本篇文章正文内容，下面案例可供参考

一、SA是什么？

SA 是元启发式的一种，为了跳出局部解，以一定的概率可以接受非改进解的算法。

通过对温度T进行改变，此处是迭代10次温度下降0.9。

温度越低，非改进路线选取的概率越低，但仍然有一定概率被选中

二、使用步骤

1.引入库

代码如下（示例）：

import copyimport matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import math
import random

2.定义SA-VRP

代码如下（示例）：

class vrp_SA():def __init__(self,file_path,veh_capacity):self.file_path =file_pathself.veh_capacity=veh_capacitydef readfile(self):file =self.file_pathData =pd.read_csv(file)x_cor =list(Data['x_coord'])y_cor =list(Data['y_coord'])demand =list(Data['demand'])index =list(Data['id'])##create dict():nodes={}for i in range(len(demand)):if demand == 0:depot_non_deman = demand[i]nodes[i]=(depot_non_deman,x_cor[i],y_cor[i])else:cus_deman = demand[i]nodes[i] = (cus_deman, x_cor[i], y_cor[i])##depot node:depot_node =nodes[0]###project depot node :nodes[-1] = depot_nodereturn nodes###define initial solution for TSPdef initial(self,nodes):##drop out 0 and -1 nodecount =len(nodes)-2##randomly create nodes listinitial_path =[i for i in range(1,count+1)]random.seed(0)np.random.shuffle(initial_path)return initial_path####define the TSP swap rulesdef swap_single_Nodes(self,path):swap_si_path =copy.deepcopy(path)index1,index2 =np.random.randint(1,100,1)[0],np.random.randint(1,100,1)[0]swap_si_path[index1],swap_si_path[index2] = path[index2],path[index1]print('swap num:',(swap_si_path[index1],swap_si_path[index2]))return swap_si_pathdef swap_seq(self,path,num):oldpath =copy.deepcopy(path)count =len(new_path)swap_seq_path =[]for i in range(0,count,num):if i%2==0:# new_list=[ele1,ele2,ele3,ele4]ele1 = oldpath[i]ele2 = oldpath[i + 1]ele3 = oldpath[i + 2]ele4 = oldpath[i + 3]swap_seq_path.append(ele1)swap_seq_path.append(ele2)swap_seq_path.append(ele3)swap_seq_path.append(ele4)else:ele1 = oldpath[i]ele2 = oldpath[i + 1]ele3 = oldpath[i + 2]ele4 = oldpath[i + 3]swap_seq_path.insert(0,ele1)swap_seq_path.insert(0,ele2)swap_seq_path.insert(0,ele3)swap_seq_path.insert(0,ele4)return swap_seq_path##split TSP routes and get the vehicle num and veh_path:def splitRoutes(self,path,nodes):''':return:vehicle numbervehicle routesvehicle capacity'''num_veh=1route_veh=[]route =[]reminded_capacity =self.veh_capacityfor node in path:if reminded_capacity -nodes[node][0] >=0:route.append(node)reminded_capacity=reminded_capacity -nodes[node][0]else:route_veh.append(route)num_veh = num_veh + 1#update new route nodes:reminded_capacity =self.veh_capacityroute=[node]reminded_capacity =reminded_capacity-nodes[node][0]route_veh.append(route)return num_veh,route_vehdef no_dis(self,point1,point2):''':param point1::param point2::return: two point distance'''node_dis =np.hypot(point1[1]-point2[1],point1[2]-point2[2])return node_disdef vrp_dis(self,route_veh,nodes):''':param route_veh: vehicle routes output from TSP route split:param nodes: node information (x,y):return: a list of vehicle route distance for VRP routing route'''distance =0##get single routes:all_distance =[]for i in range(len(route_veh)):# print(i)##get total pathall_path =[0]+route_veh[i]+[-1]# print('all path:',all_path)each_path_dis=0dis_j = []for j in range(len(all_path)):if j ==len(all_path)-1:point1 =all_path[j]point2 =all_path[0]point1 =nodes[point1]point2=nodes[point2]point_dis =self.no_dis(point1,point2)each_path_dis =each_path_dis +point_diselse:point1 = all_path[j]point2=all_path[j+1]point1 = nodes[point1]point2 = nodes[point2]point_dis = self.no_dis(point1, point2)each_path_dis =each_path_dis +point_dis#print(each_path_dis)dis_j.append(each_path_dis)all_distance.append(dis_j[0])# print('path distance:{}'.format(dis_j))# print(all_distance)return all_distancedef calObj(self,veh_routes):''':param nodes: the (x,y) in file:return: each VRP routing distance'''nodes=self.readfile()total_Obj =sum(self.vrp_dis(veh_routes,nodes=nodes))return total_Obj#########plotdef plotObj(self,Obj_list):''':param Obj_list: list of each path total_Obj(each VRP RROUTING distance):return: plot'''plt.rcParams['axes.unicode_minus']=False #show minus sign# plt.plot(np.arange(1,len(Obj_list)+1),Obj_list)x = [x for x in range(len(Obj_list))]plt.clf()plt.plot(x, Obj_list, label='linear')plt.xlabel('Iterations')plt.ylabel('Obj value')plt.grid()plt.xlim(1,len(Obj_list)+1)return plt.show()###define SA algorithm for VRP:def SA_VRP(self,current_tsp_path,new_tsp_path,t):''':param T0: Initial temportature:param Tend: Termination temportature:param deltaQ: the fraction of delta/q(temporature) ,:param v_cap: Vehicle capacity:param opt_type: Optimization type: 0: Minimize the number of vehicles1: Minimize travel distance:return:核心：TSP变换-新TSP-切分TSP 成VRP-对比成本来模拟退火！！！'''# veh_cap =self.veh_capacity# nodes =self.readfile()# init_TSP_path=self.initial(nodes=nodes)# new_TSP_path =self.swap_single_Nodes(init_TSP_path)curr_num ,curr_vrp =self.splitRoutes(current_tsp_path,nodes)new_veh_num,new_vrp = self.splitRoutes(new_tsp_path, nodes)dis_curr =self.calObj(curr_vrp)dis_new = self.calObj(new_vrp)deltaQ =dis_new-dis_currprint('delta',deltaQ)min_list=[]if deltaQ<0:current_tsp_path =copy.deepcopy(new_tsp_path)dis =self.calObj(new_vrp)min_list.append(dis)else:df = math.exp(-deltaQ / t)if  df >=random.randint(0,1):dis =self.calObj(new_vrp)current_tsp_path = copy.deepcopy(new_tsp_path)min_list.append(dis)else:dis =self.calObj(curr_vrp)current_tsp_path=copy.deepcopy(current_tsp_path)min_list.append(dis)print(current_tsp_path,min_list)return current_tsp_path, min_list

运行

if __name__ == '__main__':##read nodes data:file ='cvrp.csv'veh_cap=800vrpsa =vrp_SA(file,veh_cap)nodes =vrpsa.readfile()print(nodes)# ## define initial data:initial_path =vrpsa.initial(nodes)new_path =vrpsa.swap_single_Nodes(initial_path)##initializeT0=1000Tend =0.01MaxIter =500##para value:t = T0num = 0path_list = []dis_list = []rate =0.5# new_TSP_path = vrpsa.swap_single_Nodes(init_TSP_path)# curr_tsp_path, min_dis = vrpsa.SA_VRP(current_tsp_path=init_TSP_path, new_tsp_path=new_TSP_path, t=t)init_TSP_path = vrpsa.initial(nodes=nodes)while t > Tend and MaxIter > 0:if MaxIter % 10 == 0:t = t * rate# else:#     t=tprint('t:',t)###find the new pathnew_TSP_path =vrpsa.swap_single_Nodes(path=init_TSP_path)curr_tsp_path, min_dis = vrpsa.SA_VRP(current_tsp_path=init_TSP_path, new_tsp_path=new_TSP_path, t=t)path_list.append(curr_tsp_path)dis_list.append(min_dis)MaxIter -= 1print('maxiter:', MaxIter)#最小值位置min_dis = min(dis_list)dis_index = dis_list.index(min_dis)#最小值对应的路径shortest_path = path_list[dis_index]new_veh_num, new_vrp = vrpsa.splitRoutes(shortest_path, nodes)print('vehcile distance:{}, best Obj routes:{}:'.format(min_dis,new_vrp))###draw plot:vrpsa.plotObj(dis_list)

此处对迭代算法进行评估-以图为导向。（100个点的VRP问题）

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VRP_SA-模拟退火

文章目录

前言

一、SA是什么？

二、使用步骤

1.引入库

2.定义SA-VRP

运行

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