import numpy as np
import shed
import path
import sys
import matplotlib.pyplot as plt
from scipy.spatial import Delaunay
import networkx as nx
from scipy.spatial import distance
from scipy.optimize import linprog
def simplexNewPaths (G,edge,points,V):
print ("Вход в фунцкию с ",edge,G[edge[0]][edge[1]]['flow'],G[edge[0]][edge[1]]['capacity'])
old_paths = G[edge[0]][edge[1]]['flow']
w = G[edge[0]][edge[1]]
capacity = G[edge[0]][edge[1]]['capacity']
G.remove_edge (edge[0],edge[1])
new_paths = []
k = []
for p in old_paths:
try:
new_paths.append (path.Path(nx.shortest_path(G,p[0],p[-1]),None))
k.append(p.getK(points))
except nx.NetworkXNoPath as e:
print(e)
return None,None
for p in new_paths:
k.append(p.getK(points))
size = len(old_paths)
A_e = []
A_u = [[]]
b_u = [capacity]
b_e = []
for i in range(size):
A_e.append([])
b_e.append(V[old_paths[i][0]][old_paths[i][-1]])
for j in range(size*2):
if j==2*i or j==2*i+1:
A_e[i].append(1)
else:
A_e[i].append(0)
for j in range(size*2):
if j%2==0:
A_u[0].append(1)
else:
A_u[0].append(0)
res = linprog(k, A_ub=A_u, b_ub=b_u, A_eq = A_e, b_eq=b_e,bounds=(0,None))
G.add_edge(edge[0],edge[1],w)
for i in range(size):
new_paths[i].flow = res.x[i*2+1]
old_paths[i].flow = res.x[i*2]
# G.remove_edge (edge[0],edge[1])
print ("o"*25, res.x)
return old_paths, new_paths
#Создание случайного графа при помощи триангуляции Делоне
N = 6
p = shed.builtPoints(N,10,10)
tri = Delaunay(p)
e,f = shed.getEdgesDelaunay(tri)
G = nx.DiGraph()
for edge in e:
G.add_edge(edge[0],edge[1],weight = round(distance.euclidean(p[edge[0]],p[edge[1]]),3), capacity = np.random.randint(50)+1,flow=[], problem = True)
#Создание случайной матрциы перевозок
V = shed.builtRandomTransit(N,10)
shed.pprint (V)
#Матрица, содержащая итоговый план перевозок
result_flows = [[[] for i in range(N)] for j in range(N)]
#Поиск всех кратчайших путей и добавление путей к ребрам
paths = nx.all_pairs_dijkstra_path(G)
shed.pprint (paths)
for i in range(N):
for j in range(N):
for k in range(len(paths[i][j])-1):
G[paths[i][j][k]][paths[i][j][k+1]]['flow'].append(path.Path(paths[i][j],V[i][j]))
#Первая пробверка на проблемные ребра
for u,v,d in G.edges(data=True):
sum_flow = sum([paths_edge.flow for paths_edge in d['flow'] ])
if sum_flow<=d['capacity']:
d['problem']=False
for u,v,d in G.edges(data=True):
print (u,v, d['problem'],d['flow'],d['capacity'])
#Получение остаточного графа
for i in range(N):
for j in range(N):
if i==j:
result_flows[i][j]=path.Path([i],0)
else:
tmp_path = path.Path(paths[i][j],None)
if tmp_path.complete(V[i][j],G):
result_flows[i][j]=path.Path(paths[i][j],V[i][j])
V[i][j] = 0
for k in range(len(tmp_path.chain)-1):
G[tmp_path[k]][tmp_path[k+1]]['capacity']-=V[i][j]
if G[tmp_path[k]][tmp_path[k+1]]['capacity']==0:
G.remove_edge([tmp_path[k]][tmp_path[k+1]])
else:
G[tmp_path[k]][tmp_path[k+1]]['flow'].remove(tmp_path)
#Отрисовка графа
positions_vertexes = [(p[i][0], p[i][1]) for i in range(N)]
edge_labels=dict([((u,v,),(d['capacity'])) for u,v,d in G.edges(data=True)])
nx.draw_networkx_edge_labels(G,positions_vertexes,edge_labels=edge_labels,label_pos=0.75)
nx.draw_networkx(G, positions_vertexes, with_labels=True, arrows=True, node_color='Red')
plt.show()
#Предварительные результаты, полученные сразу
shed.ppprint(result_flows)
#Список проблемных ребер
problem_edges = []
for u,v,d in G.edges(data=True):
if d['problem']:
problem_edges.append((u,v,d))
#Пока есть проблемные ребра
while (len(problem_edges)!=0):
print (problem_edges)
for u,v,d in problem_edges:
if d['problem']:
# Получаем старые пути и их аналоги с распределенныеми потоками
old_paths, new_paths = simplexNewPaths(G,(u,v),p,V)
if old_paths is None:
sys.exit("Задача неразрешима. Нет пути")
for i in range(len(old_paths)):
print (old_paths[i],"---->",new_paths[i])
# Корректируем пути в ребрах
for oP in old_paths:
for j in range(len(oP.chain)-1):
if (oP[j],oP[j+1]) not in nx.non_edges(G):
if oP.flow == 0.0:
G[oP[j]][oP[j+1]]['flow'].remove(oP)
print ("Удалили",oP, oP[j],oP[j+1])
else:
index = G[oP[j]][oP[j+1]]['flow'].index(oP)
G[oP[j]][oP[j+1]]['flow'][index].flow = oP.flow
if sum([paths_edge.flow for paths_edge in G[oP[j]][oP[j+1]]['flow']])<=G[oP[j]][oP[j+1]]['capacity']:
G[oP[j]][oP[j+1]]['problem']=False
for nP in new_paths:
if nP.flow != 0.0:
for j in range(len(nP.chain)-1):
if nP not in G[nP[j]][nP[j+1]]['flow']:
G[nP[j]][nP[j+1]]['flow'].append(path.Path(nP.chain, nP.flow))
else:
index = G[nP[j]][nP[j+1]]['flow'].index(nP)
G[nP[j]][nP[j+1]]['flow'][index].flow = nP.flow
if sum([paths_edge.flow for paths_edge in G[nP[j]][nP[j+1]]['flow']])>G[nP[j]][nP[j+1]]['capacity']:
G[nP[j]][nP[j+1]]['problem']=True
else:
for j in range(len(nP.chain)-1):
if nP in G[nP[j]][nP[j+1]]['flow']:
G[nP[j]][nP[j+1]]['flow'].remove(nP)
G[u][v]['problem']=False
for i in G[u][v]['flow']:
if i.complete(i.flow,G):
result_flows[i[0]][i[-1]].append(i)
V[i[0]][i[-1]]-=i.flow
for j in range(len(i.chain)-1):
G[i[j]][i[j+1]]['flow'].remove(i)
G[i[j]][i[j+1]]['capacity'] -= i.flow
guv = G[u][v]['flow']
print ("Не убитые пути!!!!!!!!!!!!!!!!!!!!!",guv, u,v, d['capacity'])
if G[u][v]['capacity']==0:
G.remove_edge(u,v)
print ("Убитые пути!!!!!!!!!!!!!!!!!!!!!",guv)
# Обновление проблемных путей
problem_edges = []
for u,v,d in G.edges(data=True):
if d['problem']:
problem_edges.append((u,v,d))
for u,v,d in G.edges(data=True):
print (u,v, d['problem'],d['flow'],d['capacity'])
ost_paths = {}
for u,v,d in G.edges(data=True):
for f in d['flow']:
if ost_paths.get((f[0],f[-1])) is None:
ost_paths[(f[0],f[-1])] = [f]
else:
if f not in ost_paths[(f[0],f[-1])]:
ost_paths[(f[0],f[-1])].append(f)
print (ost_paths)
for i in ost_paths:
sum_flow = sum([ip.flow for ip in ost_paths[i]])
result_flows[i[0]][i[1]] = ost_paths[i]
V[i[0]][i[1]]-= sum_flow
print ("Edges")
for u,v,d in G.edges(data=True):
print (u,v, d['problem'],d['flow'],d['capacity'])
shed.ppprint (result_flows)
shed.pprint (V)