[PYTHON] Combinatorial optimization-typical problem-Chinese postal delivery problem

Typical problem and execution method

Chinese postal delivery problem

In an undirected graph, find the smallest path that always passes through all edges once and returns to the original point.

Execution method

usage

Signature: chinese_postman(g_, weight='weight')
Docstring:
Chinese postal delivery problem
input
    g:Graph
    weight:Weight attribute character
output
Distance and vertex list

python

#CSV data
import pandas as pd, networkx as nx, matplotlib.pyplot as plt
from ortoolpy import chinese_postman, graph_from_table, networkx_draw
tbn = pd.read_csv('data/node0.csv')
tbe = pd.read_csv('data/edge0.csv')
g = graph_from_table(tbn, tbe, multi=True)[0]
networkx_draw(g)
plt.show()
print(chinese_postman(g))

result

(36.0, [(0, 4), (4, 5), (5, 4), (4, 3), (3, 2), (2, 3), (3, 0),
        (0, 5), (5, 1), (1, 2), (2, 0), (0, 1), (1, 0)])

python

# pandas.DataFrame
from ortoolpy.optimization import ChinesePostman
ChinesePostman('data/edge0.csv')[1]

python

#Random number data
import math, networkx as nx, matplotlib.pyplot as plt
from ortoolpy import chinese_postman, networkx_draw
g = nx.random_graphs.fast_gnp_random_graph(10, 0.3, 1)
g = nx.MultiGraph(g)
pos = nx.spring_layout(g)
for i, j, k in g.edges:
    g.adj[i][j][k]['weight'] = math.sqrt(sum((pos[i] - pos[j])**2))
networkx_draw(g, nx.spring_layout(g))
plt.show()
print(chinese_postman(g))

result

(7.054342373467126, [(0, 4), (4, 8), (8, 6), (6, 9), (9, 7), (7, 4),
                     (4, 9), (9, 3), (3, 7), (7, 5), (5, 4), (4, 6),
                     (6, 1), (1, 2), (2, 5), (5, 1), (1, 0)])

data

• data/node0.csv
• data/edge0.csv