我是PuLP和LP的新手。虽然translating the code适用于gurobipi库，因此它可以与PuLP一起使用，但我仍然坚持使用以下创建变量的gurobipy代码。
# Create variables.
# x[i, j] is 1 if the edge i->j is on the optimal tour, and 0 otherwise.
x = {}
for i in range(n):
for j in range(i+1):
x[i,j] = m.addVar(obj=dist[i][j], vtype=GRB.BINARY,
name='x'+str(i)+'_'+str(j))
x[j,i] = x[i,j]
m.addVar允许使用obj参数定义目标系数。如何在PuLP中完成同样的工作？它的docs for pulp.LpVariable似乎没有类似的参数......
另外，有没有使用PuLP在Python中解决TSP的示例代码？这将有助于作为参考！
到目前为止，这是我的代码，没有查看小计。决策变量x_ij的结果似乎非常错误，仅在1.0时才等于i == j。到目前为止，我的尝试是否正确？
结果
0_0: 1.0
0_5: 1.0
1_1: 1.0
1_15: 1.0
2_2: 1.0
2_39: 1.0
3_3: 1.0
3_26: 1.0
4_4: 1.0
4_42: 1.0
5_5: 1.0
5_33: 1.0
6_6: 1.0
6_31: 1.0
7_7: 1.0
7_38: 1.0
8_8: 1.0
8_24: 1.0
9_9: 1.0
9_26: 1.0
10_4: 1.0
10_10: 1.0
11_11: 1.0
11_12: 1.0
12_11: 1.0
12_12: 1.0
13_13: 1.0
13_17: 1.0
14_14: 1.0
14_18: 1.0
15_1: 1.0
15_15: 1.0
16_3: 1.0
16_16: 1.0
17_13: 1.0
17_17: 1.0
18_14: 1.0
18_18: 1.0
19_19: 1.0
19_20: 1.0
20_4: 1.0
20_20: 1.0
21_21: 1.0
21_25: 1.0
22_22: 1.0
22_27: 1.0
23_21: 1.0
23_23: 1.0
24_8: 1.0
24_24: 1.0
25_21: 1.0
25_25: 1.0
26_26: 1.0
26_43: 1.0
27_27: 1.0
27_38: 1.0
28_28: 1.0
28_47: 1.0
29_29: 1.0
29_31: 1.0
30_30: 1.0
30_34: 1.0
31_29: 1.0
31_31: 1.0
32_25: 1.0
32_32: 1.0
33_28: 1.0
33_33: 1.0
34_30: 1.0
34_34: 1.0
35_35: 1.0
35_42: 1.0
36_36: 1.0
36_47: 1.0
37_36: 1.0
37_37: 1.0
38_27: 1.0
38_38: 1.0
39_39: 1.0
39_44: 1.0
40_40: 1.0
40_43: 1.0
41_41: 1.0
41_45: 1.0
42_4: 1.0
42_42: 1.0
43_26: 1.0
43_43: 1.0
44_39: 1.0
44_44: 1.0
45_15: 1.0
45_45: 1.0
46_40: 1.0
46_46: 1.0
47_28: 1.0
47_47: 1.0
...
PuLP代码
def get_dist(tsp):
with open(tsp, 'rb') as tspfile:
r = csv.reader(tspfile, delimiter='\t')
d = [row for row in r]
d = d[1:] # skip header row
locs = set([r[0] for r in d]) | set([r[1] for r in d])
loc_map = {l:i for i, l in enumerate(locs)}
idx_map = {i:l for i, l in enumerate(locs)}
dist = [(loc_map[r[0]], loc_map[r[1]], r[2]) for r in d]
return dist, idx_map
def dist_from_coords(dist, n):
points = []
for i in range(n):
points.append([0] * n)
for i, j, v in dist:
points[i][j] = points[j][i] = float(v)
return points
def find_tour():
tsp_file = `/Users/test/` + 'my-waypoints-dist-dur.tsv'
coords, idx_map = get_dist(tsp_file)
n = len(idx_map)
dist = dist_from_coords(coords, n)
# Define the problem
m = pulp.LpProblem('TSP', pulp.LpMinimize)
# Create variables
# x[i,j] is 1 if edge i->j is on the optimal tour, and 0 otherwise
# Also forbid loops
x = {}
for i in range(n):
for j in range(n):
lowerBound = 0
upperBound = 1
# Forbid loops
if i == j:
upperBound = 0
print i,i
x[i,j] = pulp.LpVariable('x' + str(i) + '_' + str(j), lowerBound, upperBound, pulp.LpBinary)
x[j,i] = x[i,j]
# Define the objective function to minimize
m += pulp.lpSum([dist[i][j] * x[i,j] for i in range(n) for j in range(n)])
# Add degree-2 constraint
for i in range(n):
m += pulp.lpSum([x[i,j] for j in range(n)]) == 2
status = m.solve()
print pulp.LpStatus[status]
for i in range(n):
for j in range(n):
if pulp.value(x[i,j]) >0:
print str(i) + '_' + str(j) + ': ' + str( pulp.value(x[i,j]) )
find_tour()
my-waypoints-dist-dur.tsv (Full version)
waypoint1 waypoint2 distance_m duration_s
Michigan State Capitol, Lansing, MI 48933 Rhode Island State House, 82 Smith Street, Providence, RI 02903 1242190 41580
Minnesota State Capitol, St Paul, MN 55155 New Mexico State Capitol, Santa Fe, NM 87501 1931932 64455
答案 0 :(得分：0)
创建变量时：
x[j,i] = x[i,j]不正确。这是Python的参考概念。 Python中的所有对象都有一个引用，当您将一个变量分配给两个名称x [i，j]和x [j，i]时，这会导致它们都指向同一个对象。如果在配方中修改x [i，j]，x [j，i]也会改变。 就旅行销售人员问题而言，这意味着如果你从A - > B（即x [A] [B] == 1），那么你也从B - > A旅行。这是为什么你的路径变量中会得到无穷无尽的1.0值。
更正后的变量定义变为：
x[i,j] = pulp.LpVariable('x_%s_%s'%(i,j), lowerBound, upperBound, pulp.LpBinary)
x[j,i] = pulp.LpVariable('x_%s_%s'%(j,i), lowerBound, upperBound, pulp.LpBinary)