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Question

Trying to solve TSP as linear programming task using cvxpy and have problem with this. It is my first experience so thanks for help. As a result I want to have matrix with 0 and 1 that shows every next city for salesman.

need to use exactly cvxpy

here you can read theory

cvxpy website

thanks for help

import cvxpy as cp
import numpy as np

np.random.seed(1)
N = 10
distances = np.random.rand(N, N)  

x = cp.Variable((N, N), boolean=True)
u = cp.Variable(N, integer=True)

constraints = []

for j in range(N):                                      
    indices = list(range(0, j)) + list(range(j + 1, N))
    constraints.append(cp.sum(x[indices, j]) == 1)
for i in range(N):
    indices = list(range(0, i)) + list(range(i + 1, N)) 
    constraints.append(cp.sum(x[i, indices]) == 1)
for i in range(1, N):                      
    for j in range(1, N):
        if i != j:
            constraints.append(u[i] - u[j] + N*x[i, j] <= N-1)

for i in range(N):
    for j in range(N):
        if i != j:
            сost += (x[i,j]*distances[i,j]) 

prob = cp.Problem(cp.Minimize(cost), constraints)
prob.solve()
print(prob.value)

receive "None"

feel like the problem in cost defining, but don`t know how to make it correct maybe I should use cvxpy.multiply or cvxpy.sum?

Answer 1

The default MIP-solver coming with cvxpy is just a proof of concept and very unstable in non-tiny instances. Things like that happen then and there is not much you can do.

Like Erwin asked for in aboves comment: activate verbose=True and you might recognize the solver in use. I'm guessing: ECOS_BB . It's the only one available in the default install.

The situation in regards to deploying a MIP solver which:

• is easily installed on windows
• is of high-quality
• is open-source

is not great.

The easiest approach of obtaining a usable one on windows is using pre-built glpk through cvxopt.

Answer 2

don't know what was the problem. maybe smth with Jupyter. everything became ok after it refreshing thanks all for help!

Answer 3

Though it's not the problem here, be sure to call prob.solve() . Otherwise, prob.value is None