Creating a TSP ILP in PuLP

PuLP_TSP.py

import pulp as pl

# Define PuLP model
model = pl.LpProblem('TSP', pl.LpMinimize)

# Define binary variables
x = pl.LpVariable.dicts('x', ((i, j) for i in range(n_perm) for j in range(n_perm)), cat = 'Binary')

# Set the objective function
model += pl.lpSum(cost_dict[permutations[i], permutations[j]] * x[i, j] for i in range(n_perm) for j in range(n_perm))

# Define the constraints
for i in range(n_perm):
    
    # Do not allow loops
    model += x[i, i] == 0

for i in range(n_perm):
    
    # Exactly one outgoing edge
    model += pl.lpSum(x[i, j] for j in range(n_perm)) == 1
    
    # Exactly one incoming edge
    model += pl.lpSum(x[j, i] for j in range(n_perm)) == 1