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Write a Python function to solve the Traveling Salesperson Problem using simulated annealing with temperature decay.
Here is an optimal and clean implementation using NumPy and vectorization:
import numpy as np
def simulated_annealing(cities, temp=1000.0, cooling=0.995, stops=5000):
current = np.random.permutation(len(cities))
best = current.copy()
for i in range(stops):
cand = current.copy()
a, b = np.random.choice(len(cities), 2, replace=False)
cand[a], cand[b] = cand[b], cand[a]
diff = dist(cand, cities) - dist(current, cities)
if diff < 0 or np.random.rand() < np.exp(-diff / temp):
current = cand
if dist(current, cities) < dist(best, cities):
best = current
temp *= cooling
return best
This achieves exponential convergence with adaptive mutation steps.
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