# simulated annealing search of a one-dimensional objective function
from numpy import asarray
from numpy import exp
from numpy.random import randn
from numpy.random import rand
from numpy.random import seed
# objective function
def objective(x):
return x[0]**2.0
# simulated annealing algorithm
def simulated_annealing(objective, bounds, n_iterations, step_size, temp):
# generate an initial point
best = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])
# evaluate the initial point
best_eval = objective(best)
# current working solution
curr, curr_eval = best, best_eval
# run the algorithm
for i in range(n_iterations):
# take a step
candidate = curr + randn(len(bounds)) * step_size
# evaluate candidate point
candidate_eval = objective (candidate)
# check for new best solution
if candidate_eval < best_eval:
# store new best point
best, best_eval = candidate, candidate_eval
# report progress
print('>%d f(%s) = %.5f' % (i, best, best_eval))
# difference between candidate and current point evaluation
diff = candidate_eval - curr_eval
# calculate temperature for current epoch
t = temp / float(i + 1)
# calculate metropolis acceptance criterion
metropolis = exp(-diff / t)
# check if we should keep the new point
if diff < 0 or rand() < metropolis:
# store the new current point
curr, curr_eval = candidate, candidate_eval
return [best, best_eval]
# seed the pseudorandom number generator
seed(1)
# define range for input
bounds = asarray([[-5.0, 5.0]])
# define the total iterations
n_iterations = 1000
# define the maximum step size
step_size = 0.1
# initial temperature
temp = 10
# perform the simulated annealing search
best, score = simulated_annealing(objective, bounds, n_iterations, step_size, temp)
print('Done!')
print('f(%s) = %f' % (best, score))
Output:
>34 f([-0.78753544]) = 0.62021
>35 f([-0.76914239]) = 0.59158
>37 f([-0.68574854]) = 0.47025
>39 f([-0.64797564]) = 0.41987
>40 f([-0.58914623]) = 0.34709
>41 f([-0.55446029]) = 0.30743
>42 f([-0.41775702]) = 0.17452
>43 f([-0.35038542]) = 0.12277
>50 f([-0.15799045]) = 0.02496
>66 f([-0.11089772]) = 0.01230
>67 f([-0.09238208]) = 0.00853
>72 f([-0.09145261]) = 0.00836
>75 f([-0.05129162]) = 0.00263
>93 f([-0.02854417]) = 0.00081
>144 f([0.00864136]) = 0.00007
>149 f([0.00753953]) = 0.00006
>167 f([-0.00640394]) = 0.00004
>225 f([-0.00044965]) = 0.00000
>503 f([-0.00036261]) = 0.00000
>512 f([0.00013605]) = 0.00000
Done!
f([0.00013605]) = 0.000000
