模擬退火算法的三種形式+Python實現

3 types of Simulated Annealing

模擬退火有三種具體形式
‘fast’:

u ~ Uniform(0, 1, size = d)
y = sgn(u - 0.5) * T * ((1 + 1/T)**abs(2*u - 1) - 1.0)

xc = y * (upper - lower)
x_new = x_old + xc

c = n * exp(-n * quench)
T_new = T0 * exp(-c * k**quench)

‘cauchy’:

u ~ Uniform(-pi/2, pi/2, size=d)
xc = learn_rate * T * tan(u)
x_new = x_old + xc

T_new = T0 / (1 + k)

‘boltzmann’:

std = minimum(sqrt(T) * ones(d), (upper - lower) / (3*learn_rate))
y ~ Normal(0, std, size = d)
x_new = x_old + learn_rate * y

T_new = T0 / log(1 + k)

代碼示例

1. Fast Simulated Annealing

-> Demo code: examples/demo_sa.py#s4

from sko.SA import SAFast

sa_fast = SAFast(func=demo_func, x0=[1, 1, 1], T_max=1, T_min=1e-9, q=0.99, L=300, max_stay_counter=150)
sa_fast.run()
print('Fast Simulated Annealing: best_x is ', sa_fast.best_x, 'best_y is ', sa_fast.best_y)

2. Boltzmann Simulated Annealing

-> Demo code: examples/demo_sa.py#s5

from sko.SA import SABoltzmann

sa_boltzmann = SABoltzmann(func=demo_func, x0=[1, 1, 1], T_max=1, T_min=1e-9, q=0.99, L=300, max_stay_counter=150)
sa_boltzmann.run()
print('Boltzmann Simulated Annealing: best_x is ', sa_boltzmann.best_x, 'best_y is ', sa_fast.best_y)

3. Cauchy Simulated Annealing

-> Demo code: examples/demo_sa.py#s6

from sko.SA import SACauchy

sa_cauchy = SACauchy(func=demo_func, x0=[1, 1, 1], T_max=1, T_min=1e-9, q=0.99, L=300, max_stay_counter=150)
sa_cauchy.run()
print('Cauchy Simulated Annealing: best_x is ', sa_cauchy.best_x, 'best_y is ', sa_cauchy.best_y)

以上全部代碼已整理到scikit-opt ， 保證可以運行