2025.7.30 Simulated Annealing法による2D-Rastrigin関数の最適化

code:p.py

import numpy as np

import matplotlib.pyplot as plt

def rastrigin_function2d(x, y):

A, n = 10, 2

ret = A * n

ret += x**2 - A * np.cos(2 * np.pi * x)

ret += y**2 - A * np.cos(2 * np.pi * y)

return ret

def create_x():

return np.array((x, y))

def solve_sa(func, rho, iter_max):

global x_hist, f_hist, T_hist, chk_hist, x_escape_hist, f_escape_hist

T = 1.

x_now = create_x()

x_best, f_best = x_now, f_now

iter_count = 0

x_hist.append(x_now)

f_hist.append(f_now)

while True:

T *= rho

x_new = create_x()

n_now = np.linalg.norm(x_now)

n_new = np.linalg.norm(x_new)

metro_rand = np.random.rand()

metro_exp = np.exp(- (f_new - f_now)/n_now / T)

if (f_new < f_now) or (metro_rand < metro_exp):

if f_new >= f_now:

print('escape at {}'.format(iter_count))

x_escape_hist.append(x_now)

f_escape_hist.append(f_now)

x_now, f_now = x_new, f_new

if f_new < f_best:

x_best, f_best = x_new, f_new

if iter_count == iter_max:

print('計算回数が上限に達したので計算を打ち切った', T, iter_count)

break

if T <= eps:

print('Tが小さくなったので計算を打ち切った', T, iter_count)

break

x_hist.append(x_now)

f_hist.append(f_now)

iter_count += 1

T_hist.append(T)

chk_hist.append(metro_exp)

return x_best, f_best

############################

rho = 0.9999

eps = 10e-8

iter_max = 10000

x_range = -5.12, 5.12

f_range = -5.12, 5.12

x_hist, f_hist = [], []

x_best_hist, f_best_hist = [], []

T_hist, chk_hist = [], []

x_escape_hist, f_escape_hist = [], []

func = rastrigin_function2d

x_best, f_best = solve_sa(func, rho, iter_max)

print('x best', x_best)

print('f best', f_best)

x_hist = np.stack(x_hist)

f_hist = np.stack(f_hist)

# plot

xxx, yyy = np.meshgrid(xx, yy)

n = 2 # 2-dim

zzz = func(xxx, yyy)

fig = plt.figure()

ax = fig.add_subplot(projection='3d')

# ax.plot_surface(xxx, yyy, zzz)

ax.plot_wireframe(xxx, yyy, zzz)

plt.show()