scikit-opt——SA（模拟退火）

一、SA求函数最值

第一步： 定义您的问题

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + x[2] ** 2

第二步：执行SA

from sko.SA import SA

sa = SA(func=demo_func, x0=[1, 1, 1], T_max=1, T_min=1e-9, L=300, max_stay_counter=150)
best_x, best_y = sa.run()
print('best_x:', best_x, 'best_y', best_y)

第三步：绘制结果

import matplotlib.pyplot as plt
import pandas as pd

plt.plot(pd.DataFrame(sa.best_y_history).cummin(axis=0))
plt.show()

而且，scikit-opt提供了3种类型的模拟退火：快速，玻尔兹曼，柯西。查看更多sa

二、SA解决TSP问题

第一步：定义问题。TSP是什么自己百度。

file_name = sys.argv[1] if len(sys.argv) > 1 else 'data/nctu.csv'
points_coordinate = np.loadtxt(file_name, delimiter=',')
num_points = points_coordinate.shape[0]
distance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')
distance_matrix = distance_matrix * 111000  # 1 degree of lat/lon ~ = 111000m


def cal_total_distance(routine):
    '''The objective function. input routine, return total distance.
    cal_total_distance(np.arange(num_points))
    '''
    num_points, = routine.shape
    return sum([distance_matrix[routine[i % num_points], routine[(i + 1) % num_points]] for i in range(num_points)])

读取数据nctu.csv，定义距离计算函数。

第二步：为TSP做SA

from sko.SA import SA_TSP

sa_tsp = SA_TSP(func=cal_total_distance, x0=range(num_points), T_max=100, T_min=1, L=10 * num_points)

best_points, best_distance = sa_tsp.run()
print(best_points, best_distance, cal_total_distance(best_points))

第三步：绘制结果

# %% Plot the best routine
from matplotlib.ticker import FormatStrFormatter

fig, ax = plt.subplots(1, 2)

best_points_ = np.concatenate([best_points, [best_points[0]]])
best_points_coordinate = points_coordinate[best_points_, :]
ax[0].plot(sa_tsp.best_y_history)
ax[0].set_xlabel("Iteration")
ax[0].set_ylabel("Distance")
ax[1].plot(best_points_coordinate[:, 0], best_points_coordinate[:, 1],
           marker='o', markerfacecolor='b', color='c', linestyle='-')
ax[1].xaxis.set_major_formatter(FormatStrFormatter('%.3f'))
ax[1].yaxis.set_major_formatter(FormatStrFormatter('%.3f'))
ax[1].set_xlabel("Longitude")
ax[1].set_ylabel("Latitude")
plt.show()

更多：绘制动画

# %% Plot the animation
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from matplotlib.ticker import FormatStrFormatter

best_x_history = sa_tsp.best_x_history

fig2, ax2 = plt.subplots(1, 1)
ax2.set_title('title', loc='center')
line = ax2.plot(points_coordinate[:, 0], points_coordinate[:, 1],
                marker='o', markerfacecolor='b', color='c', linestyle='-')
ax2.xaxis.set_major_formatter(FormatStrFormatter('%.3f'))
ax2.yaxis.set_major_formatter(FormatStrFormatter('%.3f'))
ax2.set_xlabel("Longitude")
ax2.set_ylabel("Latitude")
plt.ion()
p = plt.show()


def update_scatter(frame):
    ax2.set_title('iter = ' + str(frame))
    points = best_x_history[frame]
    points = np.concatenate([points, [points[0]]])
    point_coordinate = points_coordinate[points, :]
    plt.setp(line, 'xdata', point_coordinate[:, 0], 'ydata', point_coordinate[:, 1])
    return line


ani = FuncAnimation(fig2, update_scatter, blit=True, interval=25, frames=len(best_x_history))
plt.show()

ani.save('sa_tsp.gif', writer='pillow')

参考链接：scikit-opt官方文档-SA部分