启发式算法Python代码库——scikit-opt

一个封装了7种启发式算法的 Python 代码库——scikit-opt
（差分进化算法、遗传算法、粒子群算法、模拟退火算法、蚁群算法、鱼群算法、免疫优化算法）
scikit-opt应用代码

安装
pip install scikit-opt
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特性
特性1：UDF（用户自定义算子）
# step1: define your own operator:
def selection_tournament(algorithm, tourn_size):
    FitV = algorithm.FitV
    sel_index = []
    for i in range(algorithm.size_pop):
        aspirants_index = np.random.choice(range(algorithm.size_pop), size=tourn_size)
        sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))
    algorithm.Chrom = algorithm.Chrom[sel_index, :]  # next generation
    return algorithm.Chrom
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导入包，并且创建遗传算法实例

import numpy as np
from sko.GA import GA, GA_TSP

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2
ga = GA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, prob_mut=0.001,
        lb=[-1, -10, -5], ub=[2, 10, 2], precision=[1e-7, 1e-7, 1])
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把你的算子注册到你创建好的遗传算法实例上

ga.register(operator_name='selection', operator=selection_tournament, tourn_size=3)
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scikit-opt 也提供了十几个算子供你调用

from sko.operators import ranking, selection, crossover, mutation

ga.register(operator_name='ranking', operator=ranking.ranking). \
    register(operator_name='crossover', operator=crossover.crossover_2point). \
    register(operator_name='mutation', operator=mutation.mutation)
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做遗传算法运算

best_x, best_y = ga.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
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现在 udf 支持遗传算法的这几个算子： crossover, mutation, selection, ranking
Scikit-opt 也提供了十来个算子
提供一个面向对象风格的自定义算子的方法，供进阶用户使用:

class MyGA(GA):
    def selection(self, tourn_size=3):
        FitV = self.FitV
        sel_index = []
        for i in range(self.size_pop):
            aspirants_index = np.random.choice(range(self.size_pop), size=tourn_size)
            sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))
        self.Chrom = self.Chrom[sel_index, :]  # next generation
        return self.Chrom

    ranking = ranking.ranking

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2
my_ga = MyGA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, lb=[-1, -10, -5], ub=[2, 10, 2],
             precision=[1e-7, 1e-7, 1])
best_x, best_y = my_ga.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
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完整的代码如下：

# step1: define your own operator:
def selection_tournament(algorithm, tourn_size):
    FitV = algorithm.FitV
    sel_index = []
    for i in range(algorithm.size_pop):
        aspirants_index = np.random.choice(range(algorithm.size_pop), size=tourn_size)
        sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))
    algorithm.Chrom = algorithm.Chrom[sel_index, :]  # next generation
    return algorithm.Chrom

# %% step2: import package and build ga, as usual.
import numpy as np
from sko.GA import GA, GA_TSP

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2
ga = GA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, prob_mut=0.001,
        lb=[-1, -10, -5], ub=[2, 10, 2], precision=[1e-7, 1e-7, 1])

# %% step3: register your own operator
ga.register(operator_name='selection', operator=selection_tournament, tourn_size=3)
# %% Or import the operators scikit-opt already defined.
from sko.operators import ranking, selection, crossover, mutation

ga.register(operator_name='ranking', operator=ranking.ranking). \
    register(operator_name='crossover', operator=crossover.crossover_2point). \
    register(operator_name='mutation', operator=mutation.mutation)
# %% Run ga
best_x, best_y = ga.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
# %% For advanced users
class MyGA(GA):
    def selection(self, tourn_size=3):
        FitV = self.FitV
        sel_index = []
        for i in range(self.size_pop):
            aspirants_index = np.random.choice(range(self.size_pop), size=tourn_size)
            sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))
        self.Chrom = self.Chrom[sel_index, :]  # next generation
        return self.Chrom

    ranking = ranking.ranking

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2
my_ga = MyGA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, lb=[-1, -10, -5], ub=[2, 10, 2],
             precision=[1e-7, 1e-7, 1])
best_x, best_y = my_ga.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
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特性2：断点继续运行
例如，先跑10代，然后在此基础上再跑20代，可以这么写：

from sko.GA import GA

func = lambda x: x[0] ** 2
ga = GA(func=func, n_dim=1)
ga.run(10)
ga.run(20)
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特性3：4种加速方法
矢量化计算：vectorization
多线程计算：multithreading，适用于 IO 密集型目标函数
多进程计算：multiprocessing，适用于 CPU 密集型目标函数
缓存化计算：cached，适用于目标函数的每次输入有大量重复
特性4: GPU 加速
GPU加速功能还比较简单，将会在 1.0.0 版本大大完善。

import numpy as np
import torch
import time

def schaffer(p):
    '''
    This function has plenty of local minimum, with strong shocks
    global minimum at (0,0) with value 0
    '''
    x1, x2 = p
    x = np.square(x1) + np.square(x2)
    return 0.5 + (np.square(np.sin(x)) - 0.5) / np.square(1 + 0.001 * x)

import torch
from sko.GA import GA

device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")

ga = GA(func=schaffer, n_dim=2, size_pop=50, max_iter=800, lb=[-1, -1], ub=[1, 1], precision=1e-7)
ga.to(device=device)
start_time = time.time()
best_x, best_y = ga.run()
print(time.time() - start_time)
print('best_x:', best_x, '\n', 'best_y:', best_y)

ga = GA(func=schaffer, n_dim=2, size_pop=50, max_iter=800, lb=[-1, -1], ub=[1, 1], precision=1e-7)
start_time = time.time()
best_x, best_y = ga.run()
print(time.time() - start_time)
print('best_x:', best_x, '\n', 'best_y:', best_y)
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启发式算法
1. 差分进化算法
Step1：定义你的问题，这个demo定义了有约束优化问题

'''
min f(x1, x2, x3) = x1^2 + x2^2 + x3^2
s.t.
    x1*x2 >= 1
    x1*x2 <= 5
    x2 + x3 = 1
    0 <= x1, x2, x3 <= 5
'''

def obj_func(p):
    x1, x2, x3 = p
    return x1 ** 2 + x2 ** 2 + x3 ** 2

constraint_eq = [
    lambda x: 1 - x[1] - x[2]
]

constraint_ueq = [
    lambda x: 1 - x[0] * x[1],
    lambda x: x[0] * x[1] - 5
]
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Step2: 做差分进化算法

from sko.DE import DE

de = DE(func=obj_func, n_dim=3, size_pop=50, max_iter=800, lb=[0, 0, 0], ub=[5, 5, 5],
        constraint_eq=constraint_eq, constraint_ueq=constraint_ueq)

best_x, best_y = de.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
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2. 遗传算法（GA）
第一步：定义你的问题

import numpy as np

def schaffer(p):
    '''
    This function has plenty of local minimum, with strong shocks
    global minimum at (0,0) with value 0
    '''
    x1, x2 = p
    x = np.square(x1) + np.square(x2)
    return 0.5 + (np.square(np.sin(x)) - 0.5) / np.square(1 + 0.001 * x)
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第二步：运行遗传算法

from sko.GA import GA

ga = GA(func=schaffer, n_dim=2, size_pop=50, max_iter=800, prob_mut=0.001, lb=[-1, -1], ub=[1, 1], precision=1e-7)
best_x, best_y = ga.run()
print('best_x:', best_x, '\n', 'best_y:', best_y)
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第三步：用 matplotlib 画出结果

import pandas as pd
import matplotlib.pyplot as plt

Y_history = pd.DataFrame(ga.all_history_Y)
fig, ax = plt.subplots(2, 1)
ax[0].plot(Y_history.index, Y_history.values, '.', color='red')
Y_history.min(axis=1).cummin().plot(kind='line')
plt.show()
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2.2 遗传算法用于旅行商问题
GA_TSP 针对TSP问题重载了 交叉(crossover)、变异(mutation) 两个算子

第一步，定义问题
这里作为demo，随机生成距离矩阵. 实战中从真实数据源中读取。

import numpy as np
from scipy import spatial
import matplotlib.pyplot as plt

num_points = 50

points_coordinate = np.random.rand(num_points, 2)  # generate coordinate of points
distance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')

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)])
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第二步，调用遗传算法进行求解

from sko.GA import GA_TSP

ga_tsp = GA_TSP(func=cal_total_distance, n_dim=num_points, size_pop=50, max_iter=500, prob_mut=1)
best_points, best_distance = ga_tsp.run()
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第三步，画出结果：

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(best_points_coordinate[:, 0], best_points_coordinate[:, 1], 'o-r')
ax[1].plot(ga_tsp.generation_best_Y)
plt.show()
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总代码

import numpy as np
from scipy import spatial
import matplotlib.pyplot as plt

num_points = 50

points_coordinate = np.random.rand(num_points, 2)  # generate coordinate of points
distance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')

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)])

# %% do GA

from sko.GA import GA_TSP

ga_tsp = GA_TSP(func=cal_total_distance, n_dim=num_points, size_pop=50, max_iter=500, prob_mut=1)
best_points, best_distance = ga_tsp.run()

# %% plot
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(best_points_coordinate[:, 0], best_points_coordinate[:, 1], 'o-r')
ax[1].plot(ga_tsp.generation_best_Y)
plt.show()
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3. 粒子群算法（PSO, Particle swarm optimization）
3.1 粒子群算法
第一步，定义问题

def demo_func(x):
    x1, x2, x3 = x
    return x1 ** 2 + (x2 - 0.05) ** 2 + x3 ** 2
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第二步，做粒子群算法

from sko.PSO import PSO

pso = PSO(func=demo_func, n_dim=3, pop=40, max_iter=150, lb=[0, -1, 0.5], ub=[1, 1, 1], w=0.8, c1=0.5, c2=0.5)
pso.run()
print('best_x is ', pso.gbest_x, 'best_y is', pso.gbest_y)
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第三步，画出结果

import matplotlib.pyplot as plt

plt.plot(pso.gbest_y_hist)
plt.show()
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例子

import numpy as np
from sko.PSO import PSO

def demo_func(x):
    x1, x2 = x
    return -20 * np.exp(-0.2 * np.sqrt(0.5 * (x1 ** 2 + x2 ** 2))) - np.exp(
        0.5 * (np.cos(2 * np.pi * x1) + np.cos(2 * np.pi * x2))) + 20 + np.e

constraint_ueq = (
    lambda x: (x[0] - 1) ** 2 + (x[1] - 0) ** 2 - 0.5 ** 2
    ,
)

max_iter = 50
pso = PSO(func=demo_func, n_dim=2, pop=40, max_iter=max_iter, lb=[-2, -2], ub=[2, 2]
          , constraint_ueq=constraint_ueq)
pso.record_mode = True
pso.run()
print('best_x is ', pso.gbest_x, 'best_y is', pso.gbest_y)

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

record_value = pso.record_value
X_list, V_list = record_value['X'], record_value['V']

fig, ax = plt.subplots(1, 1)
ax.set_title('title', loc='center')
line = ax.plot([], [], 'b.')

X_grid, Y_grid = np.meshgrid(np.linspace(-2.0, 2.0, 40), np.linspace(-2.0, 2.0, 40))
Z_grid = demo_func((X_grid, Y_grid))
ax.contour(X_grid, Y_grid, Z_grid, 30)

ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)

t = np.linspace(0, 2 * np.pi, 40)
ax.plot(0.5 * np.cos(t) + 1, 0.5 * np.sin(t), color='r')

plt.ion()
p = plt.show()

def update_scatter(frame):
    i, j = frame // 10, frame % 10
    ax.set_title('iter = ' + str(i))
    X_tmp = X_list[i] + V_list[i] * j / 10.0
    plt.setp(line, 'xdata', X_tmp[:, 0], 'ydata', X_tmp[:, 1])
    return line

ani = FuncAnimation(fig, update_scatter, blit=True, interval=25, frames=max_iter * 10)
plt.show()

ani.save('pso.gif', writer='pillow')
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3.2 带非线性约束的粒子群算法（PSO with nonlinear constraint）
加入你的非线性约束是个圆内的面积 (x[0] - 1) ^ 2 + (x[1] - 0) ^2 - 0.5 ^2<=0
这样写代码:

constraint_ueq = (
    lambda x: (x[0] - 1) ** 2 + (x[1] - 0) ** 2 - 0.5 ** 2
    ,
)
pso = PSO(func=demo_func, n_dim=2, pop=40, max_iter=max_iter, lb=[-2, -2], ub=[2, 2]
          , constraint_ueq=constraint_ueq)
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可以有多个非线性约束，向 constraint_ueq 加就行了。

4. 模拟退火算法(SA, Simulated Annealing)
4.1 模拟退火算法用于多元函数优化
第一步：定义问题

demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + x[2] ** 2
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第二步，运行模拟退火算法

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)
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第三步，画出结果

import matplotlib.pyplot as plt
import pandas as pd

plt.plot(pd.DataFrame(sa.best_y_history).cummin(axis=0))
plt.show()
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另外，scikit-opt 还提供了三种模拟退火流派（3 types of Simulated Annealing）: Fast, Boltzmann, Cauchy.
模拟退火有三种具体形式
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)
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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)
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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)
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代码示例
1.1 Fast Simulated Annealing

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)
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1.2 Fast Simulated Annealing with bounds

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,
                 lb=[-1, 1, -1], ub=[2, 3, 4])
sa_fast.run()
print('Fast Simulated Annealing with bounds: best_x is ', sa_fast.best_x, 'best_y is ', sa_fast.best_y)
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2.1 Boltzmann Simulated Annealing

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)
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2.2 Boltzmann Simulated Annealing with bounds

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,
                           lb=-1, ub=[2, 3, 4])
sa_boltzmann.run()
print('Boltzmann Simulated Annealing with bounds: best_x is ', sa_boltzmann.best_x, 'best_y is ', sa_fast.best_y)
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3.1 Cauchy Simulated Annealing

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)
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3.2 Cauchy Simulated Annealing with bounds

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,
                     lb=[-1, 1, -1], ub=[2, 3, 4])
sa_cauchy.run()
print('Cauchy Simulated Annealing with bounds: best_x is ', sa_cauchy.best_x, 'best_y is ', sa_cauchy.best_y)
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4.2 模拟退火算法解决TSP问题（旅行商问题）
第一步，定义问题。
这里作为demo，随机生成距离矩阵. 实战中从真实数据源中读取。

import numpy as np
from scipy import spatial
import matplotlib.pyplot as plt

num_points = 50

points_coordinate = np.random.rand(num_points, 2)  # generate coordinate of points
distance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')

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)])
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第二步，调用模拟退火算法

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))
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第三步，画出结果

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()
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迭代动画

5. 蚁群算法(ACA, Ant Colony Algorithm)
5.1 蚁群算法解决TSP问题
from sko.ACA import ACA_TSP

aca = ACA_TSP(func=cal_total_distance, n_dim=num_points,
              size_pop=50, max_iter=200,
              distance_matrix=distance_matrix)

best_x, best_y = aca.run()
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总代码

import numpy as np
from scipy import spatial
import pandas as pd
import matplotlib.pyplot as plt

num_points = 25

points_coordinate = np.random.rand(num_points, 2)  # generate coordinate of points
distance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')

def cal_total_distance(routine):
    num_points, = routine.shape
    return sum([distance_matrix[routine[i % num_points], routine[(i + 1) % num_points]] for i in range(num_points)])

# %% Do ACA
from sko.ACA import ACA_TSP

aca = ACA_TSP(func=cal_total_distance, n_dim=num_points,
              size_pop=50, max_iter=200,
              distance_matrix=distance_matrix)

best_x, best_y = aca.run()

# %% Plot
fig, ax = plt.subplots(1, 2)
best_points_ = np.concatenate([best_x, [best_x[0]]])
best_points_coordinate = points_coordinate[best_points_, :]
ax[0].plot(best_points_coordinate[:, 0], best_points_coordinate[:, 1], 'o-r')
pd.DataFrame(aca.y_best_history).cummin().plot(ax=ax[1])
plt.show()
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6. 免疫优化算法
from sko.IA import IA_TSP

ia_tsp = IA_TSP(func=cal_total_distance, n_dim=num_points, size_pop=500, max_iter=800, prob_mut=0.2,
                T=0.7, alpha=0.95)
best_points, best_distance = ia_tsp.run()
print('best routine:', best_points, 'best_distance:', best_distance)
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7. 人工鱼群算法(artificial fish swarm algorithm, AFSA)
def func(x):
    x1, x2 = x
    return 1 / x1 ** 2 + x1 ** 2 + 1 / x2 ** 2 + x2 ** 2

from sko.AFSA import AFSA

afsa = AFSA(func, n_dim=2, size_pop=50, max_iter=300,
            max_try_num=100, step=0.5, visual=0.3,
            q=0.98, delta=0.5)
best_x, best_y = afsa.run()
print(best_x, best_y)
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[0.99997696 1.00000193] 4.00000000213762
————————————————
版权声明：本文为CSDN博主「Fo*(Bi)」的原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/weixin_48615832/article/details/120754522