一个封装了7种启发式算法的 Python 代码库（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）

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安装

pip install scikit-opt

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或者直接把源代码中的 sko 文件夹下载下来放本地也调用可以

特性

特性1：UDF（用户自定义算子）

举例来说，你想出一种新的“选择算子”，如下 -> Demo code:

step1: define your own operator: def selection_tournament(algorithm, tourn_size):

FitV = algorithm.FitVsel_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 -> Demo code:

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, 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 -> Demo code:

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 -> Demo code:

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

-> Demo code:

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，参考这里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:

-> Demo code:

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: 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。有个 demo 已经可以在现版本运行了:

特性3：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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快速开始

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 -> Demo code:

'''
min f(x1, x2, x3) = x1^2 + x2^2 + x3^2
s.t.
x1x2 >= 1
x1x2 <= 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 -> Demo code:

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

第一步：定义你的问题 -> Demo code:

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.sin(x) - 0.5) / np.square(1 + 0.001 * x)

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第二步：运行遗传算法 -> Demo code:

from sko.GA import GA

ga = GA(func=schaffer, n_dim=2, size_pop=50, max_iter=800, 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 -> Demo code:

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。

-> Demo code:

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 -> Demo code:

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： -> Demo code:

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 带约束的粒子群算法

第一步，定义问题 -> Demo code:

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 -> Demo code:

from sko.PSO import PSO

pso = PSO(func=demo_func, 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 -> Demo code:

import matplotlib.pyplot as plt

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

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3.2 不带约束的粒子群算法

-> Demo code:

pso = PSO(func=demo_func, dim=3)
fitness = pso.run()
print('best_x is ', pso.gbest_x, 'best_y is', pso.gbest_y)

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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 code:

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 -> Demo code:

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 -> Demo code:

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: Fast, Boltzmann, Cauchy.

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。（我猜你已经无聊了，所以不黏贴这一步了）

第二步，调用模拟退火算法 -> Demo code:

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 -> Demo code:

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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咱还有个动画

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5. 蚁群算法

蚁群算法(ACA, Ant Colony Algorithm)解决TSP问题

-> Demo code:

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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6. 免疫优化算法

(immune algorithm, IA) -> Demo code:

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

人工鱼群算法(artificial fish swarm algorithm, AFSA)

-> Demo code:

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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