简介： # [scikit-opt](https://github.com/guofei9987/scikit-opt) [](https://pypi.org/project/scikit-opt/) [
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）
安装
pip install scikit-opt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: examples/demo_ga_udf.py#s1
-
# 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
-
导入包，并且创建遗传算法实例
-> Demo code: examples/demo_ga_udf.py#s2
-
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])
把你的算子注册到你创建好的遗传算法实例上
-> Demo code: examples/demo_ga_udf.py#s3
ga.register(operator_name='selection', operator=selection_tournament, tourn_size=3)scikit-opt 也提供了十几个算子供你调用
-> Demo code: examples/demo_ga_udf.py#s4
-
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)
做遗传算法运算
-> Demo code: examples/demo_ga_udf.py#s5
-
best_x, best_y = ga.run()
-
print(
'best_x:', best_x,
'\n',
'best_y:', best_y)
现在 udf 支持遗传算法的这几个算子：
crossover,mutation,selection,rankingScikit-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: examples/demo_ga_udf.py#s6
-
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)
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: https://github.com/guofei9987/scikit-opt/blob/master/examples/demo_ga_gpu.py
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)
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: examples/demo_de.py#s1
-
'''
-
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
-
]
Step2: 做差分进化算法
-> Demo code: examples/demo_de.py#s2
-
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)
2. 遗传算法
第一步：定义你的问题
-> Demo code: examples/demo_ga.py#s1
-
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)
-
第二步：运行遗传算法
-> Demo code: examples/demo_ga.py#s2
-
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)
第三步：用 matplotlib 画出结果
-> Demo code: examples/demo_ga.py#s3
-
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()
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: examples/demo_ga_tsp.py#s1
-
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)])
-
第二步，调用遗传算法进行求解
-> Demo code: examples/demo_ga_tsp.py#s2
-
-
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
()
第三步，画出结果：
-> Demo code: examples/demo_ga_tsp.py#s3
-
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()
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: examples/demo_pso.py#s1
-
def demo_func(x):
-
x1, x
2, x
3 = x
-
return x
1 **
2 + (x
2 -
0.
05) **
2 + x
3 **
2
-
第二步，做粒子群算法
-> Demo code: examples/demo_pso.py#s2
-
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, c
1=
0.
5, c
2=
0.
5)
-
pso.run()
-
print('best_x is ', pso.gbest_x, 'best_y is', pso.gbest_y)
第三步，画出结果
-> Demo code: examples/demo_pso.py#s3
-
import
matplotlib
.pyplot
as
plt
-
-
plt
.plot(
pso
.gbest_y_hist)
-
plt
.show()
↑see examples/demo_pso.py
3.2 不带约束的粒子群算法
-> Demo code: examples/demo_pso.py#s4
-
pso =
PSO(
func=demo_func, dim=3)
-
fitness =
pso.
run
()
-
print('best_x
is ', pso.gbest_x, 'best_y
is', pso.gbest_y)
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: examples/demo_sa.py#s1
demo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + x[2] ** 2
第二步，运行模拟退火算法
-> Demo code: examples/demo_sa.py#s2
-
from sko.SA import SA
-
-
sa = SA(func=demo_func, x
0=[
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，画出结果
-> Demo code: examples/demo_sa.py#s3
-
import matplotlib.pyplot
as plt
-
import pandas
as pd
-
-
plt.plot(pd.
DataFrame(sa.best_y_history).cummin(axis=
0))
-
plt.show()
另外，scikit-opt 还提供了三种模拟退火流派: Fast, Boltzmann, Cauchy. 更多参见 more sa
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: examples/demo_sa_tsp.py#s2
-
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，画出结果
-> Demo code: examples/demo_sa_tsp.py#s3
-
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()
咱还有个动画 
↑参考代码 examples/demo_sa_tsp.py
5. 蚁群算法
蚁群算法(ACA, Ant Colony Algorithm)解决TSP问题
-> Demo code: examples/demo_aca_tsp.py#s2
-
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
()
6. 免疫优化算法
(immune algorithm, IA)
-> Demo code: examples/demo_ia.py#s2
-
-
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)
7. 人工鱼群算法
人工鱼群算法(artificial fish swarm algorithm, AFSA)
-> Demo code: examples/demo_afsa.py#s1
-
def func(x):
-
x1, x
2 = x
-
return
1 / x
1 **
2 + x
1 **
2 +
1 / x
2 **
2 + x
2 **
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)
原文链接
本文为阿里云原创内容，未经允许不得转载。
转载：https://blog.csdn.net/yunqiinsight/article/details/108144993