老师推荐的一篇知乎北大大神非常好的文章：
主要介绍的是scikit-opt
https://github.com/guofei9987/scikit-opt
主要计算：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
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 <= 0 1 2 5 x2 + x3="1" <="x1," x2, ''' def obj_func(p): x1, return x1 ** constraint_eq="[" lambda x: - x[1] x[2] ] constraint_ueq="[" x[0] * x[1], ]< code></=>
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)
第一步：定义你的问题
import numpy as np
def schaffer(p):
'''
This function has plenty of <a href="https://www.zhihu.com/search?q=local+minimum&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="local minimum">local minimum</a>, 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)
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, 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
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()
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(<a href="https://www.zhihu.com/search?q=points_coordinate&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="points_coordinate">points_coordinate</a>, 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()
(PSO, Particle swarm optimization)
第一步，定义问题
-> Demo code:examples/demo_pso.py#s1
def demo_func(x):
x1, x2, x3 = x
return x1 ** 2 + (x2 - 0.05) ** 2 + x3 ** 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, 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)
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()
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< code><br>这样写代码:<!--=0<-->
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]
, <a href="https://www.zhihu.com/search?q=constraint_ueq&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="constraint_ueq">constraint_ueq</a>=constraint_ueq)
可以有多个非线性约束，向 constraint_ueq 加就行了。
(SA, Simulated Annealing)
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, 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，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
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]]])
<a href="https://www.zhihu.com/search?q=best_points_coordinate&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="best_points_coordinate">best_points_coordinate</a> = 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_<a href="https://www.zhihu.com/search?q=major_formatter&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="major_formatter">major_formatter</a>(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
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()
(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('<a href="https://www.zhihu.com/search?q=best+routine&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="best routine">best routine</a>:', best_points, 'best_distance:', best_distance)
人工鱼群算法(artificial fish swarm algorithm, AFSA)
-> Demo code:examples/demo_afsa.py#s1
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)
举例来说，你想出一种新的”选择算子”，如下 -> Demo code:
examples/demo_ga_udf.py#s1github.com/guofei9987/scikit-opt/blob/master/examples/demo_ga_udf.py#L1
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
%% 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, 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
%% step3: register your own operator
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
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', <a href="https://www.zhihu.com/search?q=operator%3Dmutation.mutation&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="operator=mutation.mutation">operator=mutation.mutation</a>)
做遗传算法运算
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, ranking
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:
%% For advanced users
class MyGA(GA):
def selection(self, tourn_size=3):
FitV = self.FitV
sel_index = []
for i in range(self.size_pop):
<a href="https://www.zhihu.com/search?q=aspirants_index&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22article%22%2C%22sourceId%22%3A371637604%7D" title="aspirants_index">aspirants_index</a> = 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)
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)
- 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
see
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:
三、参数说明
可以使用类似 help(GA), GA? 查看详细介绍，例如：
import sko
help(sko.GA.GA)
help(sko.GA.GA_TSP)
help(sko.PSO.PSO)
help(sko.DE.DE)
help(sko.SA.SA)
help(sko.SA.SA_TSP)
help(sko.ACA.ACA_TSP)
help(sko.IA.IA_TSP)
help(sko.AFSA.AFSA)
ga.generation_best_Y每一代的最优函数值ga.generation_best_X每一代的最优函数值对应的输入值ga.all_history_FitV每一代的每个个体的适应度ga.all_history_Y每一代每个个体的函数值ga.best_y最优函数值-
*
ga.best_x最优函数值对应的输入值 -
de.generation_best_Y每一代的最优函数值 de.generation_best_X每一代的最优函数值对应的输入值de.all_history_Y每一代每个个体的函数值de.best_y最优函数值-
*
de.best_x最优函数值对应的输入值 -
pso.record_value每一代的粒子位置、粒子速度 、对应的函数值。pso.record_mode = True才开启记录 pso.gbest_y_hist历史最优函数值pso.best_y最优函数值 （迭代中使用的是pso.gbest_x,pso.gbest_y）-
*
pso.best_x最优函数值对应的输入值 -
de.generation_best_Y每一代的最优函数值 de.generation_best_X每一代的最优函数值对应的输入值sa.best_x最优函数值-
*
sa.best_y最优函数值对应的输入值 -
de.generation_best_Y每一代的最优函数值 de.generation_best_X每一代的最优函数值对应的输入值aca.best_y最优函数值-
*
aca.best_x最优函数值对应的输入值 -
afsa.best_x最优函数值 -
*
afsa.best_y最优函数值对应的输入值 -
ia.generation_best_Y每一代的最优函数值 ia.generation_best_X每一代的最优函数值对应的输入值ia.all_history_FitV每一代的每个个体的适应度ia.all_history_Y每一代每个个体的函数值ia.best_y最优函数值- *
ia.best_x最优函数值对应的输入值
Original: https://blog.csdn.net/m0_51330713/article/details/121749922
Author: AstheHollowman
Title: 七种启发式算法
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