简介： # [scikit-opt](https://github.com/guofei9987... [![PyPI](https://img.shields.io/pypi/v...](https://pypi.org/project/scik... [![release](https://img.shields.io/github...

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）

装置

pip install scikit-opt

或者间接把源代码中的 sko 文件夹下载下来放本地也调用能够

个性

个性1：UDF（用户自定义算子）

举例来说，你想出一种新的“抉择算子”，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，并且创立遗传算法实例
-> Demo code: examples/demo_ga_udf.py#s2

import numpy as npfrom sko.GA import GA, GA_TSPdemo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2ga = 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立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, mutationga.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)

当初 udf 反对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

提供一个面向对象格调的自定义算子的办法，供进阶用户应用:

-> 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.rankingdemo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2my_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)

个性2: GPU 减速

GPU减速性能还比较简单，将会在 1.0.0 版本大大欠缺。
有个 demo 曾经能够在现版本运行了: https://github.com/guofei9987/scikit-opt/blob/master/examples/demo_ga_gpu.py

个性3：断点持续运行

例如，先跑10代，而后在此基础上再跑20代，能够这么写：

from sko.GA import GAfunc = lambda x: x[0] ** 2ga = GA(func=func, n_dim=1)ga.run(10)ga.run(20)

疾速开始

1. 差分进化算法

Step1：定义你的问题，这个demo定义了有束缚优化问题
-> Demo code: examples/demo_de.py#s1

'''min f(x1, x2, x3) = x1^2 + x2^2 + x3^2s.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 ** 2constraint_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 DEde = 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 npdef 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 GAga = 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 画出后果
-> Demo code: examples/demo_ga.py#s3

import pandas as pdimport matplotlib.pyplot as pltY_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 穿插(crossover)、变异(mutation) 两个算子

第一步，定义问题。
这里作为demo，随机生成间隔矩阵. 实战中从实在数据源中读取。

-> Demo code: examples/demo_ga_tsp.py#s1

import numpy as npfrom scipy import spatialimport matplotlib.pyplot as pltnum_points = 50points_coordinate = np.random.rand(num_points, 2)  # generate coordinate of pointsdistance_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_TSPga_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，画出后果：
-> 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 带束缚的粒子群算法

第一步，定义问题
-> Demo code: examples/demo_pso.py#s1

def demo_func(x):    x1, 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 PSOpso = 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)

第三步，画出后果
-> Demo code: examples/demo_pso.py#s3

import matplotlib.pyplot as pltplt.plot(pso.gbest_y_hist)plt.show()

↑see examples/demo_pso.py

3.2 不带束缚的粒子群算法

-> 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 SAsa = 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，画出后果
-> Demo code: examples/demo_sa.py#s3

import matplotlib.pyplot as pltimport pandas as pdplt.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。（我猜你曾经无聊了，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_TSPsa_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，画出后果
-> Demo code: examples/demo_sa_tsp.py#s3

from matplotlib.ticker import FormatStrFormatterfig, 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_TSPaca = 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_TSPia_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, x2 = x    return 1 / x1 ** 2 + x1 ** 2 + 1 / x2 ** 2 + x2 ** 2from sko.AFSA import AFSAafsa = 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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