鲁达 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: example
# step1: define your own operator: def selection_tournament(algorithm, tourn_size): FitV = algori sel_index = [] for i in range): aspirants_index = np.random.choice(range), size=tourn_size) (max(aspirants_index, key=lambda i: FitV[i])) algori = algori[sel_index, :] # next generation return algori 导入包，并且创建遗传算法实例
-> Demo code: example
import numpy as np from 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: example
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: example
from import ranking, selection, crossover, mutation ga.register(operator_name='ranking', operator=ranking.ranking). \ register(operator_name='crossover', operator=cro). \ register(operator_name='mutation', operator=mu)做遗传算法运算
-> Demo code: example
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
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: example
class MyGA(GA): def selection(self, tourn_size=3): FitV = sel_index = [] for i in range): aspirants_index = np.random.choice(range), size=tourn_size) (max(aspirants_index, key=lambda i: FitV[i])) = [sel_index, :] # next generation return 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
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 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: example
''' 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: example
from 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: example
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 + (x) - 0.5) / np.square(1 + 0.001 * x) 第二步：运行遗传算法
-> Demo code: example
from 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: example
import pandas as pd import ma as plt Y_history = ) fig, ax = (2, 1) ax[0].plo, Y_, '.', color='red') Y_(axis=1).cummin().plot(kind='line') () 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: example
import numpy as np from scipy import spatial import ma as plt num_points = 50 points_coordinate = np.random.rand(num_points, 2) # generate coordinate of points distance_matrix = (points_coordinate, points_coordinate, metric='euclidean') def cal_total_distance(routine): '''The objective function. input routine, return total distance. cal_total_distance(num_points)) ''' num_points, = rou 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: example
from 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_() 第三步，画出结果：
-> Demo code: example
fig, ax = (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].plo) () 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: example
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: example
from 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) () print('best_x is ', , 'best_y is', ) 第三步，画出结果
-> Demo code: example
import ma as plt (_hist) ()
↑see example
3.2 不带约束的粒子群算法
-> Demo code: example#s4
pso = PSO(func=demo_func, dim=3) fitness = () print('best_x is ', , 'best_y is', )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: example
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: example
from 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 = () print('best_x:', best_x, 'best_y', best_y) 第三步，画出结果
-> Demo code: example
import ma as plt import pandas as pd ().cummin(axis=0)) () 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: example
from 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_() print(best_points, best_distance, cal_total_distance(best_points))第三步，画出结果
-> Demo code: example
from ma import FormatStrFormatter fig, ax = (1, 2) best_points_ = np.concatenate([best_points, [best_points[0]]]) best_points_coordinate = points_coordinate[best_points_, :] ax[0].plo) 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") () 咱还有个动画
↑参考代码 example
5. 蚁群算法
蚁群算法(ACA, Ant Colony Algorithm)解决TSP问题
-> Demo code: example
from 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: example
from 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_() 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: example
def func(x): x1, x2 = x return 1 / x1 ** 2 + x1 ** 2 + 1 / x2 ** 2 + x2 ** 2 from 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 = af() print(best_x, best_y)本文为阿里云原创内容，未经允许不得转载。