使用遗传算法求解函数具有最大值的点X

"""
Visualize Genetic Algorithm to find a maximum point in a function.
"""
import numpy as np
import matplotlib.pyplot as pltDNA_SIZE = 10  # DNA length
POP_SIZE = 100  # population size
CROSS_RATE = 0.8  # mating probability (DNA crossover)
MUTATION_RATE = 0.003  # mutation probability
N_GENERATIONS = 200  # stop evolution rule
X_BOUND = [0, 5]  # x upper and lower bounds# to find the maximum of this function
def F(x):return np.sin(10 * x) * x + np.cos(2 * x) * x# 适应性函数（一个值域非负、与Ｆ有相同极值点的函数）
def get_fitness(pred):return pred + 1e-3 - np.min(pred)# 选择算子（适者生存，不适者遭淘汰）
def select(pop, fitness):idx = np.random.choice(np.arange(POP_SIZE), size=POP_SIZE, replace=True, p=fitness / fitness.sum())  # 比例选择规则（另外可用“模拟退火算子”）return pop[idx]# 杂交算子（促进进化的主要手段）
def crossover(parent, pop):if np.random.rand() < CROSS_RATE:  # 多点杂交（另外还有“单点杂交”、“两点杂交”、“均匀杂交”）i_ = np.random.randint(0, POP_SIZE, size=1)  # select another individual from popcross_points = np.random.randint(0, 2, size=DNA_SIZE).astype(np.bool)  # choose crossover pointsparent[cross_points] = pop[i_, cross_points]  # mating and produce one childreturn parent# 变异算子（使算法达到局部极值时有逃离局部极值“陷阱”的可能性）
def mutate(child):for point in range(DNA_SIZE):if np.random.rand() < MUTATION_RATE:child[point] = 1 if child[point] == 0 else 0return child# 将二进制的DNA转换为实数并且标准化到[0, 5]
def translateDNA(pop):return pop.dot(2 ** np.arange(DNA_SIZE)[::-1]) / float(2 ** DNA_SIZE - 1) * X_BOUND[1]
# np.arange(5)[::-1] 逆序：[4 3 2 1 0]
# 2 ** np.arange(5)[::-1]  幂次：[16  8  4  2  1]
# pop.dot(2 ** np.arange(5)[::-1])  进制转换：二进制DNA转换为十进制数
# float(2 ** DNA_SIZE - 1) 最大十进制数：31=[16+8+4+2+1]
# pop.dot(2 ** np.arange(DNA_SIZE)[::-1]) / float(2 ** DNA_SIZE - 1) * X_BOUND[1]  将X范围缩放到：[0, 5]pop = np.random.randint(2, size=(POP_SIZE, DNA_SIZE))  # 初始化DNA
# [[1 0 1 1 0 0]
#  [0 1 1 1 0 0]
#  [1 0 0 1 1 1]]
plt.ion()  # something about plotting
x = np.linspace(*X_BOUND, 200)
plt.plot(x, F(x))for _ in range(N_GENERATIONS):F_values = F(translateDNA(pop))  # compute function value by extracting DNA# something about plottingif 'sca' in globals(): sca.remove()sca = plt.scatter(translateDNA(pop), F_values, s=200, lw=0, c='red', alpha=0.5);plt.pause(0.05)# GA part (evolution)fitness = get_fitness(F_values)print("Most fitted DNA: ", pop[np.argmax(fitness), :])pop = select(pop, fitness)pop_copy = pop.copy()for parent in pop:child = crossover(parent, pop_copy)child = mutate(child)parent[:] = child  # 自然选择（另外还有“父子混合选择”策略）print("the X: ", translateDNA(pop[np.argmax(fitness), :]))  # 具有最高点的X值plt.ioff();
plt.show()