写一段基于遗传算法进行波束赋形的代码

以下是一个示例遗传算法进行波束赋形的代码：

import numpy as np

# 定义目标函数，即波束方向图
def objective_function(theta, a):
    N = len(theta)
    a_theta = np.zeros(N, dtype=complex)
    for i in range(N):
        a_theta[i] = np.exp(1j*np.pi*np.sin(theta[i]))
    return np.abs(np.dot(a, a_theta))

# 定义遗传算法参数
POP_SIZE = 50
GENE_SIZE = 20
CROSS_RATE = 0.8
MUTATION_RATE = 0.01
N_GENERATIONS = 500

# 初始化种群
pop = np.random.randint(2, size=(POP_SIZE, GENE_SIZE))

# 定义交叉函数
def crossover(parent, pop):
    if np.random.rand() < CROSS_RATE:
        i_ = np.random.randint(0, POP_SIZE, size=1)
        cross_points = np.random.randint(0, 2, size=GENE_SIZE).astype(np.bool)
        parent[cross_points] = pop[i_, cross_points]
    return parent

# 定义变异函数
def mutation(child):
    for point in range(GENE_SIZE):
        if np.random.rand() < MUTATION_RATE:
            child[point] = 1 if child[point] == 0 else 0
    return child

# 开始迭代
for generation in range(N_GENERATIONS):
    # 计算适应度
    fitness = np.zeros(POP_SIZE)
    for i in range(POP_SIZE):
        theta = np.linspace(-np.pi/2, np.pi/2, GENE_SIZE)[pop[i]==1]
        fitness[i] = objective_function(theta, a)
    # 选择
    fitness = (fitness - np.min(fitness)) / (np.max(fitness) - np.min(fitness))
    idx = np.random.choice(range(POP_SIZE), size=POP_SIZE, replace=True, p=fitness)
    pop = pop[idx]
    # 繁殖
    for i in range(POP_SIZE // 2):
        parent1, parent2 = pop[i], pop[POP_SIZE-i-1]
        child1 = crossover(parent1.copy(), parent2.copy())
        child2 = crossover(parent2.copy(), parent1.copy())
        child1 = mutation(child1)
        child2 = mutation(child2)
        pop[i] = child1
        pop[POP_SIZE-i-1] = child2

# 输出结果
theta = np.linspace(-np.pi/2, np.pi/2, GENE_SIZE)[pop[np.argmax(fitness)]==1]
print("Optimal theta:", theta)

其中，`objective_function` 函数用于计算波束方向图的适应度，`crossover` 函数用于交叉操作，`mutation` 函数用于变异操作。在主函数中，首先初始化种群，然后迭代进行选择、交叉、变异等操作，最终得到最优解。