用人工免疫算法计算f(x,y)=(a-x)^2+b(y-x^2)^2最优解的Python代码

以下是使用人工免疫算法计算f(x,y)=(a-x)^2 b(y-x^2)^2最优解的Python代码：

import random
import math

# 目标函数
def f(x, y, a, b):
    return (a - x) ** 2 + b * (y - x ** 2) ** 2

# 人工免疫算法
def AIS(a, b, n, m, l_bound, u_bound, max_iter, p_mutation):
    # 初始化抗体群体
    antibodies = []
    for i in range(n):
        x = random.uniform(l_bound, u_bound)
        y = random.uniform(l_bound, u_bound)
        antibodies.append((x, y))

    # 开始迭代
    for iter in range(max_iter):
        # 计算抗体和克隆抗体的适应值
        fitnesses = []
        for antibody in antibodies:
            fitness = f(antibody[0], antibody[1], a, b)
            fitnesses.append(fitness)
        clone_size = [math.floor(m / (1 + fitness)) for fitness in fitnesses]

        # 克隆操作
        clones = []
        for i in range(n):
            for j in range(clone_size[i]):
                clones.append(antibodies[i])

        # 变异操作
        for i in range(len(clones)):
            if random.random() < p_mutation:
                clones[i] = (clones[i][0] + random.uniform(-1, 1) * l_bound,
                             clones[i][1] + random.uniform(-1, 1) * l_bound)

        # 选择操作
        antibodies = []
        fitnesses = []
        for clone in clones:
            if clone[0] > u_bound or clone[0] < l_bound or clone[1] > u_bound or clone[1] <l_bound:
                continue
            fitness = f(clone[0], clone[1], a, b)
            antibodies.append(clone)
            fitnesses.append(fitness)
        if len(antibodies) < n:
            for i in range(n - len(antibodies)):
                x = random.uniform(l_bound, u_bound)
                y = random.uniform(l_bound, u_bound)
                antibodies.append((x, y))
                fitnesses.append(f(x, y, a, b))

        # 输出当前迭代的最优解
        best_fitness = min(fitnesses)
        best_antibody = antibodies[fitnesses.index(best_fitness)]
        print('Iteration {}: f(x,y) = {}'.format(iter+1, best_fitness))

    # 返回最优解
    return best_antibody[0], best_antibody[1]

# 运行示例
a = 1
b = 100
n = 50
m = 10
l_bound = -10
u_bound = 10
max_iter = 100
p_mutation = 0.1
x, y = AIS(a, b, n, m, l_bound, u_bound, max_iter, p_mutation)
print('最优解：x = {}, y = {}, f(x,y) = {}'.format(x, y, f(x, y, a, b)))