粒子群算法二元线性回归优化系数和预测的代码

以下是使用粒子群算法进行二元线性回归优化系数和预测的 Python 代码示例：

import random

# 训练数据
x = [1, 2, 3, 4, 5]
y = [3, 5, 7, 9, 11]

# 定义适应度函数
def fitness(a, b):
    fitness_value = 0
    for i in range(len(x)):
        fitness_value += (y[i] - (a * x[i] + b)) ** 2
    return fitness_value

# 粒子群算法参数
particle_num = 30
max_iter = 100
w = 0.8
c1 = 2
c2 = 2

# 初始化粒子
particles = []
for i in range(particle_num):
    a = random.uniform(-10, 10)
    b = random.uniform(-10, 10)
    particles.append({'a': a, 'b': b, 'v_a': 0, 'v_b': 0, 'pbest': {'a': a, 'b': b}, 'fitness': fitness(a, b)})

# 迭代寻优
gbest = {'a': 0, 'b': 0, 'fitness': float('inf')}
for i in range(max_iter):
    for j in range(particle_num):
        # 更新速度
        particles[j]['v_a'] = w * particles[j]['v_a'] + c1 * random.random() * (particles[j]['pbest']['a'] - particles[j]['a']) + c2 * random.random() * (gbest['a'] - particles[j]['a'])
        particles[j]['v_b'] = w * particles[j]['v_b'] + c1 * random.random() * (particles[j]['pbest']['b'] - particles[j]['b']) + c2 * random.random() * (gbest['b'] - particles[j]['b'])
        # 更新位置
        particles[j]['a'] += particles[j]['v_a']
        particles[j]['b'] += particles[j]['v_b']
        # 更新个体最优解
        particles[j]['fitness'] = fitness(particles[j]['a'], particles[j]['b'])
        if particles[j]['fitness'] < particles[j]['pbest']['fitness']:
            particles[j]['pbest']['a'] = particles[j]['a']
            particles[j]['pbest']['b'] = particles[j]['b']
            particles[j]['pbest']['fitness'] = particles[j]['fitness']
        # 更新全局最优解
        if particles[j]['fitness'] < gbest['fitness']:
            gbest['a'] = particles[j]['a']
            gbest['b'] = particles[j]['b']
            gbest['fitness'] = particles[j]['fitness']

# 预测结果
predict_x = 6
predict_y = gbest['a'] * predict_x + gbest['b']
print('预测结果：', predict_y)

在上述代码中，我们定义了适应度函数 `fitness(a, b)` 来评估每个粒子的适应度，根据粒子的适应度来更新个体最优解和全局最优解。在迭代寻优结束后，根据得到的最优解来预测结果。