用粒子群优化算法对已训练好的多变量高斯过程预测算法进行优化python代码

粒子群优化算法（Particle Swarm Optimization, PSO）是一种基于群体智能的优化算法，常用于求解多维非线性优化问题。下面是使用PSO算法对已训练好的多变量高斯过程预测算法进行优化的Python代码：

import numpy as np
from scipy.optimize import minimize

# 定义多变量高斯过程预测算法
def gp_predict(X_train, y_train, X_test, kernel, noise):
    n_train = X_train.shape[0]
    n_test = X_test.shape[0]
    K_train = kernel(X_train, X_train)
    K_inv = np.linalg.inv(K_train + noise * np.eye(n_train))
    K_star = kernel(X_train, X_test)
    mean = np.dot(K_star.T, np.dot(K_inv, y_train))
    cov = kernel(X_test, X_test) - np.dot(K_star.T, np.dot(K_inv, K_star))
    return mean, cov

# 定义目标函数
def objective_func(x, X_train, y_train, X_test, kernel, noise):
    # 将x转换为多变量高斯过程预测算法所需的参数
    theta = x[:-1]
    sigma = x[-1]
    kernel = lambda X1, X2: sigma**2 * np.exp(-0.5 * np.sum(theta * (X1[:, None] - X2[None, :])**2, axis=2))
    # 计算多变量高斯过程预测算法的均方误差
    y_pred, _ = gp_predict(X_train, y_train, X_test, kernel, noise)
    mse = np.mean((y_pred - y_test)**2)
    return mse

# 定义PSO算法
def pso(objective_func, bounds, n_particles, n_iterations, X_train, y_train, X_test, kernel, noise):
    # 初始化粒子的位置和速度
    n_dims = len(bounds)
    particles_pos = np.random.uniform(bounds[:, 0], bounds[:, 1], size=(n_particles, n_dims))
    particles_vel = np.zeros_like(particles_pos)
    # 记录全局最优解的位置和适应值
    global_best_pos = None
    global_best_val = np.inf
    # 迭代优化
    for i in range(n_iterations):
        # 计算每个粒子的适应值
        particles_val = np.array([objective_func(particles_pos[j], X_train, y_train, X_test, kernel, noise) for j in range(n_particles)])
        # 更新全局最优解
        idx = np.argmin(particles_val)
        if particles_val[idx] < global_best_val:
            global_best_pos = particles_pos[idx]
            global_best_val = particles_val[idx]
        # 更新每个粒子的速度和位置
        w = 0.729
        c1 = 1.49445
        c2 = 1.49445
        rand1 = np.random.rand(n_particles, n_dims)
        rand2 = np.random.rand(n_particles, n_dims)
        particles_vel = w * particles_vel + c1 * rand1 * (particles_best_pos - particles_pos) + c2 * rand2 * (global_best_pos - particles_pos)
        particles_pos = particles_pos + particles_vel
        # 将粒子的位置限制在搜索空间内
        particles_pos = np.clip(particles_pos, bounds[:, 0], bounds[:, 1])
    # 返回全局最优解的位置和适应值
    return global_best_pos, global_best_val

# 假设已经读入了训练集X_train和y_train，以及测试集X_test和y_test
# 定义搜索空间和PSO算法的参数
bounds = np.array([(1e-4, 10)] * X_train.shape[1] + [(1e-6, 1)])
n_particles = 20
n_iterations = 50
# 调用PSO算法进行优化
theta, sigma = pso(objective_func, bounds, n_particles, n_iterations, X_train, y_train, X_test, kernel, noise)
# 根据优化结果重新定义多变量高斯过程预测算法
kernel = lambda X1, X2: sigma**2 * np.exp(-0.5 * np.sum(theta * (X1[:, None] - X2[None, :])**2, axis=2))
# 计算优化后的多变量高斯过程预测算法的均方误差
y_pred, _ = gp_predict(X_train, y_train, X_test, kernel, noise)
mse = np.mean((y_pred - y_test)**2)
print('优化后的均方误差：', mse)