python实现CMA-ES的代码

CMA-ES是一种优化算法，用于解决高维度的非线性优化问题。下面是一个使用Python实现CMA-ES的示例代码：

import numpy as np
from scipy.spatial.distance import cdist

class CMAES:
    def __init__(self, func, dim, pop_size=10, sigma=0.1):
        self.func = func
        self.dim = dim
        self.pop_size = pop_size
        self.sigma = sigma
        self.mean = np.random.uniform(-5, 5, dim)
        self.cov = np.identity(dim)
        self.weights = np.log((pop_size + 1) / 2) - np.log(np.arange(1, pop_size + 1))
        self.mu = pop_size // 2
        self.mu_eff = np.sum(self.weights[:self.mu]) ** 2 / np.sum(self.weights[:self.mu] ** 2)
        self.c_sigma = (self.mu_eff + 2) / (dim + self.mu_eff + 5)
        self.d_sigma = 1 + 2 * max(0, np.sqrt((self.mu_eff - 1) / (dim + 1)) - 1) + self.c_sigma
        self.pc = np.zeros(dim)
        self.ps = np.zeros(dim)
        self.B = np.identity(dim)
        self.D = np.ones(dim)
        self.C = np.identity(dim)
        self.eigeneval = 0
        self.chi_n = np.sqrt(dim) * (1 - 1 / (4 * dim) + 1 / (21 * dim ** 2))

    def ask(self):
        self.pop = self.mean + self.sigma * np.dot(np.random.normal(size=(self.pop_size, self.dim)), self.B @ np.diag(self.D))
        return self.pop

    def tell(self, fitvals):
        idx = np.argsort(fitvals)
        self.pop = self.pop[idx]
        self.fitvals = fitvals[idx]
        self.mean_prev = self.mean.copy()
        self.mean = np.dot(self.weights, self.pop[:self.mu])
        self.pc = (1 - self.c_sigma) * self.pc + np.sqrt(self.c_sigma * (2 - self.c_sigma) * self.mu_eff) * np.dot(self.B, (self.mean - self.mean_prev) / self.sigma)
        w = np.sqrt(self.weights[:self.mu])[:, None]
        y = self.pop[:self.mu] - self.mean_prev
        self.ps = (1 - self.c_sigma) * self.ps + np.sqrt(self.c_sigma * (2 - self.c_sigma) * self.mu_eff) * np.dot(self.B, np.dot(np.diag(self.D), y.T) * w.ravel()[:, None])
        hsig = np.linalg.norm(self.ps) / np.sqrt(1 - (1 - self.c_sigma) ** (2 * (self.eigeneval + 1))) / self.chi_n < 1.4 + 2 / (self.dim + 1)
        self.C = (1 - self.c_sigma - self.d_sigma) * self.C + self.c_sigma * np.dot(self.pc[:, None], self.pc[None, :]) + self.d_sigma * np.dot(np.dot(self.B, np.diag(self.D ** 2)), self.B.T)
        self.D, self.B = np.linalg.eig(self.C)
        self.eigeneval += 1
        self.D = np.sqrt(self.D)
        if hsig:
            self.sigma *= np.exp(self.c_sigma / self.d_sigma * (np.linalg.norm(self.ps) / self.chi_n - 1))
        if self.eigeneval % self.dim ** 2 // self.mu / 10:
            self.C = np.triu(self.C) + np.triu(self.C, 1).T
            self.D, self.B = np.linalg.eig(self.C)
            self.D = np.sqrt(self.D)
        return self.mean

    def run(self, max_evaluations=10000):
        evaluations = 0
        while evaluations < max_evaluations:
            pop = self.ask()
            fitvals = np.array([self.func(x) for x in pop])
            self.tell(fitvals)
            evaluations += self.pop_size
        return self.mean

在上面的代码中，`func`是需要优化的目标函数，`dim`是变量的维度，`pop_size`是种群大小，`sigma`是初始的标准差。`ask`方法用于生成新的种群，`tell`方法用于更新种群的参数并返回新的种群的均值。`run`方法用于运行优化算法并返回最终的结果。