rbf 遗传算法代码

由于RBF（径向基函数）网络的训练需要遗传算法来优化权值和偏置，因此以下是一个简单的RBF网络遗传算法的Python代码示例：

import numpy as np
import random

# 初始化参数
num_inputs = 2
num_hidden = 4
num_outputs = 1
population_size = 20
num_generations = 100
mutation_rate = 0.1
crossover_rate = 0.8

# 定义RBF网络类
class RBFNetwork:
    def __init__(self, num_inputs, num_hidden, num_outputs):
        self.num_inputs = num_inputs
        self.num_hidden = num_hidden
        self.num_outputs = num_outputs
        self.hidden_weights = np.random.rand(num_inputs, num_hidden)
        self.hidden_biases = np.random.rand(num_hidden)
        self.output_weights = np.random.rand(num_hidden, num_outputs)
        self.output_biases = np.random.rand(num_outputs)

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def forward(self, inputs):
        hidden_inputs = np.dot(inputs, self.hidden_weights) + self.hidden_biases
        hidden_outputs = self.sigmoid(hidden_inputs)
        output_inputs = np.dot(hidden_outputs, self.output_weights) + self.output_biases
        output = self.sigmoid(output_inputs)
        return output

# 定义遗传算法类
class GeneticAlgorithm:
    def __init__(self, population_size, num_genes):
        self.population_size = population_size
        self.num_genes = num_genes
        self.population = np.random.rand(population_size, num_genes)

    def fitness(self, individual):
        # 转换为网络的参数
        hidden_weights = individual[:num_inputs*num_hidden].reshape(num_inputs, num_hidden)
        hidden_biases = individual[num_inputs*num_hidden:num_inputs*num_hidden+num_hidden]
        output_weights = individual[num_inputs*num_hidden+num_hidden:num_inputs*num_hidden+num_hidden+num_hidden*num_outputs].reshape(num_hidden, num_outputs)
        output_biases = individual[-num_outputs:]

        # 初始化RBF网络
        network = RBFNetwork(num_inputs, num_hidden, num_outputs)
        network.hidden_weights = hidden_weights
        network.hidden_biases = hidden_biases
        network.output_weights = output_weights
        network.output_biases = output_biases

        # 计算损失函数（MSE）
        inputs = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
        targets = np.array([[0], [1], [1], [0]])
        outputs = np.array([network.forward(input) for input in inputs])
        loss = np.mean((outputs - targets) ** 2)

        # 计算适应度（倒数）
        fitness = 1 / (loss + 1e-6)
        return fitness

    def selection(self, fitnesses):
        # 选择2个最优个体
        indices = np.argsort(fitnesses)[::-1][:2]
        parents = self.population[indices]
        return parents

    def crossover(self, parents):
        # 单点交叉
        child = np.zeros(self.num_genes)
        if random.random() < crossover_rate:
            crossover_point = random.randint(1, self.num_genes-1)
            child[:crossover_point] = parents[0][:crossover_point]
            child[crossover_point:] = parents[1][crossover_point:]
        else:
            child = parents[0]
        return child

    def mutation(self, child):
        # 随机突变
        for i in range(self.num_genes):
            if random.random() < mutation_rate:
                child[i] += np.random.randn() * 0.1
        return child

    def evolve(self):
        fitnesses = np.array([self.fitness(individual) for individual in self.population])
        parents = self.selection(fitnesses)
        children = [self.crossover(parents) for _ in range(self.population_size-2)]
        children = [self.mutation(child) for child in children]
        self.population = np.vstack((parents, children))

# 初始化遗传算法
ga = GeneticAlgorithm(population_size, num_inputs*num_hidden+num_hidden+num_hidden*num_outputs+num_outputs)

# 训练网络
for _ in range(num_generations):
    ga.evolve()
best_individual = ga.population[np.argmax([ga.fitness(individual) for individual in ga.population])]

# 输出结果
hidden_weights = best_individual[:num_inputs*num_hidden].reshape(num_inputs, num_hidden)
hidden_biases = best_individual[num_inputs*num_hidden:num_inputs*num_hidden+num_hidden]
output_weights = best_individual[num_inputs*num_hidden+num_hidden:num_inputs*num_hidden+num_hidden+num_hidden*num_outputs].reshape(num_hidden, num_outputs)
output_biases = best_individual[-num_outputs:]
network = RBFNetwork(num_inputs, num_hidden, num_outputs)
network.hidden_weights = hidden_weights
network.hidden_biases = hidden_biases
network.output_weights = output_weights
network.output_biases = output_biases
inputs = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
outputs = np.array([network.forward(input) for input in inputs])
print(outputs)

请注意，上述代码中的RBF网络只使用了1个隐藏层和1个输出层。如果需要更复杂的网络，可以增加隐藏层和输出层的数量，并相应地调整遗传算法的参数。此外，为了简化代码，此示例并未使用优化算法（如梯度下降）来训练RBF网络，而是直接计算损失函数和适应度。在实际应用中，建议使用更高级的优化算法来训练网络。