进化算法中的基因表达式编程（Gene Expression Programming）

pythonCopy codeimport numpy as np
# 定义适应度评估函数，计算每个基因表达式树的适应度值
def evaluate_fitness(expression_tree, data):
    X = data[:, :-1]  # 输入特征
    y_true = data[:, -1]  # 真实标签
    y_pred = expression_tree.evaluate(X)  # 预测标签
    error = np.mean((y_pred - y_true) ** 2)  # 均方误差作为适应度值
    return 1 / (1 + error)  # 将误差转化为适应度值
# 定义基因表达式树的节点类
class Node:
    def __init__(self, value, left=None, right=None):
        self.value = value
        self.left = left
        self.right = right
    def evaluate(self, X):
        if self.value == '+':
            return self.left.evaluate(X) + self.right.evaluate(X)
        elif self.value == '-':
            return self.left.evaluate(X) - self.right.evaluate(X)
        elif self.value == '*':
            return self.left.evaluate(X) * self.right.evaluate(X)
        elif self.value == '/':
            return self.left.evaluate(X) / self.right.evaluate(X)
        else:
            return X[:, int(self.value)]
# 定义基因表达式树的生成和演化操作
class ExpressionTree:
    def __init__(self, max_depth):
        self.max_depth = max_depth
        self.root = None
    def generate(self, depth, terminals, functions):
        if depth < self.max_depth:
            if np.random.rand() < 0.5 and len(functions) > 0:
                value = np.random.choice(functions)
                left = self.generate(depth + 1, terminals, functions)
                right = self.generate(depth + 1, terminals, functions)
                return Node(value, left, right)
            else:
                value = np.random.choice(terminals)
                return Node(value)
        else:
            value = np.random.choice(terminals)
            return Node(value)
    def evaluate(self, X):
        return self.root.evaluate(X)
    def crossover(self, other):
        new_tree = ExpressionTree(self.max_depth)
        new_tree.root = self._crossover(self.root, other.root)
        return new_tree
    def _crossover(self, node1, node2):
        if np.random.rand() < 0.5:
            return node1
        else:
            new_node = Node(node2.value, node2.left, node2.right)
            if node2.left:
                new_node.left = self._crossover(node1, node2.left)
            if node2.right:
                new_node.right = self._crossover(node1, node2.right)
            return new_node
    def mutation(self, terminals, functions):
        self._mutation(self.root, terminals, functions)
    def _mutation(self, node, terminals, functions):
        if node.left:
            self._mutation(node.left, terminals, functions)
        if node.right:
            self._mutation(node.right, terminals, functions)
        if np.random.rand() < 0.1:  # 突变概率为0.1
            if node.left or node.right:  # 如果有子节点，则随机替换节点的值
                node.value = np.random.choice(terminals + functions)
            else:  # 如果是叶子节点，则随机生成一个新的子节点
                new_node = self.generate(0, terminals, functions)
                node.value = new_node.value
                node.left = new_node.left
                node.right = new_node.right
# 定义基因表达式编程算法
class GEP:
    def __init__(self, pop_size, max_depth, num_generations, terminals, functions, data):
        self.pop_size = pop_size
        self.max_depth = max_depth
        self.num_generations = num_generations
        self.terminals = terminals
        self.functions = functions
        self.data = data
    def run(self):
        pop = []
        for _ in range(self.pop_size):
            tree = ExpressionTree(self.max_depth)
            tree.root = tree.generate(0, self.terminals, self.functions)
            pop.append(tree)
        for gen in range(self.num_generations):
            # 计算适应度值
            fitness = [evaluate_fitness(tree, self.data) for tree in pop]
            # 选择操作
            selected_indices = np.random.choice(range(self.pop_size), size=self.pop_size, p=fitness/np.sum(fitness))
            selected_pop = [pop[i] for i in selected_indices]
            # 交叉操作
            new_pop = []
            for i in range(0, self.pop_size, 2):
                parent1 = selected_pop[i]
                parent2 = selected_pop[i+1]
                child = parent1.crossover(parent2)
                new_pop.append(child)
            # 变异操作
            for tree in new_pop:
                tree.mutation(self.terminals, self.functions)
            # 更新种群
            pop = new_pop
        # 返回最优解
        best_tree = max(pop, key=lambda tree: evaluate_fitness(tree, self.data))
        return best_tree
# 数据集
data = np.array([[1, 3, 4], [2, 5, 7], [3, 7, 10], [4, 9, 13]])
# 定义终止条件和参数
pop_size = 50
max_depth = 3
num_generations = 100
terminals = ['0', '1', '2']
functions = ['+', '-', '*', '/']
# 创建并运行基因表达式编程算法
gep = GEP(pop_size, max_depth, num_generations, terminals, functions, data)
best_tree = gep.run()
# 输出最优解的表达式
print("Best Expression Tree:")
print(best_tree.root.value)

pythonCopy codeimport cv2
# 加载图像
image = cv2.imread('image.jpg')
# 将图像转换为灰度图
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
# 对图像进行高斯模糊
blurred = cv2.GaussianBlur(gray, (5, 5), 0)
# 进行图像边缘检测
edges = cv2.Canny(blurred, 50, 150)
# 显示图像
cv2.imshow('Original Image', image)
cv2.imshow('Gray Image', gray)
cv2.imshow('Blurred Image', blurred)
cv2.imshow('Edges Image', edges)
# 等待用户按下任意按键
cv2.waitKey(0)
# 释放窗口资源
cv2.destroyAllWindows()