引用中提及差分进化算法在C++和Python中的实现。以下分别给出简单的C++和Python代码示例。 ### C++代码示例 ```cpp #include <iostream> #include <vector> #include <cmath> #include <cstdlib> #include <ctime> // 目标函数 double objectiveFunction(const std::vector<double>& x) { double sum = 0.0; for (double val : x) { sum += val * val; } return sum; } // 差分进化算法 std::vector<double> differentialEvolution(int dim, int popSize, int maxGenerations, double F, double CR) { std::srand(std::time(0)); // 初始化种群 std::vector<std::vector<double>> population(popSize, std::vector<double>(dim)); for (int i = 0; i < popSize; ++i) { for (int j = 0; j < dim; ++j) { population[i][j] = (double)std::rand() / RAND_MAX * 10 - 5; } } // 迭代 for (int gen = 0; gen < maxGenerations; ++gen) { for (int i = 0; i < popSize; ++i) { // 选择三个不同的个体 int r1, r2, r3; do { r1 = std::rand() % popSize; } while (r1 == i); do { r2 = std::rand() % popSize; } while (r2 == i || r2 == r1); do { r3 = std::rand() % popSize; } while (r3 == i || r3 == r1 || r3 == r2); // 变异 std::vector<double> mutant(dim); for (int j = 0; j < dim; ++j) { mutant[j] = population[r1][j] + F * (population[r2][j] - population[r3][j]); } // 交叉 std::vector<double> trial(dim); int jrand = std::rand() % dim; for (int j = 0; j < dim; ++j) { if ((double)std::rand() / RAND_MAX < CR || j == jrand) { trial[j] = mutant[j]; } else { trial[j] = population[i][j]; } } // 选择 if (objectiveFunction(trial) < objectiveFunction(population[i])) { population[i] = trial; } } } // 找到最优个体 double bestFitness = objectiveFunction(population[0]); std::vector<double> bestSolution = population[0]; for (const auto& individual : population) { double fitness = objectiveFunction(individual); if (fitness < bestFitness) { bestFitness = fitness; bestSolution = individual; } } return bestSolution; } int main() { int dim = 10; int popSize = 50; int maxGenerations = 100; double F = 0.5; double CR = 0.9; std::vector<double> bestSolution = differentialEvolution(dim, popSize, maxGenerations, F, CR); std::cout << "Best solution: "; for (double val : bestSolution) { std::cout << val << " "; } std::cout << std::endl; return 0; } ``` ### Python代码示例 ```python import numpy as np # 目标函数 def objective_function(x): return np.sum(x**2) # 差分进化算法 def differential_evolution(dim, pop_size, max_generations, F, CR): # 初始化种群 population = np.random.uniform(-5, 5, (pop_size, dim)) # 迭代 for _ in range(max_generations): for i in range(pop_size): # 选择三个不同的个体 r1, r2, r3 = np.random.choice(pop_size, 3, replace=False) while r1 == i: r1 = np.random.choice(pop_size) while r2 == i or r2 == r1: r2 = np.random.choice(pop_size) while r3 == i or r3 == r1 or r3 == r2: r3 = np.random.choice(pop_size) # 变异 mutant = population[r1] + F * (population[r2] - population[r3]) # 交叉 jrand = np.random.randint(dim) trial = np.where(np.random.rand(dim) < CR, mutant, population[i]) trial[jrand] = mutant[jrand] # 选择 if objective_function(trial) < objective_function(population[i]): population[i] = trial # 找到最优个体 fitness_values = np.array([objective_function(individual) for individual in population]) best_index = np.argmin(fitness_values) best_solution = population[best_index] return best_solution # 参数设置 dim = 10 pop_size = 50 max_generations = 100 F = 0.5 CR = 0.9 best_solution = differential_evolution(dim, pop_size, max_generations, F, CR) print("Best solution:", best_solution) ```