C++实现蝴蝶优化的算法

以下是一个简单的C++代码实现蝴蝶优化算法：

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>

using namespace std;

// 目标函数
double func(vector<double> x) {
    double sum = 0.0;
    for (int i = 0; i < x.size(); i++) {
        sum += x[i] * x[i];
    }
    return sum;
}

// 随机生成一个解
vector<double> generate_solution(int dim, double lb, double ub) {
    vector<double> x(dim);
    for (int i = 0; i < dim; i++) {
        x[i] = lb + (ub - lb) * rand() / RAND_MAX;
    }
    return x;
}

// 蝴蝶优化算法
vector<double> butterfly_optimization(int dim, int num, int iterations, double lb, double ub) {
    vector<double> best_position(dim);
    double best_fitness = INFINITY;
    vector<vector<double>> positions(num, vector<double>(dim));
    vector<double> fitness(num);
    for (int i = 0; i < num; i++) {
        positions[i] = generate_solution(dim, lb, ub);
        fitness[i] = func(positions[i]);
        if (fitness[i] < best_fitness) {
            best_fitness = fitness[i];
            best_position = positions[i];
        }
    }
    for (int it = 0; it < iterations; it++) {
        for (int i = 0; i < num; i++) {
            int a = rand() % num;
            while (a == i) {
                a = rand() % num;
            }
            int b = rand() % num;
            while (b == i || b == a) {
                b = rand() % num;
            }
            int c = rand() % num;
            while (c == i || c == a || c == b) {
                c = rand() % num;
            }
            double r1 = rand() * 1.0 / RAND_MAX;
            double r2 = rand() * 1.0 / RAND_MAX;
            double r3 = rand() * 1.0 / RAND_MAX;
            vector<double> x(dim);
            for (int j = 0; j < dim; j++) {
                x[j] = positions[i][j] + r1 * (best_position[j] - r2 * positions[a][j] - r3 * positions[b][j]);
                x[j] = max(x[j], lb);
                x[j] = min(x[j], ub);
            }
            double f = func(x);
            if (f < fitness[i]) {
                positions[i] = x;
                fitness[i] = f;
                if (f < best_fitness) {
                    best_fitness = f;
                    best_position = x;
                }
            }
        }
    }
    return best_position;
}

int main() {
    int dim = 10;
    int num = 20;
    int iterations = 100;
    double lb = -5.12;
    double ub = 5.12;
    vector<double> best_position = butterfly_optimization(dim, num, iterations, lb, ub);
    double best_fitness = func(best_position);
    cout << "Best Fitness: " << best_fitness << endl;
    cout << "Best Position: ";
    for (int i = 0; i < dim; i++) {
        cout << best_position[i] << " ";
    }
    cout << endl;
    return 0;
}

其中，`dim`是目标函数的维度，`num`是蝴蝶的数量，`iterations`是迭代次数，`lb`和`ub`是变量范围。在函数`func`中定义了目标函数，函数`generate_solution`用于随机生成一个解，算法的主体部分在函数`butterfly_optimization`中实现。在每次迭代中，对于每个蝴蝶，随机选择三个不同的蝴蝶，并按照公式更新位置。最后返回最优解。