用ｃ＋＋写一个用差分进化算法拟合分段连续线性函数的示例

好的，以下是一个简单的用差分进化算法拟合分段连续线性函数的示例（仅供参考）：

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

using namespace std;

// 定义函数类型为分段连续线性函数
typedef double (*piecewise_linear_function)(double, const vector<double>&);

double piecewise_linear(double x, const vector<double>& params) {
    double result = 0.0;
    int n = params.size();
    for (int i = 0; i < n; i += 3) {
        if (x <= params[i]) {
            result += params[i+1];
            break;
        }
        else if (i+3 == n) {
            result += params[i+2];
            break;
        }
        else {
            double slope = (params[i+2] - params[i+1]) / (params[i+3] - params[i]);
            result += slope * (x - params[i]) + params[i+1];
        }
    }
    return result;
}

// 定义差分进化算法的参数结构体
struct DE_params {
    int pop_size;  // 种群大小
    int max_gen;   // 最大迭代次数
    double F;      // 缩放因子
    double CR;     // 交叉概率
};

// 差分进化算法
vector<double> differential_evolution(piecewise_linear_function f, const vector<double>& x_lower, const vector<double>& x_upper, const DE_params& params) {
    int n = x_lower.size();
    vector<vector<double>> population(params.pop_size, vector<double>(n));
    vector<double> fitness(params.pop_size);
    vector<double> best_individual(n);
    double best_fitness = numeric_limits<double>::max();
    mt19937 rng(random_device{}());
    uniform_real_distribution<double> uni(0, 1);

    // 初始化种群
    for (int i = 0; i < params.pop_size; ++i) {
        for (int j = 0; j < n; ++j) {
            population[i][j] = x_lower[j] + uni(rng) * (x_upper[j] - x_lower[j]);
        }
        fitness[i] = f(population[i][0], population[i]);
        if (fitness[i] < best_fitness) {
            best_individual = population[i];
            best_fitness = fitness[i];
        }
    }

    // 迭代优化
    for (int gen = 0; gen < params.max_gen; ++gen) {
        for (int i = 0; i < params.pop_size; ++i) {
            // 选择三个不同的个体
            int r1, r2, r3;
            do {
                r1 = uni(rng) * params.pop_size;
            } while (r1 == i);
            do {
                r2 = uni(rng) * params.pop_size;
            } while (r2 == i || r2 == r1);
            do {
                r3 = uni(rng) * params.pop_size;
            } while (r3 == i || r3 == r1 || r3 == r2);

            // 变异操作
            vector<double> mutant(n);
            for (int j = 0; j < n; ++j) {
                mutant[j] = population[r1][j] + params.F * (population[r2][j] - population[r3][j]);
                mutant[j] = max(x_lower[j], min(x_upper[j], mutant[j]));  // 判断是否越界
            }

            // 交叉操作
            vector<double> trial(n);
            int j_rand = uni(rng) * n;
            for (int j = 0; j < n; ++j) {
                if (uni(rng) < params.CR || j == j_rand) {
                    trial[j] = mutant[j];
                }
                else {
                    trial[j] = population[i][j];
                }
            }

            // 评估个体适应度
            double trial_fitness = f(trial[0], trial);
            if (trial_fitness < fitness[i]) {
                population[i] = trial;
                fitness[i] = trial_fitness;
                if (trial_fitness < best_fitness) {
                    best_individual = trial;
                    best_fitness = trial_fitness;
                }
            }
        }
    }

    return best_individual;
}

int main() {
    // 示例使用的分段连续线性函数为 f(x) = 2x + 1 (x <= 0) 和 f(x) = -3x + 2 (x > 0)
    piecewise_linear_function f = [](double x, const vector<double>& params) -> double {
        if (x <= 0) {
            return params[0] * x + params[1];
        }
        else {
            return params[2] * x + params[3];
        }
    };

    // 定义差分进化算法的参数
    DE_params params;
    params.pop_size = 50;
    params.max_gen = 100;
    params.F = 0.5;
    params.CR = 0.9;

    // 定义变量的取值范围
    vector<double> x_lower = {-1.0, -1.0, -1.0, -1.0};
    vector<double> x_upper = {1.0, 1.0, 1.0, 1.0};

    // 用差分进化算法拟合分段连续线性函数
    vector<double> best_params = differential_evolution(f, x_lower, x_upper, params);

    // 输出结果
    cout << "f(x) = ";
    if (best_params[0] < 0) {
        cout << best_params[0] << "x";
    }
    else {
        cout << "+" << best_params[0] << "x";
    }
    if (best_params[1] < 0) {
        cout << best_params[1];
    }
    else {
        cout << "+" << best_params[1];
    }
    cout << " (x <= 0)" << endl;

    cout << "f(x) = ";
    if (best_params[2] < 0) {
        cout << best_params[2] << "x";
    }
    else {
        cout << "+" << best_params[2] << "x";
    }
    if (best_params[3] < 0) {
        cout << best_params[3];
    }
    else {
        cout << "+" << best_params[3];
    }
    cout << " (x > 0)" << endl;

    return 0;
}

这个示例程序中，我们定义了一个 piecewise_linear_function 类型，以便于传递分段连续线性函数；并且定义了一个差分进化算法的参数结构体 DE_params，用于传递算法参数。在 differential_evolution 函数中，我们使用了 vector<vector<double>> 类型来存储种群，vector<double> 类型来存储个体，其中个体的第一个元素表示分段点，其他元素表示线性函数的参数。在主函数中，我们使用了一个 lambda 表达式来定义分段连续线性函数，并且指定了变量的取值范围。最后，我们用 differential_evolution 函数拟合了这个分段连续线性函数，并输出了拟合结果。