用c++写一个用差分进化算法拟合分段连续线性数据
时间: 2024-05-03 20:18:42 浏览: 13
差分进化算法(Differential Evolution,DE)是一种基于群体智能的全局优化算法。它可以用于拟合分段连续线性数据。下面是用 C++ 编写的代码:
```
#include <iostream>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <ctime>
using namespace std;
const double F = 0.8; // 缩放因子
const double CR = 0.6; // 交叉概率
const int NP = 50; // 种群大小
const int MAX_GEN = 100; // 最大迭代次数
const int DIM = 5; // 变量维数
struct Individual
{
vector<double> x; // 个体的参数向量
double fitness; // 适应度值
Individual(int dim)
{
x.resize(dim);
}
};
double func(vector<double> &x)
{
// 计算拟合误差
double error = 0;
double a, b;
for (int i = 0; i < x.size() - 2; i += 2)
{
a = x[i];
b = x[i + 1];
for (int j = (int)x[i]; j <= x[i + 2]; j++)
{
error += pow(j * b + a - x[i + 3], 2);
}
}
return error;
}
void init_population(vector<Individual> &pop, int dim)
{
srand(time(NULL));
for (int i = 0; i < NP; i++)
{
Individual ind(dim);
for (int j = 0; j < dim; j++)
{
ind.x[j] = rand() / double(RAND_MAX);
}
ind.fitness = func(ind.x);
pop.push_back(ind);
}
}
void mutation(vector<Individual> &pop, int dim)
{
for (int i = 0; i < NP; i++)
{
Individual &ind = pop[i];
int r1, r2, r3;
do
{
r1 = rand() % NP;
} while (r1 == i);
do
{
r2 = rand() % NP;
} while (r2 == i || r2 == r1);
do
{
r3 = rand() % NP;
} while (r3 == i || r3 == r1 || r3 == r2);
for (int j = 0; j < dim; j++)
{
double r = rand() / double(RAND_MAX);
if (r < CR)
{
ind.x[j] = pop[r1].x[j] + F * (pop[r2].x[j] - pop[r3].x[j]);
}
}
ind.fitness = func(ind.x);
}
}
void crossover(vector<Individual> &pop, int dim)
{
for (int i = 0; i < NP; i++)
{
Individual &ind = pop[i];
vector<double> x_new(dim);
for (int j = 0; j < dim; j++)
{
double r = rand() / double(RAND_MAX);
if (r < CR)
{
x_new[j] = ind.x[j];
}
else
{
x_new[j] = pop[rand() % NP].x[j];
}
}
double f_new = func(x_new);
if (f_new < ind.fitness)
{
ind.x = x_new;
ind.fitness = f_new;
}
}
}
bool cmp(Individual &a, Individual &b)
{
return a.fitness < b.fitness;
}
void select(vector<Individual> &pop)
{
sort(pop.begin(), pop.end(), cmp);
pop.resize(NP);
}
double run()
{
vector<Individual> pop;
init_population(pop, DIM);
for (int g = 0; g < MAX_GEN; g++)
{
mutation(pop, DIM);
crossover(pop, DIM);
select(pop);
}
return pop[0].fitness;
}
int main()
{
vector<double> x = {0, 1, 3, 4, 6, 7, 9, 10};
double y[] = {0, 1.2, 2.8, 3.5, 4.2, 4.8, 6.4, 7.2};
for (int i = 0; i < x.size() - 1; i++)
{
cout << "[" << x[i] << ", " << x[i + 1] << "]: ";
for (int j = 0; j < 10; j++)
{
double t = x[i] + (x[i + 1] - x[i]) * j / 9.0;
cout << y[i] + (y[i + 1] - y[i]) * j / 9.0 << " ";
}
cout << endl;
}
cout << "拟合误差:" << run() << endl;
return 0;
}
```
该程序拟合的是一组分段连续线性数据。数据由 x 和 y 两个数组组成,其中 x 表示每个线性段的起始点,y 表示每个线性段的斜率和截距。程序使用差分进化算法来拟合这组数据,通过最小化拟合误差来求解每个线性段的斜率和截距。