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p2woakbh8 1 year ago
parent 529b85643a
commit 7489e81064
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main.cpp
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#include<cmath>
#include<ctime>
#include<iostream>
#include<cstdlib>
using namespace std;
const int Length{ 50 };//染色体长度。使精度可以达到0.01
const int population_size{ 30 };//种群大小
const int double_size{ 2 * population_size };//方便选择函数的操作
const int numbers{ 3 };
const int trilength{ 3 * Length };//交叉函数
const double Error = 1e-6;
double coefficients[numbers][numbers];
double constants[numbers];
class individual;
class Population;
class chromosome
{
private:
double* Chromosome;
public:
friend void exchange(chromosome& c1, chromosome& c2, int j);//染色体交换
chromosome() {
Chromosome = new double[Length];
for (int i = 0; i < Length; ++i)
{
Chromosome[i] = rand() % 2;
}
}
~chromosome()
{
if (!Chromosome)
delete[] Chromosome;
}
double transform()
{
double x = 0;
for (int i = 0; i < Length - 2; ++i) {
x += Chromosome[Length - 1 - i] * pow(2.0, i);
}
if (Chromosome[0] == 1) x = -x; // 处理最高位的符号
return x * 0.000000001; // 转换到实际数值范围
}//转换成十进制
void print_chromosome()
{
for (int i{ 0 }; i < Length; ++i)
{
cout << Chromosome[i];
}
cout << '\n';
};
void print_value()
{
cout << transform() << '\n';
}
void copy_chromosome(const chromosome& c1)
{
delete[]Chromosome;
Chromosome = new double[Length];
for (int i{ 0 }; i < Length; ++i)
{
Chromosome[i] = c1.Chromosome[i];
}
}
friend class individual;
friend class Population;
};
void exchange(chromosome& c1, chromosome& c2, int j)
{
double useless{ 0 };
useless = c1.Chromosome[j];
c1.Chromosome[j] = c2.Chromosome[j];
c2.Chromosome[j] = useless;
//cout << "第" << j + 1 << "条染色体" << endl;
}
class individual
{
private:
chromosome individual_chromosomes[numbers];//染色体
double fitness;//适应度
double error;//代入方程的误差
public:
individual();//初始化
~individual()
{
if (!individual_chromosomes)
delete[]individual_chromosomes;
}
void calculate_error()//求误差
{
double error1{ Error };
for (int i = 0; i < numbers; ++i)
{
double a = coefficients[i][0] * individual_chromosomes[0].transform() + coefficients[i][1] * individual_chromosomes[1].transform() + coefficients[i][2] * individual_chromosomes[2].transform();
error1 += pow(constants[i] - a, 2);
}
error = error1;
}
//求适应度
double calculate_fitness()
{
calculate_error();
double log = std::log(error);
if (log < 0)
{
fitness = 100 - pow(10, log) * 10;
}
else
{
fitness = 90 - 10 * log;
}
return fitness;
}
void print_chromosomes()
{
for (int i{ 0 }; i < numbers; ++i)
{
cout << "第" << i + 1 << "条染色体为：";
individual_chromosomes[i].print_chromosome();
}
}
void print_values()
{
for (int i{ 0 }; i < numbers; ++i)
{
cout << "第" << i + 1 << "个未知数为：";
individual_chromosomes[i].print_value();
}
}
void copy_individual(const individual& i1)
{
for (int i{ 0 }; i < numbers; ++i)
{
individual_chromosomes[i].copy_chromosome(i1.individual_chromosomes[i]);
}
fitness = i1.fitness;
error = i1.error;
}
double get_fitness()
{
return fitness;
}
friend class Population;
friend void exchange(individual& i1, individual& i2);
};
individual::individual()
{
for (int i{ 0 }; i < numbers; ++i)
{
individual_chromosomes[i] = chromosome();
}
calculate_error();
fitness = calculate_fitness();
}
void exchange(individual& i1, individual& i2)
{
int max_digit = static_cast<int>(floor(sqrt(trilength)));//最多改变sqrt位
int digit{ max_digit };
while (digit > 0)
{
int i = rand() % trilength;
int j = i % Length;
i = i / Length;
exchange(i1.individual_chromosomes[i], i2.individual_chromosomes[i], j);
digit -= 1;
}
}
class Population
{
double variation_rate;
double variation_degree;//变异率和最大变异幅度
public:
int selection();//选择函数
void produce();//繁殖函数
int generation;//迭代次数
void mutate();//变异
individual population[double_size + 1];//种群，2倍+1为了交叉和后续交换顺序
Population(int _generation = 100) : variation_rate(0.02), variation_degree(0.14), generation(_generation)
{
for (int i = 0; i < population_size; ++i)
{
population[i] = individual();
}
} // 构造函数初始化变异率和变异幅度,设置迭代次数,初始化种群
//种群初始化
void print_population()
{
for (int i{ 0 }; i < population_size; ++i)
{
cout << "第" << i + 1 << "个个体：" << endl;
population[i].print_chromosomes();
}
}
double get_max_fitness()
{
double max_fitness = population[0].fitness;
for (int i = 0; i < double_size + 1; ++i)
{
if (population[i].fitness > max_fitness)
{
max_fitness = population[i].fitness;
}
}
return max_fitness;
}
};
void exchange(Population& a, Population& b)
{
int times = rand() % population_size;
while (times > 0)
{
int i = rand() % population_size;
int j = (i + rand()) % population_size;
if (i == j)times -= 1;
else
{
exchange(a.population[j], b.population[j]);
//cout << "交换了第" << j + 1 << "个个体的" << endl;
a.population[j].calculate_fitness();
b.population[j].calculate_fitness();
times -= 1;
}
}
}
void Population::mutate()
{
for (int i = 0; i < population_size; ++i)
{
for (int j = 0; j < numbers; ++j)
{
double random = rand() * 1.0 / RAND_MAX;//产生一个0到1之间的随机数
if (random < variation_rate)
{
int position = rand() % 20;
if (population[i].individual_chromosomes[j].Chromosome[position] == 1)
population[i].individual_chromosomes[j].Chromosome[position] = 0;
else
population[i].individual_chromosomes[j].Chromosome[position] = 1;
}
}
}
}
int Population::selection()
{
double total_fitness = 0;
for (int i = 0; i < population_size; ++i) {
total_fitness += population[i].calculate_fitness();
}
double random = (double)rand() / RAND_MAX * total_fitness;
double current_sum = 0;
for (int i = 0; i < population_size; ++i) {
current_sum += population[i].calculate_fitness();
if (current_sum >= random)
{
return i;
}
}
return -1;
}//选择适应度最高的，给予下标
void Population::produce()
{
for (int i{ population_size }; i < double_size; ++i)
{
population[i].copy_individual(population[i - population_size]);
}
for (int i{ 0 }; i < population_size - 1; ++i)
{
exchange(population[i], population[i + 1]);
}
for (int i{ 0 }; i < population_size - 1; ++i)
{
if (population[i].calculate_fitness() < population[i + population_size].calculate_fitness())
{
population[double_size].copy_individual(population[i]);
population[i].copy_individual(population[i + population_size]);
population[i + population_size].copy_individual(population[double_size]);
}
}
}
int main()
{
srand(static_cast<unsigned int>(time(0)));
/*int a;
cout << "请输入迭代次数";
cin >> a;
generation = a;*/
for (int i = 0; i < numbers; ++i)
{
cout << "请输入第 " << i + 1 << " 个方程的系数 (用空格分隔): ";
for (int j = 0; j < numbers; ++j)
{
cin >> coefficients[i][j];
}
cout << "请输入第 " << i + 1 << " 个方程的常数项: ";
cin >> constants[i];
}
int _generation;
cout << "请输入迭代次数：";
cin >> _generation;
Population a(_generation);
a.print_population();
int one1 = a.selection();
cout << "初始值：" << endl;
a.population[one1].print_values();
int times = 0;
Population b;
while (a.get_max_fitness() < 100)
{
a.mutate();
a.produce();
if (times % 1000 == 0&&times!=0)
{
cout << "这是第" << times << "迭代,最合适的解为：";
int one = a.selection();
a.population[one].print_values();
}
++times;
if (times > a.generation)
{
break;
}
}
int one = a.selection();
cout << "迭代最终解为：" << endl;
a.print_population();
a.population[one].print_values();
}
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