例题1:求目标函数Max{1-x2},-1-3。
遗传算法的实现,流程如下:
1.初始化种群:随机生成一定数量的染色体,每个染色体由一定数量的基因组成,每个基因的值为0或1。
2.评估种群:对于每个染色体,计算其适应度,即目标函数的值。
3.选择:根据染色体的适应度,选择一定数量的染色体作为下一代的父代。
4.交叉:对于每一对父代,以一定的概率进行交叉操作,生成一个新的子代。
5.变异:对于每个子代,以一定的概率进行变异操作,改变其中的一个或多个基因的值。
6.生成下一代种群:将父代和子代合并,得到下一代种群。
重复2-6步,直到达到停止条件(例如达到最大迭代次数或找到满足要求的解)。
解:在本题中,目标函数为f(x) = Max{1-x^2},-1
参数配置
- POPULATION_SIZE:种群大小,即每一代中包含的个体数量,这里设置为100。
- CHROMOSOME_LENGTH:染色体长度,即每个个体的基因数量,这里设置为10。
- MUTATION_RATE:变异率,即每个基因发生变异的概率,这里设置为0.1。
- CROSSOVER_RATE:交叉率,即两个个体进行交叉的概率,这里设置为0.9。
- MAX_GENERATIONS:最大迭代次数,即算法运行的最大代数,这里设置为1000。
- PRECISION:精度,即当个体的适应度达到1.0时,算法停止运行,这里设置为0.001。
初始化种群
void initialize_population(vector& population) {
for (int i = 0; i
评估种群
double decode(vector genes) {
double x = 0.0;
for (int i = 0; i genes) {
double x = decode(genes);
return 1.0 - x * x;
}
void evaluate(vector& population) {
for (int i = 0; i
选择
void sort_population(vector& population) {
sort(population.begin(), population.end(), compare);
}
bool compare(Chromosome a, Chromosome b) {
return a.fitness > b.fitness;
}
交叉
vector crossover(vector parent1, vector parent2) {
vector child;
for (int i = 0; i
变异
void mutate(vector& genes) {
for (int i = 0; i
生成下一代种群
void next_generation(vector& population) {
vector new_population;
for (int i = 0; i parent1_genes = population[i].genes;
vector parent2_genes = population[dis(gen)].genes;
vector child_genes = crossover(parent1_genes, parent2_genes);
mutate(child_genes);
Chromosome child;
child.genes = child_genes;
new_population.push_back(child);
}
evaluate(new_population);
sort_population(new_population);
population = new_population;
}
停止条件
for (int i = 0; i = 1.0 - PRECISION) {
break;
}
next_generation(population);
}
程序结果
最优解:x = 0.000977517,f(x) = 0.999999
完整代码
#include
#include
#include
#include
#include
using namespace std;
const int POPULATION_SIZE = 100;
const int CHROMOSOME_LENGTH = 10;
const double MUTATION_RATE = 0.1;
const double CROSSOVER_RATE = 0.9;
const int MAX_GENERATIONS = 1000;
const double PRECISION = 0.001;
random_device rd;
mt19937 gen(rd());
uniform_real_distribution dis(-1.0, 1.0);
uniform_real_distribution dis2(0.0, 1.0);
struct Chromosome {
vector genes;
double fitness;
};
double decode(vector genes) {
double x = 0.0;
for (int i = 0; i genes) {
double x = decode(genes);
return 1.0 - x * x;
}
void evaluate(vector& population) {
for (int i = 0; i b.fitness;
}
void sort_population(vector& population) {
sort(population.begin(), population.end(), compare);
}
void initialize_population(vector& population) {
for (int i = 0; i crossover(vector parent1, vector parent2) {
vector child;
for (int i = 0; i & genes) {
for (int i = 0; i & population) {
vector new_population;
for (int i = 0; i parent1_genes = population[i].genes;
vector parent2_genes = population[dis(gen)].genes;
vector child_genes = crossover(parent1_genes, parent2_genes);
mutate(child_genes);
Chromosome child;
child.genes = child_genes;
new_population.push_back(child);
}
evaluate(new_population);
sort_population(new_population);
population = new_population;
}
int main() {
vector population;
initialize_population(population);
evaluate(population);
sort_population(population);
for (int i = 0; i = 1.0 - PRECISION) {
break;
}
next_generation(population);
}
cout
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