简单介绍
遗传算法（Genetic Algorithm）是一种基于模拟生物进化过程的优化算法。它模拟了生物进化的过程中的选择、交叉和变异等操作，通过不断地迭代演化来搜索问题的最优解。遗传算法通常适用于优化问题，尤其是在搜索空间较大、连续或离散性较高的问题中具有较好的效果。
应用示例
下面是一个用C++语言实现的遗传算法的示例，演示了如何使用遗传算法来解决简单的最大化函数的优化问题。
#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
const int POPULATION_SIZE = 50; // 种群大小
const int CHROMOSOME_LENGTH = 10; // 染色体长度
const int MAX_GENERATIONS = 100; // 最大迭代次数
const double CROSSOVER_RATE = 0.8; // 交叉概率
const double MUTATION_RATE = 0.1; // 变异概率
// 表示一个个体（染色体）
struct Individual {
std::vector<int> genes;
double fitness;
Individual() {
genes.resize(CHROMOSOME_LENGTH, 0);
fitness = 0.0;
}
};
// 初始化种群
void initializePopulation(std::vector<Individual>& population) {
for (int i = 0; i < POPULATION_SIZE; ++i) {
for (int j = 0; j < CHROMOSOME_LENGTH; ++j) {
population[i].genes[j] = rand() % 2; // 随机生成0或1
}
}
}
// 计算个体的适应度
double calculateFitness(const Individual& individual) {
// 这里以一个简单的函数作为示例，目标是最大化函数 f(x) = x^2
int x = 0;
for (int i = 0; i < CHROMOSOME_LENGTH; ++i) {
x = (x << 1) | individual.genes[i];
}
return x * x;
}
// 选择操作
void selection(std::vector<Individual>& population) {
std::vector<Individual> newPopulation(POPULATION_SIZE);
// 轮盘赌选择
double totalFitness = 0.0;
for (const Individual& individual : population) {
totalFitness += individual.fitness;
}
for (int i = 0; i < POPULATION_SIZE; ++i) {
double r = static_cast<double>(rand()) / RAND_MAX * totalFitness;
double sum = 0.0;
for (const Individual& individual : population) {
sum += individual.fitness;
if (sum >= r) {
newPopulation[i] = individual;
break;
}
}
}
population = newPopulation;
}
// 交叉操作
void crossover(std::vector<Individual>& population) {
for (int i = 0; i < POPULATION_SIZE - 1; i += 2) {
if (static_cast<double>(rand()) / RAND_MAX < CROSSOVER_RATE) {
int point = rand() % (CHROMOSOME_LENGTH - 1) + 1;
for (int j = point; j < CHROMOSOME_LENGTH; ++j) {
std::swap(population[i].genes[j], population[i + 1].genes[j]);
}
}
}
}
// 变异操作
void mutation(std::vector<Individual>& population) {
for (int i = 0; i < POPULATION_SIZE; ++i) {
for (int j = 0; j < CHROMOSOME_LENGTH; ++j) {
if (static_cast<double>(rand()) / RAND_MAX < MUTATION_RATE) {
population[i].genes[j] = 1 - population[i].genes[j];
}
}
}
}
// 打印种群中最优个体的适应度
void printBestFitness(const std::vector<Individual>& population) {
double bestFitness = population[0].fitness;
for (int i = 1; i < POPULATION_SIZE; ++i) {
if (population[i].fitness > bestFitness) {
bestFitness = population[i].fitness;
}
}
std::cout << "Best Fitness: " << bestFitness << std::endl;
}
int main() {
srand(static_cast<unsigned int>(time(nullptr)));
std::vector<Individual> population(POPULATION_SIZE);
initializePopulation(population);
for (int generation = 0; generation < MAX_GENERATIONS; ++generation) {
for (int i = 0; i < POPULATION_SIZE; ++i) {
population[i].fitness = calculateFitness(population[i]);
}
printBestFitness(population);
selection(population);
crossover(population);
mutation(population);
}
return 0;
}
该示例使用遗传算法优化了一个简单的函数，其中 x 是一个二进制数（长度为10位）。 f ( x ) = x 2 f(x) = x^2 f(x)=x2
文章小结
遗传算法的主要步骤包括初始化种群、计算适应度、选择、交叉和变异。程序迭代执行这些步骤，并输出每一代中最优个体的适应度。实际应用中可能需要根据具体问题进行适当的调整和改进。