```cpp
#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <numeric>
// 个体类
class Individual {
public:
std::vector<int> genes; // 基因，即二进制编码
double fitness; // 适应度
Individual(int geneLength) : genes(geneLength), fitness(0.0) {
// 初始化基因
for (int& g : genes) {
g = rand() % 2;
}
}
void calculateFitness() {
// 假设目标函数是要最大化二进制编码表示的十进制数
fitness = std::accumulate(genes.begin(), genes.end(), 0.0,
[](double total, int bit) { return total * 2 + bit; });
}
};
// 轮盘赌选择
Individual rouletteWheelSelection(const std::vector<Individual>& population) {
double totalFitness = std::accumulate(population.begin(), population.end(), 0.0,
[](double total, const Individual& ind) { return total + ind.fitness; });
double pick = static_cast<double>(rand()) / RAND_MAX * totalFitness;
double current = 0.0;
for (const auto& individual : population) {
current += individual.fitness;
if (current > pick) {
return individual;
}
}
// 默认返回最后一个个体
return population.back();
}
// 遗传算法主循环
void geneticAlgorithm(int populationSize, int geneLength, int generations) {
srand(static_cast<unsigned int>(time(nullptr)));
std::vector<Individual> population(populationSize);
for (auto& individual : population) {
individual.genes.resize(geneLength);
}
for (int generation = 0; generation < generations; ++generation) {
for (auto& individual : population) {
individual.calculateFitness();
}
// 打印当前最优个体的适应度
std::sort(population.begin(), population.end(),
[](const Individual& a, const Individual& b) { return a.fitness > b.fitness; });
std::cout << "Generation " << generation << ": Best Fitness = " << population.front().fitness << std::endl;
std::vector<Individual> newPopulation;
while (newPopulation.size() < populationSize) {
Individual parent1 = rouletteWheelSelection(population);
Individual parent2 = rouletteWheelSelection(population);
// 进行交叉和变异，生成新个体
Individual child = parent1; // 假设无交叉，直接复制父代
// 变异操作
for (int i = 0; i < geneLength; ++i) {
if (static_cast<double>(rand()) / RAND_MAX < 0.05) { // 变异概率5%
child.genes = 1 - child.genes;
}
}
newPopulation.push_back(child);
}
population = newPopulation;
}
}
int main() {
geneticAlgorithm(100, 10, 100); // 100个个体，每个个体10个基因，运行100代
return 0;
}
```
在上述代码中，我们定义了一个`Individual`类来表示个体，它包含了一组基因（`genes`）和一个适应度值（`fitness`）。遗传算法的主要循环包括计算适应度、轮盘赌选择、交叉和变异等步骤。这里为了简化，我们省略了交叉操作，只进行了变异。轮盘赌选择是基于个体适应度的大小来进行选择，适应度越高的个体被选中的概率越大。
请注意，遗传算法的效果很大程度上取决于问题的特性、种群大小、基因长度、交叉和变异策略等参数的设置。在实际应用中，可能需要对这些参数进行调整以获得最佳效果。
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