通过遗传算法求函数f(x) = x sin(10πx) + 2.0, x∈[-1,2]的最大值使用c++

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遗传算法是一种基于自然选择和遗传学原理的搜索算法，在求解优化问题的时候非常有效。下面是使用C++实现遗传算法求解函数f(x) = x sin(10πx) + 2.0, x∈[-1,2]的最大值的代码示例：

#include <bits/stdc++.h>
using namespace std;

const int POPULATION_SIZE = 100; // 种群大小
const int CHROMOSOME_LENGTH = 20; // 染色体长度
const int MAX_GENERATION = 1000; // 最大迭代次数
const double MUTATION_RATE = 0.01; // 变异率
const double CROSSOVER_RATE = 0.8; // 交叉率

// 定义个体结构体
struct Individual {
    bitset<CHROMOSOME_LENGTH> chromosome;
    double fitness;
};

// 计算个体适应度函数
double calcFitness(Individual& ind) {
    double x = ind.chromosome.to_ulong() / pow(2, CHROMOSOME_LENGTH) * 3 - 1; // 将二进制转换成实数
    return x * sin(10 * M_PI * x) + 2.0;
}

// 初始化种群
vector<Individual> initPopulation() {
    vector<Individual> population(POPULATION_SIZE);
    for (int i = 0; i < POPULATION_SIZE; i++) {
        population[i].chromosome = bitset<CHROMOSOME_LENGTH>(rand() % (1 << CHROMOSOME_LENGTH));
        population[i].fitness = calcFitness(population[i]);
    }
    return population;
}

// 选择操作
vector<Individual> selection(vector<Individual>& population) {
    vector<Individual> selectedPopulation(POPULATION_SIZE);
    double sumFitness = 0;
    for (int i = 0; i < POPULATION_SIZE; i++) {
        sumFitness += population[i].fitness;
    }
    for (int i = 0; i < POPULATION_SIZE; i++) {
        double randFitness = (double)rand() / RAND_MAX * sumFitness;
        double tmpFitness = 0;
        for (int j = 0; j < POPULATION_SIZE; j++) {
            tmpFitness += population[j].fitness;
            if (tmpFitness >= randFitness) {
                selectedPopulation[i] = population[j];
                break;
            }
        }
    }
    return selectedPopulation;
}

// 交叉操作
void crossover(vector<Individual>& population) {
    for (int i = 0; i < POPULATION_SIZE; i += 2) {
        if ((double)rand() / RAND_MAX < CROSSOVER_RATE) {
            int pos = rand() % CHROMOSOME_LENGTH;
            bitset<CHROMOSOME_LENGTH> tmp = population[i].chromosome;
            population[i].chromosome |= (population[i + 1].chromosome >> pos);
            population[i + 1].chromosome |= (tmp >> pos);
        }
    }
}

// 变异操作
void mutation(vector<Individual>& population) {
    for (int i = 0; i < POPULATION_SIZE; i++) {
        if ((double)rand() / RAND_MAX < MUTATION_RATE) {
            int pos = rand() % CHROMOSOME_LENGTH;
            population[i].chromosome.flip(pos);
        }
    }
}

// 获取最优个体
Individual getBestIndividual(vector<Individual>& population) {
    int bestIndex = 0;
    for (int i = 1; i < POPULATION_SIZE; i++) {
        if (population[i].fitness > population[bestIndex].fitness) {
            bestIndex = i;
        }
    }
    return population[bestIndex];
}

int main() {
    srand(time(NULL));
    vector<Individual> population = initPopulation();
    for (int i = 0; i < MAX_GENERATION; i++) {
        vector<Individual> selectedPopulation = selection(population);
        crossover(selectedPopulation);
        mutation(selectedPopulation);
        for (int j = 0; j < POPULATION_SIZE; j++) {
            selectedPopulation[j].fitness = calcFitness(selectedPopulation[j]);
        }
        population = selectedPopulation;
        cout << "Generation " << i + 1 << ": " << getBestIndividual(population).fitness << endl;
    }
    Individual bestIndividual = getBestIndividual(population);
    cout << "Best Individual: " << bestIndividual.chromosome.to_string() << endl;
    cout << "Best Fitness: " << bestIndividual.fitness << endl;
    return 0;
}

在代码中，我们定义了个体结构体，包括染色体和适应度函数。初始化种群、选择操作、交叉操作、变异操作、获取最优个体等遗传算法的基本操作也在代码中实现了。运行程序后，可以得到最优个体的二进制表示和适应度值。