C++三维获得点群最优最小路线 源代码

以下是一个简单的C++程序，用于计算三维点云数据的最优最小路径。该程序使用了遗传算法来寻找最优解。

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <ctime>
#include <cstdlib>

using namespace std;

// 三维点结构体
struct Point {
    double x, y, z;
};

// 遗传算法参数
const int POPULATION_SIZE = 100; // 种群大小
const int MAX_GENERATIONS = 1000; // 最大迭代次数
const double MUTATION_RATE = 0.01; // 变异率
const double CROSSOVER_RATE = 0.8; // 杂交率

// 三维欧几里得距离
double distance(Point a, Point b) {
    double dx = a.x - b.x;
    double dy = a.y - b.y;
    double dz = a.z - b.z;
    return sqrt(dx*dx + dy*dy + dz*dz);
}

// 计算路径长度
double pathLength(vector<Point>& path) {
    double length = 0;
    for (int i = 1; i < path.size(); i++) {
        length += distance(path[i-1], path[i]);
    }
    return length;
}

// 随机生成一个点群
vector<Point> generatePoints(int numPoints) {
    vector<Point> points(numPoints);
    for (int i = 0; i < numPoints; i++) {
        points[i].x = rand() % 1000;
        points[i].y = rand() % 1000;
        points[i].z = rand() % 1000;
    }
    return points;
}

// 生成一个随机个体
vector<int> generateIndividual(int numPoints) {
    vector<int> individual(numPoints);
    for (int i = 0; i < numPoints; i++) {
        individual[i] = i;
    }
    random_shuffle(individual.begin(), individual.end());
    return individual;
}

// 评估个体适应度
double evaluateFitness(vector<int>& individual, vector<Point>& points) {
    vector<Point> path(points.size());
    for (int i = 0; i < individual.size(); i++) {
        path[i] = points[individual[i]];
    }
    return 1.0 / pathLength(path);
}

// 选择一个个体
vector<int> selectIndividual(vector<vector<int>>& population, vector<Point>& points) {
    // 随机选择两个个体
    int index1 = rand() % population.size();
    int index2 = rand() % population.size();

    // 比较适应度，返回适应度更高的个体
    double fitness1 = evaluateFitness(population[index1], points);
    double fitness2 = evaluateFitness(population[index2], points);
    if (fitness1 > fitness2) {
        return population[index1];
    } else {
        return population[index2];
    }
}

// 变异操作
void mutate(vector<int>& individual) {
    for (int i = 0; i < individual.size(); i++) {
        if (rand()/(double)RAND_MAX < MUTATION_RATE) {
            int j = rand() % individual.size();
            swap(individual[i], individual[j]);
        }
    }
}

// 杂交操作
void crossover(vector<int>& parent1, vector<int>& parent2, vector<int>& child) {
    // 随机选择杂交点
    int crossoverPoint1 = rand() % parent1.size();
    int crossoverPoint2 = rand() % parent1.size();
    if (crossoverPoint1 > crossoverPoint2) {
        swap(crossoverPoint1, crossoverPoint2);
    }

    // 复制父代1中的部分基因
    for (int i = crossoverPoint1; i <= crossoverPoint2; i++) {
        child[i] = parent1[i];
    }

    // 复制父代2中的剩余基因
    int j = crossoverPoint2 + 1;
    for (int i = 0; i < parent2.size(); i++) {
        if (find(child.begin(), child.end(), parent2[i]) == child.end()) {
            child[j] = parent2[i];
            j++;
        }
    }
}

// 遗传算法主函数
vector<Point> geneticAlgorithm(vector<Point>& points) {
    // 随机生成初始种群
    vector<vector<int>> population(POPULATION_SIZE);
    for (int i = 0; i < POPULATION_SIZE; i++) {
        population[i] = generateIndividual(points.size());
    }

    // 迭代
    for (int generation = 0; generation < MAX_GENERATIONS; generation++) {
        // 计算种群适应度
        vector<double> fitnesses(POPULATION_SIZE);
        for (int i = 0; i < POPULATION_SIZE; i++) {
            fitnesses[i] = evaluateFitness(population[i], points);
        }

        // 选择下一代种群
        vector<vector<int>> newPopulation(POPULATION_SIZE);
        for (int i = 0; i < POPULATION_SIZE; i++) {
            // 选择两个个体进行杂交
            vector<int> parent1 = selectIndividual(population, points);
            vector<int> parent2 = selectIndividual(population, points);
            vector<int> child(points.size());
            if (rand()/(double)RAND_MAX < CROSSOVER_RATE) {
                crossover(parent1, parent2, child);
            } else {
                child = parent1;
            }
            mutate(child);
            newPopulation[i] = child;
        }

        // 更新种群
        population = newPopulation;
    }

    // 找到最优路径
    double bestFitness = -1;
    vector<int> bestIndividual;
    for (int i = 0; i < POPULATION_SIZE; i++) {
        double fitness = evaluateFitness(population[i], points);
        if (fitness > bestFitness) {
            bestFitness = fitness;
            bestIndividual = population[i];
        }
    }

    // 构造最优路径
    vector<Point> path(points.size());
    for (int i = 0; i < bestIndividual.size(); i++) {
        path[i] = points[bestIndividual[i]];
    }

    return path;
}

int main() {
    // 随机生成点群
    vector<Point> points = generatePoints(10);

    // 计算最优路径
    vector<Point> path = geneticAlgorithm(points);

    // 输出结果
    cout << "Path: ";
    for (int i = 0; i < path.size(); i++) {
        cout << "(" << path[i].x << ", " << path[i].y << ", " << path[i].z << ")";
        if (i < path.size() - 1) {
            cout << " -> ";
        }
    }
    cout << endl;

    return 0;
}

请注意，这只是一个简单的实现，并且可能不是最优的。您可以根据需要进行修改和优化。