将蚁群算法运用到NX二次开发中，实现将选取的点之间最短路径的搜索，并输出算法找到的最短路径，要求在平面上，以及在三维几何体上的随机点分别测试。c++

以下是将蚁群算法应用于NX二次开发中的示例代码，其中包括平面上和三维几何体上的随机点测试：

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

using namespace std;

const int MAX_ANT = 50;
const double ALPHA = 1.0;
const double BETA = 2.0;
const double RHO = 0.5;
const double Q = 100.0;
const int MAX_ITER = 100;

struct Point {
    double x, y, z;
    Point() {}
    Point(double _x, double _y, double _z) : x(_x), y(_y), z(_z) {}
};

struct Edge {
    int from, to;
    double weight;
    Edge(int _from, int _to, double _weight) : from(_from), to(_to), weight(_weight) {}
};

class Ant {
public:
    Ant(int num_points) : tabu_(num_points, false), tour_(num_points + 1) {}
    void Clear() {
        for (int i = 0; i < tabu_.size(); ++i) {
            tabu_[i] = false;
        }
        tour_[0] = tour_[tour_.size() - 1] = -1;
        cur_pos_ = 0;
        tour_length_ = 0.0;
    }
    void VisitPoint(int point) {
        tour_[cur_pos_++] = point;
        tabu_[point] = true;
        if (cur_pos_ == tour_.size()) {
            tour_length_ += GetEdgeWeight(tour_[cur_pos_ - 2], tour_[cur_pos_ - 1]);
            tour_length_ += GetEdgeWeight(tour_[cur_pos_ - 1], tour_[0]);
        } else {
            tour_length_ += GetEdgeWeight(tour_[cur_pos_ - 2], tour_[cur_pos_ - 1]);
        }
    }
    int ChooseNextPoint(const vector<vector<Edge>>& edges, int cur_point) {
        double sum_prob = 0.0;
        vector<double> probs(edges[cur_point].size(), 0.0);
        for (int i = 0; i < edges[cur_point].size(); ++i) {
            if (!tabu_[edges[cur_point][i].to]) {
                probs[i] = pow(edges[cur_point][i].weight, ALPHA) * pow(1.0 / GetEdgeWeight(cur_point, edges[cur_point][i].to), BETA);
                sum_prob += probs[i];
            }
        }
        if (sum_prob == 0.0) {
            for (int i = 0; i < tabu_.size(); ++i) {
                if (!tabu_[i]) {
                    return i;
                }
            }
        }
        for (int i = 0; i < probs.size(); ++i) {
            probs[i] /= sum_prob;
        }
        double r = (double)rand() / RAND_MAX;
        double sum = 0.0;
        for (int i = 0; i < probs.size(); ++i) {
            sum += probs[i];
            if (r <= sum) {
                return edges[cur_point][i].to;
            }
        }
        return -1;
    }
    double GetTourLength() const {
        return tour_length_;
    }
    const vector<int>& GetTour() const {
        return tour_;
    }
private:
    vector<bool> tabu_;
    vector<int> tour_;
    int cur_pos_ = 0;
    double tour_length_ = 0.0;
    double GetEdgeWeight(int from, int to) const {
        // Calculate the distance between two points
        Point p1, p2;
        if (from < num_points_ && to < num_points_) { // 2D case
            p1 = points_[from];
            p2 = points_[to];
        } else { // 3D case
            p1 = points_3d_[from - num_points_];
            p2 = points_3d_[to - num_points_];
        }
        double dx = p1.x - p2.x;
        double dy = p1.y - p2.y;
        double dz = p1.z - p2.z;
        return sqrt(dx * dx + dy * dy + dz * dz);
    }
    vector<Point> points_;
    vector<Point> points_3d_;
    int num_points_;
    friend class AntColonyOptimizer;
};

class AntColonyOptimizer {
public:
    AntColonyOptimizer(int num_points, const vector<Point>& points, const vector<Point>& points_3d) : num_points_(num_points), points_(points), points_3d_(points_3d) {
        srand((unsigned int)time(NULL));
        InitEdges();
    }
    void SetParams(double alpha, double beta, double rho, double q) {
        ALPHA = alpha;
        BETA = beta;
        RHO = rho;
        Q = q;
    }
    void Optimize() {
        ants_.resize(MAX_ANT, Ant(num_points_));
        for (int i = 0; i < MAX_ANT; ++i) {
            ants_[i].Clear();
        }
        for (int i = 0; i < num_points_; ++i) {
            best_tour_.push_back(i);
        }
        best_tour_length_ = GetTourLength(best_tour_);
        for (int iter = 0; iter < MAX_ITER; ++iter) {
            for (int i = 0; i < MAX_ANT; ++i) {
                ants_[i].Clear();
            }
            for (int i = 0; i < MAX_ANT; ++i) {
                int start_point = rand() % num_points_;
                ants_[i].VisitPoint(start_point);
                while (ants_[i].cur_pos_ < num_points_) {
                    int next_point = ants_[i].ChooseNextPoint(edges_, ants_[i].tour_[ants_[i].cur_pos_ - 1]);
                    if (next_point == -1) {
                        break;
                    }
                    ants_[i].VisitPoint(next_point);
                }
                ants_[i].tour_length_ += GetEdgeWeight(ants_[i].tour_[num_points_ - 1], ants_[i].tour_[0]);
                if (ants_[i].tour_length_ < best_tour_length_) {
                    best_tour_ = ants_[i].tour_;
                    best_tour_length_ = ants_[i].tour_length_;
                }
            }
            UpdatePheromones();
        }
    }
    const vector<int>& GetBestTour() const {
        return best_tour_;
    }
    double GetBestTourLength() const {
        return best_tour_length_;
    }
private:
    vector<vector<Edge>> edges_;
    int num_points_;
    vector<Point> points_;
    vector<Point> points_3d_;
    vector<Ant> ants_;
    vector<int> best_tour_;
    double best_tour_length_;
    double ALPHA;
    double BETA;
    double RHO;
    double Q;
    void InitEdges() {
        edges_.resize(num_points_ + points_3d_.size());
        for (int i = 0; i < num_points_; ++i) {
            for (int j = i + 1; j < num_points_; ++j) {
                double weight = GetEdgeWeight(i, j);
                edges_[i].push_back(Edge(i, j, weight));
                edges_[j].push_back(Edge(j, i, weight));
            }
            for (int j = 0; j < points_3d_.size(); ++j) {
                double weight = GetEdgeWeight(i, j + num_points_);
                edges_[i].push_back(Edge(i, j + num_points_, weight));
                edges_[j + num_points_].push_back(Edge(j + num_points_, i, weight));
            }
        }
        for (int i = 0; i < points_3d_.size(); ++i) {
            for (int j = i + 1; j < points_3d_.size(); ++j) {
                double weight = GetEdgeWeight(i + num_points_, j + num_points_);
                edges_[i + num_points_].push_back(Edge(i + num_points_, j + num_points_, weight));
                edges_[j + num_points_].push_back(Edge(j + num_points_, i + num_points_, weight));
            }
        }
    }
    double GetEdgeWeight(int from, int to) const {
        // Calculate the distance between two points
        Point p1, p2;
        if (from < num_points_ && to < num_points_) { // 2D case
            p1 = points_[from];
            p2 = points_[to];
        } else { // 3D case
            p1 = points_3d_[from - num_points_];
            p2 = points_3d_[to - num_points_];
        }
        double dx = p1.x - p2.x;
        double dy = p1.y - p2.y;
        double dz = p1.z - p2.z;
        return sqrt(dx * dx + dy * dy + dz * dz);
    }
    void UpdatePheromones() {
        vector<vector<double>> delta(num_points_ + points_3d_.size(), vector<double>(num_points_ + points_3d_.size(), 0.0));
        for (int i = 0; i < MAX_ANT; ++i) {
            for (int j = 0; j < num_points_; ++j) {
                delta[ants_[i].tour_[j]][ants_[i].tour_[j + 1]] += Q / ants_[i].tour_length_;
                delta[ants_[i].tour_[j + 1]][ants_[i].tour_[j]] += Q / ants_[i].tour_length_;
            }
            delta[ants_[i].tour_[num_points_]][ants_[i].tour_[0]] += Q / ants_[i].tour_length_;
            delta[ants_[i].tour_[0]][ants_[i].tour_[num_points_]] += Q / ants_[i].tour_length_;
        }
        for (int i = 0; i < num_points_ + points_3d_.size(); ++i) {
            for (int j = 0; j < num_points_ + points_3d_.size(); ++j) {
                edges_[i][j].weight = edges_[i][j].weight * (1.0 - RHO) + delta[i][j];
            }
        }
    }
    double GetTourLength(const vector<int>& tour) const {
        double length = 0.0;
        for (int i = 0; i < num_points_; ++i) {
            length += GetEdgeWeight(tour[i], tour[i + 1]);
        }
        return length;
    }
};

int main() {
    int num_points_2d = 10;
    int num_points_3d = 10;
    vector<Point> points_2d(num_points_2d);
    vector<Point> points_3d(num_points_3d);
    for (int i = 0; i < num_points_2d; ++i) {
        points_2d[i].x = (double)rand() / RAND_MAX * 100.0;
        points_2d[i].y = (double)rand() / RAND_MAX * 100.0;
    }
    for (int i = 0; i < num_points_3d; ++i) {
        points_3d[i].x = (double)rand() / RAND_MAX * 100.0;
        points_3d[i].y = (double)rand() / RAND_MAX * 100.0;
        points_3d[i].z = (double)rand() / RAND_MAX * 100.0;
    }
    AntColonyOptimizer optimizer(num_points_2d, points_2d, points_3d);
    optimizer.SetParams(1.0, 2.0, 0.5, 100.0);
    optimizer.Optimize();
    cout << "2D case:" << endl;
    cout << "Best tour length: " << optimizer.GetBestTourLength() << endl;
    cout << "Best tour: ";
    for (int i = 0; i < num_points_2d; ++i) {
        cout << optimizer.GetBestTour()[i] << " ";
    }
    cout << endl;
    optimizer = AntColonyOptimizer(num_points_3d, points_2d, points_3d);
    optimizer.SetParams(1.0, 2.0, 0.5, 100.0);
    optimizer.Optimize();
    cout << "3D case:" << endl;
    cout << "Best tour length: " << optimizer.GetBestTourLength() << endl;
    cout << "Best tour: ";
    for (int i = 0; i < num_points_3d; ++i) {
        cout << optimizer.GetBestTour()[i] << " ";
    }
    cout << endl;
    return 0;
}

在上面的代码中，Ant 类表示蚂蚁，其中包括它的禁忌表、当前路径、当前位置以及当前路径长度等属性。它的 VisitPoint 方法表示访问一个点，ChooseNextPoint 方法表示选择下一个要访问的点，GetTourLength 方法表示获取当前路径长度，GetTour 方法表示获取当前路径。

AntColonyOptimizer 类表示蚁群算法优化器，其中包括所有边的权重、所有蚂蚁、最佳路径及其长度等属性。它的 Optimize 方法表示进行蚁群算法优化，GetBestTour 方法表示获取最佳路径，GetBestTourLength 方法表示获取最佳路径长度，SetParams 方法表示设置蚁群算法的参数，InitEdges 方法表示初始化所有边的权重，GetEdgeWeight 方法表示计算两个点之间的距离，UpdatePheromones 方法表示更新信息素。

在 main 函数中，我们首先生成一些随机点，然后分别对平面和三维几何体上的随机点进行测试，输出最佳路径及其长度。