用贪心算法解决TSP问题

旅行商问题，即TSP问题（Traveling Salesman Problem）又译为旅行推销员问题、货郎担问题，是数学领域中著名问题之一。假设有一个旅行商人要拜访n个城市，他必须选择所要走的路径，路径的限制是每个城市只能拜访一次，而且最后要回到原来出发的城市。路径的选择目标是要求得的路径路程为所有路径之中的最小值。

环境：程序使用语言java，jdk版本1.8，程序中用到的jar包：poi-3.17

jar包下载地址：Apache Download Mirrors

程序中使用的数据：下载地址：TSPLIB数据:att48_蚁群算法TSP问题-Java文档类资源-优快云下载

项目导入：

3.实验主要源代码

City.java//城市类，结构体

package TSP;

public class city {
    private int name;
    private double X;
    private double Y;
    public city(int name, double x, double y) {
        super();
        this.name = name-1;
        X = x;
        Y = y;
    }
    
    public int getName() {
        return name;
    }
    
    public void setName(int name) {
        this.name = name;
    }
    
    public double getX() {
        return X;
    }
    
    public void setX(double x) {
        X = x;
    }
    
    public double getY() {
        return Y;
    }
    
    public void setY(double y) {
        Y = y;
    }
    
    @Override
    public String toString() {
        return"city [name=" + name + ",X=" + X + ", Y=" + Y + "]";
    }

}

inputData.Java//导入数据类

package TSP;

import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;

import org.apache.poi.hssf.usermodel.HSSFRow;
import org.apache.poi.hssf.usermodel.HSSFSheet;
import org.apache.poi.hssf.usermodel.HSSFWorkbook;


public class inputData {

    @SuppressWarnings("resource")
    public  static List<city> input_att48(File file){
    List<city> cityList = new ArrayList<city>();

    try {
        HSSFWorkbook wookbook = new HSSFWorkbook(new FileInputStream(file));
        HSSFSheet sheet = wookbook.getSheet("Sheet1");
        int rows = sheet.getPhysicalNumberOfRows();
        for(int i=1; i<rows; i++){
            HSSFRow row = sheet.getRow(i);
            if(row!=null){
                city cy = new city(i, row.getCell(1).getNumericCellValue(), row.getCell(2).getNumericCellValue());
                cityList.add(cy);
            }
        }
    }
    catch (FileNotFoundException e) {
        System.out.println("File not fount!");
    }
    catch (IOException e) {
        System.out.println("IO exception!");
    }
        return cityList;
    }
}

Greedy.Java//核心代码

package TSP;

import java.io.File;
import java.util.List;
import java.util.Scanner;


public class greedy {

    static double INF = Double.MAX_VALUE;
    static double[][] DT = null;
    static int[] mark = null;
    static int[] path = null;
    static double solve(int n) {

        double pathLenght = 0;
        File file = new File("E:\\Java\\arithmetic\\src\\resource\\att48.xls");
        List<city> cityList = inputData.input_att48(file);
        System.out.println("city [城市编号 城市X坐标 城市Y坐标]");

        for(int i=0; i<n; i++) {
            System.out.println(cityList.get(i).toString());
        }

        DT = new double[n][n];
        mark = new int[n];
        path = new int[n+1];

        for(int i=0; i<n; i++) {
            for(int j=i; j<n; j++) {
                if(i==j) DT[i][j] = 0;
                else {
                    double dertX = cityList.get(i).getX()-cityList.get(j).getX();
                    double dertY = cityList.get(i).getY()-cityList.get(j).getY();
                    DT[i][j] = Math.sqrt(dertX*dertX + dertY*dertY);
                    DT[j][i] = DT[i][j];
                }
            }
        }

        int s = 0;//s起点
        int v = s;//v当前点
        mark[v] = 1;
        path[0] = v;//第一个城市
        int cnt = 1;

        while(cnt<n) {
            double min = INF;
            for(int i=1; i<n; i++) {
                if(mark[i]==0) {
                    if(DT[v][i] < min) {
                        min = DT[v][i];
                        path[cnt] = i;
                    }
                }
            }
            pathLenght += min;
            v = path[cnt++];//先复制后cnt++
            mark[v] = 1;
        }

        pathLenght += DT[path[v]][s];
        path[cnt] = s;

        return pathLenght;
    }

    @SuppressWarnings("resource")
    public static void main(String[] args) {

        System.out.println("----------------贪心算法解决TSP问题----------------");
        Scanner in = new Scanner(System.in);
        while(true) {
            System.out.println();
            System.out.println("请输入城市数：");
            int n = in.nextInt();
            if(n>48) {
                System.out.println("样例有限，城市数不能超过48！");
                return;
            }
            double pathLength = solve(n);
            System.out.println("旅行路线：");
            System.out.print(path[0]);
            for(int i=1; i<=n; i++) {
                System.out.print("->");
                System.out.print(path[i]);
            }
            System.out.println();
            System.out.print("路线长度：");
            System.out.println(pathLength);
        }
    }

}

输入输出：