Java中TSP的动态编程方法 [英] Dynamic programming approach to TSP in Java
问题描述
我是一个初学者，我正在尝试使用动态编程方法编写一个行进的旅行推销员问题。
I'm a beginner, and I'm trying to write a working travelling salesman problem using dynamic programming approach.
这是我的计算函数的代码：
This is the code for my compute function:
public static int compute(int[] unvisitedSet, int dest) {
if (unvisitedSet.length == 1)
return distMtx[dest][unvisitedSet[0]];
int[] newSet = new int[unvisitedSet.length-1];
int distMin = Integer.MAX_VALUE;
for (int i = 0; i < unvisitedSet.length; i++) {
for (int j = 0; j < newSet.length; j++) {
if (j < i) newSet[j] = unvisitedSet[j];
else newSet[j] = unvisitedSet[j+1];
}
int distCur;
if (distMtx[dest][unvisitedSet[i]] != -1) {
distCur = compute(newSet, unvisitedSet[i]) + distMtx[unvisitedSet[i]][dest];
if (distMin > distCur)
distMin = distCur;
}
else {
System.out.println("No path between " + dest + " and " + unvisitedSet[i]);
}
}
return distMin;
}
代码没有给我正确的答案，我正在尝试找出发生错误的位置。我认为添加以下内容时会发生我的错误：
distCur = compute（newSet，unvisitedSet [i]）+ distMtx [unvisitedSet [i]] [dest];
所以我一直在弄乱那部分，在我返回 distMin 之前将加法移到最后，依此类推……但是我不能找出答案。
The code is not giving me the correct answers, and I'm trying to figure out where the error is occurring. I think my error occurs when I add:
distCur = compute(newSet, unvisitedSet[i]) + distMtx[unvisitedSet[i]][dest];
So I've been messing around with that part, moving the addition to the very end right before I return distMin and so on... But I couldn't figure it out.
尽管我确定可以从代码中推断出这一点，但我将陈述以下事实加以澄清。
Although I'm sure it can be inferred from the code, I will state the following facts to clarify.
distMtx 存储所有城际距离，并且距离是对称的，这意味着如果从城市A到城市B的距离为3，则从城市B到城市B的距离城市A也是3。此外，如果两个城市没有任何直接路径，则距离值为-1。
distMtx stores all the intercity distances, and distances are symmetric, meaning if distance from city A to city B is 3, then the distance from city B to city A is also 3. Also, if two cities don't have any direct paths, the distance value is -1.
任何帮助将不胜感激！
谢谢！
Any help would be very much appreciated! Thanks!
编辑：
主要功能是从文本文件读取城际距离。因为我假设城市数量总是少于100，所以全局整数变量 distMtx 是[100] [100]。
The main function reads the intercity distances from a text file. Because I'm assuming the number of cities will always be less than 100, global int variable distMtx is [100][100].
一旦矩阵中填充了必要的信息，就会创建一个包含所有城市的数组。城市的名称基本上是数字。因此，如果我有4个城市，则 set [4] = {0，1，2，3} 。
Once the matrix is filled with the necessary information, an array of all the cities are created. The names of the cities are basically numbers. So if I have 4 cities, set[4] = {0, 1, 2, 3}.
在主函数中，创建 distMtx 和 set 之后，首先调用 compute（） 称为：
In the main function, after distMtx and set is created, first call to compute() is called:
int optRoute = compute(set, 0);
System.out.println(optRoute);
样本输入：
-1 3 2 7
3 -1 10 1
2 10 -1 4
7 1 4 -1
预期输出：
10
推荐答案
这是使用动态编程对TSP进行迭代的可行解决方案。使您的生活更轻松的是将当前状态存储为位掩码，而不是存储在数组中。这具有状态表示形式紧凑且可以轻松缓存的优点。
Here's a working iterative solution to the TSP with dynamic programming. What would make your life easier is to store the current state as a bitmask instead of in an array. This has the advantage that the state representation is compact and can be cached easily.
我制作了视频详细介绍了YouTube上此问题的解决方案，请尽情享受！代码来自我的 github存储库
I made a video detailing the solution to this problem on Youtube, please enjoy! Code was taken from my github repo
/**
* An implementation of the traveling salesman problem in Java using dynamic
* programming to improve the time complexity from O(n!) to O(n^2 * 2^n).
*
* Time Complexity: O(n^2 * 2^n)
* Space Complexity: O(n * 2^n)
*
**/
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;
public class TspDynamicProgrammingIterative {
private final int N, start;
private final double[][] distance;
private List<Integer> tour = new ArrayList<>();
private double minTourCost = Double.POSITIVE_INFINITY;
private boolean ranSolver = false;
public TspDynamicProgrammingIterative(double[][] distance) {
this(0, distance);
}
public TspDynamicProgrammingIterative(int start, double[][] distance) {
N = distance.length;
if (N <= 2) throw new IllegalStateException("N <= 2 not yet supported.");
if (N != distance[0].length) throw new IllegalStateException("Matrix must be square (n x n)");
if (start < 0 || start >= N) throw new IllegalArgumentException("Invalid start node.");
this.start = start;
this.distance = distance;
}
// Returns the optimal tour for the traveling salesman problem.
public List<Integer> getTour() {
if (!ranSolver) solve();
return tour;
}
// Returns the minimal tour cost.
public double getTourCost() {
if (!ranSolver) solve();
return minTourCost;
}
// Solves the traveling salesman problem and caches solution.
public void solve() {
if (ranSolver) return;
final int END_STATE = (1 << N) - 1;
Double[][] memo = new Double[N][1 << N];
// Add all outgoing edges from the starting node to memo table.
for (int end = 0; end < N; end++) {
if (end == start) continue;
memo[end][(1 << start) | (1 << end)] = distance[start][end];
}
for (int r = 3; r <= N; r++) {
for (int subset : combinations(r, N)) {
if (notIn(start, subset)) continue;
for (int next = 0; next < N; next++) {
if (next == start || notIn(next, subset)) continue;
int subsetWithoutNext = subset ^ (1 << next);
double minDist = Double.POSITIVE_INFINITY;
for (int end = 0; end < N; end++) {
if (end == start || end == next || notIn(end, subset)) continue;
double newDistance = memo[end][subsetWithoutNext] + distance[end][next];
if (newDistance < minDist) {
minDist = newDistance;
}
}
memo[next][subset] = minDist;
}
}
}
// Connect tour back to starting node and minimize cost.
for (int i = 0; i < N; i++) {
if (i == start) continue;
double tourCost = memo[i][END_STATE] + distance[i][start];
if (tourCost < minTourCost) {
minTourCost = tourCost;
}
}
int lastIndex = start;
int state = END_STATE;
tour.add(start);
// Reconstruct TSP path from memo table.
for (int i = 1; i < N; i++) {
int index = -1;
for (int j = 0; j < N; j++) {
if (j == start || notIn(j, state)) continue;
if (index == -1) index = j;
double prevDist = memo[index][state] + distance[index][lastIndex];
double newDist = memo[j][state] + distance[j][lastIndex];
if (newDist < prevDist) {
index = j;
}
}
tour.add(index);
state = state ^ (1 << index);
lastIndex = index;
}
tour.add(start);
Collections.reverse(tour);
ranSolver = true;
}
private static boolean notIn(int elem, int subset) {
return ((1 << elem) & subset) == 0;
}
// This method generates all bit sets of size n where r bits
// are set to one. The result is returned as a list of integer masks.
public static List<Integer> combinations(int r, int n) {
List<Integer> subsets = new ArrayList<>();
combinations(0, 0, r, n, subsets);
return subsets;
}
// To find all the combinations of size r we need to recurse until we have
// selected r elements (aka r = 0), otherwise if r != 0 then we still need to select
// an element which is found after the position of our last selected element
private static void combinations(int set, int at, int r, int n, List<Integer> subsets) {
// Return early if there are more elements left to select than what is available.
int elementsLeftToPick = n - at;
if (elementsLeftToPick < r) return;
// We selected 'r' elements so we found a valid subset!
if (r == 0) {
subsets.add(set);
} else {
for (int i = at; i < n; i++) {
// Try including this element
set |= 1 << i;
combinations(set, i + 1, r - 1, n, subsets);
// Backtrack and try the instance where we did not include this element
set &= ~(1 << i);
}
}
}
public static void main(String[] args) {
// Create adjacency matrix
int n = 6;
double[][] distanceMatrix = new double[n][n];
for (double[] row : distanceMatrix) java.util.Arrays.fill(row, 10000);
distanceMatrix[5][0] = 10;
distanceMatrix[1][5] = 12;
distanceMatrix[4][1] = 2;
distanceMatrix[2][4] = 4;
distanceMatrix[3][2] = 6;
distanceMatrix[0][3] = 8;
int startNode = 0;
TspDynamicProgrammingIterative solver = new TspDynamicProgrammingIterative(startNode, distanceMatrix);
// Prints: [0, 3, 2, 4, 1, 5, 0]
System.out.println("Tour: " + solver.getTour());
// Print: 42.0
System.out.println("Tour cost: " + solver.getTourCost());
}
}
这篇关于Java中TSP的动态编程方法的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
