LinKernighan.java

package Optimisation;
import javax.swing.*;
import java.awt.*;
import java.util.Random;
import java.util.stream.IntStream;

// https://en.wikipedia.org/wiki/Lin–Kernighan_heuristic
public class LinKernighan extends JFrame {
	Random rnd = new Random(1);
	int n = rnd.nextInt(300) + 250;

	double[] x = new double[n];
	double[] y = new double[n];
	int[] bestState;
	double bestDist = Double.POSITIVE_INFINITY;

	{
		for (int i = 0; i < n; i++) {
			x[i] = rnd.nextDouble();
			y[i] = rnd.nextDouble();
		}
	}

	public void linKernighan() {
		int[] curState = IntStream.range(0,n).toArray();
		double curDist = eval(curState);
		updateBest(curState, curDist);
		for (boolean improved = true; improved; ) {
			improved = false;
			for (int rev = -1; rev <= 1; rev += 2) {
				for (int i = 0; i < n; i++) {
					int[] p = new int[n];
					for (int j = 0; j < n; j++)
						p[j] = curState[(i + rev * j + n) % n];
					boolean[][] added = new boolean[n][n];
					double cost = eval(p);
					double delta = -dist(x[p[n - 1]], y[p[n - 1]], x[p[0]], y[p[0]]);
					for (int k = 0; k < n; k++) {
						double best = Double.POSITIVE_INFINITY;
						int bestPos = -1;
						for (int j = 1; j < n - 2; j++) {
							if (added[p[j]][p[j + 1]])
								continue;
							double addedEdge = dist(x[p[n - 1]], y[p[n - 1]], x[p[j]], y[p[j]]);
							if (delta + addedEdge > 0)
								continue;
							double removedEdge = dist(x[p[j]], y[p[j]], x[p[j + 1]], y[p[j + 1]]);
							double cur = addedEdge - removedEdge;
							if (best > cur) {
								best = cur;
								bestPos = j;
							}
						}
						if (bestPos == -1)
							break;
						added[p[n - 1]][p[bestPos]] = true;
						added[p[bestPos]][p[n - 1]] = true;
						delta += best;
						reverse(p, bestPos + 1, n - 1);
						double closingEdge = dist(x[p[n - 1]], y[p[n - 1]], x[p[0]], y[p[0]]);
						if (curDist > cost + delta + closingEdge) {
							curDist = cost + delta + closingEdge;
							curState = p.clone();
							updateBest(curState, curDist);
							improved = true;
							break;
						}
					}
				}
			}
		}
		updateBest(curState, curDist);
	}

	void updateBest(int[] curState, double curDist) {
		if (bestDist > curDist) {
			bestDist = curDist;
			bestState = curState.clone();
			repaint();
		}
	}

	// reverse order from i to j
	static void reverse(int[] p, int i, int j) {
		int n = p.length;
		while (i != j) {
			int t = p[j];
			p[j] = p[i];
			p[i] = t;
			i = (i + 1) % n;
			if (i == j) break;
			j = (j - 1 + n) % n;
		}
	}

	double eval(int[] state) {
		double res = 0;
		for (int i = 0, j = state.length - 1; i < state.length; j = i++)
			res += dist(x[state[i]], y[state[i]], x[state[j]], y[state[j]]);
		return res;
	}

	static double dist(double x1, double y1, double x2, double y2) {
		double dx = x1 - x2;
		double dy = y1 - y2;
		return Math.sqrt(dx * dx + dy * dy);
	}

	// visualization code
	public LinKernighan() {
		setContentPane(new JPanel() {
			protected void paintComponent(Graphics g) {
				super.paintComponent(g);
				if (bestState == null) return;
				((Graphics2D) g).setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
				((Graphics2D) g).setStroke(new BasicStroke(3));
				int w = getWidth() - 5;
				int h = getHeight() - 30;
				for (int i = 0, j = n - 1; i < n; j = i++)
					g.drawLine((int) (x[bestState[i]] * w), (int) ((1 - y[bestState[i]]) * h),
							(int) (x[bestState[j]] * w), (int) ((1 - y[bestState[j]]) * h));
				g.drawString(String.format("length: %.3f", eval(bestState)), 5, h + 20);
			}
		});
		setSize(new Dimension(600, 600));
		setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
		setVisible(true);
		new Thread(this::linKernighan).start();
	}

	public static void main(String[] args) {
		new LinKernighan();
	}
}