Theoritical run times

Transcription

1 Touches of n Theoritical run times 2.5E+11 2E E+11 1E+11 5E Array length (n) Figure 1

2 cities A data structure containing all cities result list of cities in order to be visited initialsize = cities.size() Get number of cities currentcity = cities.get(randomnum) Get an initial city at random cities.remove(randomnum) Remove city from list Repeat until all cities have been added While (cities.size!= initialsize) Add current city to the result result.add(currentcity) distance = Infinity

3 Find the closest city to the current city and add it For (city possible in cities) If (getdistance(currentcity, possible) < distance closest = possible distance = getdistance(currentcity, possible) End if End for Remove the closest city so we don t consider it again cities.remove(closest) The closest city is now the current city currentcity = closest End while Figure 2 Begin TwoOpt repeats = 1 skip = Round(tour.Size/1000) If (skip <= 1) repeats = 2 End If While (improve < repeats)

4 distance = tour.routelength() For (i = 0; i < tour.size() - 1; i++) For (k = i + 1; k < tour.size() - 1; i++) newtour = twooptswap(tour, i, k) newdistance = newtour.routelength() If (newdistance < distance) tour = newtour distance = newdistance End If End For i += skip End For improve++ End While End TwoOpt Begin TwoOptSwap take route[0] to route[i-1] and add them in order to newroute take route[i] to route[k] and add them in reverse order to newroute take route[k+1] to end and add them in order to newroute return newroute End TwoOptSwap Begin checktour originaltour The tour that is created when loading in a TSPLib instance newtour The tour that is created when nearest neighbor algorithm or 2- opt swap are finished. If (originaltour.size()!= newtour.size()) return false The tour does not contain the correct amount of cities. End If tourset = new HashSet<City>(tour) Create a new tour that holds the city as a HashSet instead of an ArrayList, a hashset has no duplicates. If (tourset.size() < newtour.size()) return false There are duplicated cities in the tour End If return true The tour is valid End checktour

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6 Run time (seconds) Average run times Size Figure 3 Figure 4

7 Figure 5 Figure 6

8 Figure 7

9 main.java import java.awt.color; import java.awt.graphics; import javax.swing.jcomponent; import javax.swing.jframe; class MyCanvas extends JComponent Tour list; public MyCanvas(Tour list) this.list = list; public void paint(graphics g) int[] x = new int[list.size()]; int[] y = new int[list.size()]; int count = 0; g.setcolor(color.red); for(city instance:list.cities) x[count] = (int)(instance.getx()/20); y[count] = (int)(instance.gety()/20); g.drawoval(x[count]-3, y[count]-3, 6, 6); g.filloval(x[count]-3, y[count]-3, 6, 6); count++; g.setcolor(color.blue); g.drawpolygon(x, y, x.length); public class main public static void main(string[] args) final String berlin52 = "./TSP Tours/berlin52.tsp"; final String rl1304 = "./TSP Tours/rl1304.tsp"; final String rl1323 = "./TSP Tours/rl1323.tsp"; final String rl1889 = "./TSP Tours/rl1889.tsp"; final String rl5915 = "./TSP Tours/rl5915.tsp"; final String rl5934 = "./TSP Tours/rl5934.tsp"; final String rl11849= "./TSP Tours/rl11849.tsp";

10 double start = System.currentTimeMillis(); Tour originallist = new Tour(); originallist = Tour.LoadTSPLib(berlin52); // Get cities array int originaltoursize = originallist.size(); System.out.println("Checking Original tour..."); originallist.checktour(originaltoursize); double tourlength = originallist.routelength(); // Calculate tour length Tour nearestneighbourlist = originallist.nearestneighboursort(); System.out.println("Checking NN tour..."); nearestneighbourlist.checktour(originaltoursize); double rearrangedtourlength = (nearestneighbourlist.routelength()); // Calculate tour length if (rearrangedtourlength < tourlength) System.out.println("Nearest neighbour tour is shorter"); else if (rearrangedtourlength > tourlength) System.out.println("Original tour is shorter"); System.out.println("Original : " + tourlength); System.out.println("Neighbour: " + rearrangedtourlength); System.out.println("Started calculating 2-opt..."); Tour twooptlist = nearestneighbourlist.twoopt(); double twoopttourlength = (twooptlist.routelength()); System.out.println("Checking 2Opt tour..."); twooptlist.checktour(originaltoursize); System.out.println("2-opt : " + twoopttourlength); double time = System.currentTimeMillis() - start; System.out.println("Solved in: " + time * " seconds"); JFrame window = new JFrame(); window.getcontentpane().setbackground(color.white); window.settitle("nearest Neighbour Route"); window.setbounds(30, 30, 1000, 1000); window.getcontentpane().add(new MyCanvas(nearestNeighbourList)); window.setvisible(true); JFrame window2 = new JFrame(); window2.getcontentpane().setbackground(color.white); window2.settitle("2-opt Route"); window2.setbounds(30, 30, 1000, 1000); window2.getcontentpane().add(new MyCanvas(twoOptList)); window2.setvisible(true); City.java import java.awt.geom.point2d; public class City

11 Point2D coordinates; int id; // Creates a city at given coordinates public City(float x, float y, int id) this.coordinates = new Point2D.Float(x, y); this.id = id; // Gets city's x coordinate public double getx() return this.coordinates.getx(); // Gets city's y coordinate public double gety() return this.coordinates.gety(); // Calculates distance between 2 cities public double getdistance(city city) // Distance formula double xdistance = Math.abs(this.getX() - city.getx()); double ydistance = Math.abs(this.getY() - city.gety()); double distance = Math.sqrt( (xdistance*xdistance) + (ydistance*ydistance) ); return public String tostring() return getx()+", "+gety(); Tour.java import java.io.bufferedreader; import java.io.filereader; import java.io.ioexception; import java.util.arraylist; import java.util.hashset; import java.util.set; import java.util.concurrent.threadlocalrandom; public class Tour public ArrayList<City> cities; // Default constructor public Tour() cities = new ArrayList<City>(); // Constructor with parameter public Tour(ArrayList<City> cities) this.cities = new ArrayList<City>(cities); // Constructor with parameter

12 public Tour(Tour cities) this.cities = new ArrayList<City>(cities.cities); // Constructor from filename // Load in TSPLib Instance. public static Tour LoadTSPLib (String fname) Tour result = new Tour(); BufferedReader br = null; try String currentline; int dimension = 0; // Dimension of problem boolean readingnodes = false; br = new BufferedReader(new FileReader(fName)); while ((currentline = br.readline())!= null) if (currentline.contains("eof")) // Read until end of file readingnodes = false; // Check to see if expected number of cities have been loaded if (result.size()!= dimension) System.out.println("Error loading cities"); System.exit(-1); // If reading in the node data if (readingnodes) String[] tokens = currentline.split(" "); // Split by spaces // Get city id int id = Integer.parseInt(tokens[0].trim()); // Get x and y coordinates float x = Float.parseFloat(tokens[1].trim()); float y = Float.parseFloat(tokens[2].trim()); City city = new City(x, y, id); // Hold city result.cities.add(city); // Add city to arraylist if (currentline.contains("dimension")) String[] tokens = currentline.split(":"); dimension = Integer.parseInt(tokens[1].trim()); if (currentline.contains("node_coord_section")) readingnodes = true; catch (IOException e)

13 e.printstacktrace(); finally try if (br!= null)br.close(); catch (IOException ex) ex.printstacktrace(); return result; // Calculate length of a TSP route public double RouteLength() double result = 0; // Route length City prev = cities.get(cities.size() - 1); // Get previous city // Go through each city in turn for(city city: cities) result += prev.getdistance(city); // Get distance from previous city prev = city; // set current city to previous return result; // Returns a city from the tour, with the given index public City GetCity(int index) return cities.get(index); // Adds a city to the tour public void AddCity(City city) cities.add(city); // Check if a city is contained in the tour public boolean ContainsCity(City city) if (cities.contains(city)) return true; return false; // Removes a city from the tour by given index public void RemoveCity(int index) cities.remove(index); // Removes a city from Tour public void RemoveCity(City city) cities.remove(city);

14 // Tour size (Number of cities) public int Size() return cities.size(); // Sort the tour by Nearest Neighbour public Tour nearestneighboursort() int initialsize = this.size(); Tour cities = new Tour(this); Tour result = new Tour(); int randomnum = ThreadLocalRandom.current().nextInt(0, cities.size()); City currentcity = cities.getcity(randomnum); cities.removecity(randomnum); City closest = cities.getcity(randomnum); // Repeat until all cities have been added while(result.size()!= initialsize) if (!(result.containscity(currentcity))) result.addcity(currentcity); // Add current city to result double distance = Double.POSITIVE_INFINITY; for(city possible:cities.cities) double currentdistance = currentcity.getdistance(possible); if (currentdistance == 0) System.out.println(possible); if (currentdistance < distance) closest = possible; // Closest city is possible city distance = currentdistance; // Get distance between current city and possible closest city cities.removecity(closest); currentcity = closest; return result; // 2-opt swap private Tour TwoOptSwap(Tour tour, int i, int k) Tour newtour = new Tour(); int size = tour.size(); // 1. take route[0] to route[i-1] and add them in order to new_route for (int j = 0; j <= i - 1; ++j) newtour.addcity(tour.getcity(j)); // 2. take route[i] to route[k] and add them in reverse order to new_route int count = 0; for (int j = i; j <= k; ++j)

15 newtour.addcity((tour.getcity(k - count))); count++; // 3. take route[k+1] to end and add them in order to new_route for (int j = k + 1; j < size; ++j) newtour.addcity(tour.getcity(j)); return newtour; // 2-opt swap handling public Tour TwoOpt() Tour tour = this; // Copy the tour to temp variable double distance = tour.routelength(); // Current tour length Tour newtour = new Tour(); int repeats = 1; double size = tour.size(); // Size of tour int skip = (int) Math.round((size/1000)); // Decides how many nodes to skip while performing 2-opt switch // If list is small repeat through whole list twice if (skip <= 1) repeats = 2; System.out.println("Will skip: " + skip); // Most outer loop count int loop = 0; while ( loop < repeats ) distance = tour.routelength(); // Get tour length // Loop through all nodes for (int i = 0; i < size - 1; i++) for (int k = i + 1; k < size; k++) newtour = TwoOptSwap(tour, i, k); // Perform 2-opt swap double newdistance = newtour.routelength(); // Get tour length // Check if new tour is shorter, if it is, keep it if (newdistance < distance) tour = newtour; distance = newdistance; i+=skip; // Skip nodes depending on skip value loop++; // Looped through entire list return tour;

16 // Check if a TSP route is valid public boolean checktour(int noofcities) if (noofcities!= this.size()) System.out.println("Invalid no of cities, " + (noofcities - this.size()) + " cities missing."); return false; Set<City> cityset = new HashSet<City>(this.cities); if(cityset.size() < this.size()) /* There are duplicates */ System.out.println("Duplication of cities detected. No of unique cities: " + cityset.size() + ", should be: " + this.size()); return false; System.out.println("Tour is valid"); return true;