Programming Assignment Checklist: Traveling Salesperson Problem


Pair programming. On this assignment, just like the last one, you are encouraged (not required) to work with a partner provided you practice pair programming. Pair programming "is a practice in which two programmers work side-by-side at one computer, continuously collaborating on the same design, algorithm, code, or test." One partner is driving (designing and typing the code) while the other is navigating (reviewing the work, identifying bugs, and asking questions). The two partners switch roles every 30-40 minutes, and on demand, brainstorm. Before pair programming, you must read the article All I really need to know about pair programming I learned in kindergarten.

You must choose a partner from the same precept. Only one member of the partnership will turn in the assignment and readme.txt; both partners will receive the same grade.


Frequently Asked Questions

What are the main goals of this assignment? You should (i) learn about the notorious traveling salesperson problem, (ii) learn to use linked lists, and (iii) get more practice with data types.

Do I need to following the prescribed API? Yes, we will be testing the methods in the API directly. If your method has a different signature or does not behave as specified, you will lose a substantial number of points. You may not add public methods to the API; however, you may add private methods (which are only accessible in the class in which they are declared).

How do I represent infinity in Java? Use Double.POSITIVE_INFINITY.

How long should my programs take to execute? It should take less than a minute for the 13,509 city example (substantially less if you have a fast computer). If your code takes much much longer, try to discover why (think analysis of algorithms), and explain it in your readme file. When timing your program, don't animate the results on the screen or this may become the bottleneck.

How can I produce an animation of the heuristic in action? It's easy and instructive—just redraw the tour after each insertion. See the instructions in SmallestInsertion.java. It could take a while on a big input file, so you might want to modify it so that it redraws only after every 20 insertions or so.

What is the file Tour$Node.class? When you declare a nested class like Node, the Java compiler uses the $ symbol to mark its name.

What is a NullPointerException? You can get one by initializing a variable of type Node, say x, to null and then accessing x.next or x.p. This can happen in your insertion routine if you inadvertently break up the circular linked list.

When should I create a new linked list node with the keyword new? To create a tour with N elements, you should use new exactly N times with Node, once per invocation of insert(). It is unnecessary (and bad style) to use new with your list traversal variables since this allocates memory that you never use.

Can I use Java's built in LinkedList class? Absolutely not! One of the main goals of this assignment is to gain experience writing and using linked structures. The Java libraries can only take you so far, and you will quickly discover applications which cannot be solved without devising your own linked structures. Stay tuned.

For the extra credit, how fast should my solution be? It depends on the speed of your computer, but say at most 5 minutes for usa13509.txt.

Do I have to use a linked list for the extra credit? No.

Input, Output, and Testing

Input.   There are many sample data files (with extension .txt) available from the tsp directory. Most are taken from TSPLIB.

Debugging.   A good debugging strategy for most programs is to test your code on inputs that you can easily solve by hand. Start with 1 and 2 city problems. Then, do a 4 city problem. Choose the data so that it is easy to work through the code by hand. Draw pictures. If your code does not do exactly what your hand calculations indicate, determine where they differ. Use the System.out.println() method.

Checking your work.  For usa13509.txt we get distances of 77449.97941714071 and 45074.77692017051 for nearest insertion and smallest insertion, respectively. For circuit1290.txt we get 25029.790452731024 and 14596.097124575306.

Timing.   You may use the client program TSPTimer.java to help you estimate the running time as a function of the input size N. It takes a command-line argument N, runs the two heuristics on a random input of size N, and prints out how long each took.

Possible Progress Steps

These are purely suggestions for how you might make progress. You do not have to follow these steps.

  1. The subdirectory tsp from the COS 126 ftp site contains Point.java and two versions (with and without graphics) of the client programs for each heuristic. There are several small data files for debugging purposes, as well as the larger data files that you need for the readme.txt questions. There is also a client program to help you do the performance analysis part of the assignment. The directory also contains StdIn.java, StdDraw.java, StdOut.java and this assignment's readme.txt file.

  2. Study the Point.java API. Its main() method reads in data from standard input in the TSP input format and draws the points to standard draw.

  3. Create a file Tour.java. Include the standard linked list data type Node. Include one instance variable, say first, of type Node that is a reference to the "first" node of the circular linked list.

    For debugging purposes only, make a constructor that takes four points as arguments, and constructs a circular linked list using those four Point objects. First, create four nodes and assign one point to each. Then, link the nodes one to another in a circle.

  4. Implement the method show(). It should traverse each Node in the circular linked list, starting at first, and printing each Point using System.out.println(). This method requires only a few lines of code, but it is important to think about it carefully, because debugging linked-list code is notoriously difficult and frustrating. Start by just printing out the first Point. With circular linked-lists the last node on the list points back to the first node, so watch out for infinite loops.

    Test your method by writing a main() function that defines four points, creates a new Tour object using those four points, and calls its show() method. Below is a suggested four point main(). Use it for testing. 

      // main method for testing
  public static void main(String[] args) {
    // define 4 points forming a square
    Point a = new Point(100.0, 100.0);
    Point b = new Point(500.0, 100.0);
    Point c = new Point(500.0, 500.0);
    Point d = new Point(100.0, 500.0);

    // Set up a Tour with those four points
    // The constructor should link a->b->c->d->a
    Tour squareTour = new Tour(a, b, c, d);

    // Output the Tour
    squareTour.show();
  }
    If your method is working properly, you will get the following output for the 4 city problem above. 
    (100.0, 100.0)
(500.0, 100.0)
(500.0, 500.0)
(100.0, 500.0)
    Test your method show() on tours with 0, 1 and 2 points to check that it still works. You can create such instances by modifying the 4-node debugging constructor to only link 0, 1 or 2 of the four points to the Tour. (If you don't define first, you will have an empty Tour. If you define first and link it back to itself, you will have a 1 point Tour.)

    Put the debugging constructor back to the original four point Tour before continuing.

  5. Implement the method distance(). It is very similar to show(), except that you will need to invoke the method distanceTo() in the Point data type. Add a call to the Tour distance() method in the main() and print out the distance. The four point example has a distance of 1600.0.

  6. Implement the method draw(). It is also very similar to show(), except that you will need to invoke the method drawTo() in the Point data type. You will also need to include the statements 
     
StdDraw.setXscale(0, 600);
StdDraw.setYscale(0, 600);
    in your main() before you call the Tour draw() method. The four point example above should produce a square.
After arriving at this point, you should feel a sense of accomplishment: working with a linked list is quite difficult at first!
  1. For this crucial step, you must write a method to insert one point p into the tour. First, get rid of the call in main() to the debugging constructor (or you'll have 4 extra nodes in the tour). As a warmup, implement a simpler version named insertInorder() to insert a point into the tour after the point that was added last. To do this, write a loop to find the last point, and insert it after it. It's ok (and expected) that you'll have a special case for the very first point ever inserted, but you shouldn't need any other special cases.

  2. Implement insertNearest(). To determine which node to insert the point p after, compute the Euclidean distance between each point in the tour and p by traversing the circular linked list. As you proceed, store the node containing the closest point and its distance to p. After you have found the closest node, create a node containing p, and insert it after the closest node. This involves changing the next field of both the newly created node and the closest node. As a check, here is the resulting tour for the 10 city problem which has distance 1566.136. Note that the optimal tour has distance 1552.961 so this rule does not, in general, yield the best tour.

  3. After doing the nearest insertion heuristc, you should be able write the method insertSmallest() by yourself, without any hints. The only difference is that you want to insert the point p where it will result in the least possible increase in the total tour length. As a check, here is the resulting tour which has distance 1655.746. In this case, the smallest insertion heuristic actually does worse than the nearest insertion heuristic (although this is not typical).

Extra Credit

Possibilities for improvement are endless. Here are some ideas. If you are shooting for an A or A+, this is a good opportunity to impress us. However, be warned, this is a difficult extra credit. If you complete the extra credit, submit a program ExtraCredit.java along with any accompanying files. You are not required to use the Tour data type or linked lists for the extra credit, but you should exercise good modular design.

Enrichment