Programming Assignment P1
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Fall 2012
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Rush Hour puzzles
A* and heuristics for Rush Hour
The code we are providing
The code that you need to write
Exploring the results
Debugging tips
What to turn in
What you will be graded on
In this programming assignment, you will use the A* algorithm to solve instances of the Rush Hour puzzle. This will involve implementing a graph-search version of A*, along with three heuristics, and testing your implementation on several Rush Hour puzzles. Code is being provided for handling input/output, for representing states, search nodes and puzzles, etc. Your job will be simply to fill in code for A* and the heuristics.
You also are asked to submit a brief written program report, as described below.
This assignment focuses on Rush Hour puzzles such as the following:
In Rush Hour puzzles such as this one, the red car is stuck in traffic and is trying to escape. Cars can be moved up and down or left and right. They are allowed to move more than one square in a single move, but cannot move over or through other cars. The goal is to clear a path so that the red car can escape past the yellow arrow. You are encouraged to try it out yourself at puzzles.com, as well as other sites such as here. (Note that the puzzles.com site requires Internet Explorer to play.)
One of the main parts of this project is implementing A* and three heuristics for solving Rush Hour puzzles. Your implementation of A* should use a graph-search, not a tree-search. The goal of the search is to solve the puzzle in the fewest moves possible, so the cost of a search path should simply be the number of legal moves made.
Recall that when doing a graph-search, we need to check whether we have already visited a state, so that we do not explore the same part of the search space twice. In class, we discussed one way of doing this in which we maintain a set of explored states, and we then check if the state associated with a given node has already been visited after we pull the node off the frontier. Alternatively, R&N gives an approach in which this check is made before adding nodes to the frontier. This latter method may sometimes be more efficient, but may also require slightly more sophisticated data structures which can handle the required operations. For this assignment, you can use either method, provided that your implementation is correct, and provided that you use the most appropriate data structures for the required operations. In particular, you should be sure to choose data structures that can complete each operation in time that is substantially less than linear in the number of items already stored in the structure.
Here are the three heuristics that you should implement and test A* on:
In your written program report, you should include a clear and precise description of the advanced heuristic that you chose to implement. You also should include a brief but convincing argument of why both the blocking heuristic and your advanced heuristic are consistent, and therefore appropriate for use with A* graph search.
We are providing code for handling input/output, representing states, search nodes, etc. Your job is simply to fill in A* and the two non-trivial heuristics.
The class Puzzle represents an instance of a Rush Hour puzzle. This class includes methods for accessing information about the puzzle that is being represented, as well as for reading in a list of puzzles from a data file. In addition, this class maintains a counter of the number of states that have been generated for this puzzle. Methods for accessing, incrementing or resetting this counter are also provided.
Note that every car is constrained to only move horizontally or vertically. Therefore, each car has one dimension along which it is fixed, and another dimension along which it can be moved. The fixed dimension is stored here as part of the puzzle, while the variable dimension is stored as part of the state (class State).
The goal car (the one we are trying to move to the exit) is always assigned index 0.
The class State represents a state or configuration of the puzzle. Methods are provided for constructing a state, for accessing information about a state, for printing a state, and for expanding a state (i.e., obtaining a list of all states immediately reachable from it). Also provided are hashCode and equals methods which override the same methods provided by the Object class. These are provided so that State objects representing the identical configuration will be considered equal.
The class Node represents a search node of the puzzle, including an actual state, the depth of the node, and a link to the parent node that makes it possible to trace back a path to the root node. Methods are provided for accessing information about the search node, and for expanding it (i.e., obtaining a list of all nodes immediately reachable from it, corresponding to the immediately reachable states). Note the distinction between states and search nodes as discussed in class.
Your A* implementation will take as input a heuristic. Heuristics are classes that implement the Heuristic interface that we are providing. Such classes must include a method for computing the value of the heuristic at a given state. The ZeroHeuristic implementation has been provided.
We also are providing a class called BranchingFactor that includes a static method for computing average branching factor as defined in R&N.
Finally, the class RushHour consists of a simple main for running A* on all three heuristics and for all of the puzzles included in a file named in argv[0]. For instance, on unix systems, the command java RushHour jams.txt will run the program on all puzzles in the file jams.txt. The program prints out the solution for each puzzle and each heuristic, and prints a table summarizing the results. You may wish to modify this main to obtain printed results in some other form, or to test your program in some other way.
In addition to the code we are providing, as always, you are welcome to use anything provided in the Standard Java Platform. You may find some of these classes, such as HashSet or PriorityQueue, especially helpful. Although you can freely use any of these, it is your responsibility to always choose the data structures that are most appropriate for how you are using them (in terms of functionality, time efficiency, and space efficiency).
Locations on the grid of a Rush Hour puzzle are identified by their (x, y) coordinates, where the upper left corner is square (0,0). For instance, in the puzzle above, the red car occupies squares (1,2) and (2,2). The goal is to move the red car so that it occupies squares (5,2) and (6,2).
Puzzles can be read from a file into memory using the static method Puzzle.readPuzzlesFromFile(). Such puzzles should be encoded as in the following example representing the puzzle above:
example
6
1 2 h 2
2 0 v 2
4 0 h 2
3 1 v 3
4 1 v 2
4 3 h 2
.
The first line assigns a name to the puzzle, in this case "example". The next line, "6", gives the size of the grid, i.e., this puzzle is defined on a 6x6 grid. The next line, "1 2 h 2", gives a description of the red car. Note that the goal car must always be given first. The first two numbers (1,2) give the (x, y) coordinates of the upper left corner of the car. The "h" indicates that the car is horizontally oriented ("v" would have indicated vertical orientation). The last number "2" indicates that the car has size (i.e., length) 2. The next line, "2 0 v 2", describes the white car, and so on. The last line must consist of a single period, indicating the end of the description of the puzzle. Multiple puzzles may be described consecutively in a single file.
Internally, within the Puzzle class, each car is represented by its orientation (vertical or horizontal), its size and its fixed position. In addition, the variable position of its upper left corner is stored in the State class. For instance, the red car would have a fixed position of 2, and an initial variable position of 1. During the course of the search, this variable position might vary between 0 and 5 (inclusive), with 5 indicating that the goal has been attained. Similarly, the white car would have a fixed position of 2 and a variable position initially of 0, but varying between 0 and 4.
For this assignment, you can assume that the puzzle is a 6x6 grid, that the goal car always has size 2 and is horizontally oriented, and that all cars have size either 2 or 3. However, you are free to experiment with puzzles not satisfying these constraints.
Puzzles can be printed in a rudimentary text form using the State.print() method. For instance, the puzzle above would be printed as follows:
+-------------+
| . . ^ . < > |
| . . v ^ ^ . |
| . < > | v .
| . . . v < > |
| . . . . . . |
| . . . . . . |
+-------------+
We are providing a file called jams.txt of the forty puzzles appearing on the puzzles.com site. However, you will surely want to test and debug your code on smaller, simpler puzzles of your own design.
Below is a summary of how my own implementation performed on the first five puzzles with the zero and blocking heuristics.
| ZeroHeuristic | BlockingHeuristic
name | nodes dpth br.fac | nodes dpth br.fac
-----------+-----------------------+----------------------
Jam-1 | 11587 8 3.066 | 8678 8 2.950
Jam-2 | 24178 8 3.380 | 6201 8 2.820
Jam-3 | 7814 14 1.789 | 5007 14 1.728
Jam-4 | 3491 9 2.326 | 1303 9 2.061
Jam-5 | 24040 9 2.928 | 8353 9 2.583
You may notice that the results you achieve for the number of nodes searched are different, and frequently better, than the sample ones above. The number of nodes searched can vary pretty widely, even among "correct" implementations, due to slight variations involving the handling of nodes in the frontier that have the same cost. The results above were achieved for an implementation in which such ties are broken in a FIFO order, i.e., the node that was placed in the frontier earliest is removed first, an approach that actually appears to be suboptimal. In any case, any way you choose to handle ties is acceptable and the potential variation in results will be taken into account when grading your assignments.
Note that in general we will not provide full-scale "reference solutions" for the programming assignments in this course. Being able to thoroughly test and then debug computer programs is an important and often challenging task (especially for AI programs) requiring skill that is well worth developing. A good way to test your program is to run it on a variety of small problem instances where you know what the correct behavior should be. Also, sometimes the answer can be computed in two different ways; for instance, on this problem, we know that the search depth of the optimal solution should be the same regardless of which heuristic is used.
All code and data files can be obtained all at once by downloading this zip file. Documentation is available here.
Your job is to fill in the A* algorithm which belongs in the constructor of the AStar class. A template has been provided. This constructor must take as input both a puzzle and a heuristic. The solution, represented as an array of states, must be returned in the path field of the constructed object (or path should be set to null if no solution is found). You may also wish to add other fields returning other information.
You also need to provide implementations of the BlockingHeuristic and your own AdvancedHeuristic, both being implementations of the Heuristic interface. Again, templates for these have been provided.
The final code that you turn in for A* and heuristics should not write anything to standard output or standard error. You should not modify any of the "finished" code that we are providing, with the exception of RushHour.main() which you are welcome to modify (although your code must still work correctly when run with the original version of it).
Your A* code should work properly when combined with any consistent heuristic satisfying the Heuristic interface (not just the heuristics that you wrote). Likewise, the heuristics you submit should work properly when used by any other correct implementation of A*.
After you have your code working, you should run it on the forty puzzles that we are providing, in addition, optionally, to other puzzles of your own choosing. Then, examine the results, and briefly answer the following questions:
Your answers should be included in your program report.
If you are having trouble debugging your code, here are some things to think about:
First, be sure that you are checking for already explored states correctly, and using an appropriate data structure. See the note above regarding this issue. Also, be sure that you are checking if a goal state has been reached at an appropriate point in the algorithm. For A*, it matters whether this check is done for a node just before it is put on the frontier, or just after taking it off the frontier.
If you are using the Comparator or Comparable interfaces, be sure that your implementation returns consistent results. See the documentation provided with the standard java platform for more details on the requirements for such interfaces.
To be sure empirically that your heuristic is consistent, you may wish write code that insures that it always satisfies the monotonicity property discussed in class and R&N.
Using this DropBox link, you should turn in the following:
In addition, also using DropBox, you should submit a single pdf file called report.pdf containing your program report, including:
We will automatically test your code on Rush Hour puzzles, possibly different from those that we provided. Your grade will depend largely on getting the right answers. In addition, your code should use appropriate algorithms and data structures, and should be efficient enough to run reasonably fast (easily running in not more than a few minutes on all forty puzzles and all three heuristics on a typical computer) and without running out of memory. Your code should not terminate prematurely with an exception (unless given bad data, of course); code that does otherwise risks getting no credit for the automatic testing portion of the grade. As always, you should follow good programming practices, including documenting your code enough for the graders to be able to read and understand it. Ingenuity in the design of the advanced heuristic will be one factor in your overall grade.
Your written program report should be clear, precise, convincing, complete but concise, thoughtful, and perceptive.
This programming assignment will be worth about 75 points (about 35 for your implementation of all the algorithms, 10 for your choice of advanced heuristic, and 30 for the various components of the program report).
Thanks to Michael Littman from whom this assignment was liberally borrowed.
