Project 1: Search in Pacman(Thanks to John DeNero and Dan Klein.)
Due September 16, 2014, 2:30pm
In this project, your Pacman agent will find paths through his maze world, both to reach a particular location and to collect food efficiently. You will build general search algorithms and apply them to Pacman scenarios.
The code for this project consists of several Python files, some of which you will need to read and understand in order to complete the assignment, and some of which you can ignore. All the code and supporting files are in your SVN repo.
What to submit: You will fill in portions of
Evaluation: Your code will be autograded for technical correctness. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. However, the correctness of your implementation -- not the autograder's output -- will be the final judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.
Academic Dishonesty: We will be checking your code against other submissions in the class for logical redundancy. If you copy someone else's code and submit it with minor changes, we will know. These cheat detectors are quite hard to fool, so please don't try. We trust you all to submit your own work only; please don't let us down. If you do, we will pursue the strongest consequences available to us.
Getting Help: You are not alone! If you find yourself stuck on something, contact the course staff for help. Office hours, section, and the newsgroup are there for your support; please use them. If you can't make our office hours, let us know and we will schedule more. We want these projects to be rewarding and instructional, not frustrating and demoralizing. But, we don't know when or how to help unless you ask. One more piece of advice: if you don't know what a variable does or what kind of values it takes, print it out.
Welcome to PacmanAfter changing to the project0 directory in your SVN repo, you should be able to play a game of Pacman by typing the following at the command line:
python pacman.pyPacman lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this world efficiently will be Pacman's first step in mastering his domain.
The simplest agent in searchAgents.py is called the
python pacman.py --layout testMaze --pacman GoWestAgentBut, things get ugly for this agent when turning is required:
python pacman.py --layout tinyMaze --pacman GoWestAgentIf pacman gets stuck, you can exit the game by typing CTRL-c into your terminal. Soon, your agent will solve not only
python pacman.py -hAlso, all of the commands that appear in this project also appear in commands.txt, for easy copying and pasting. In UNIX/Mac OS X, you can even run all these commands in order with
Note: if you get error messages regarding Tkinter, see this page
Finding a Fixed Food Dot using Search AlgorithmsIn
python pacman.py -l tinyMaze -p SearchAgent -a fn=tinyMazeSearchThe command above tells the
Now it's time to write full-fledged generic search functions to help Pacman plan routes! Pseudocode for the search algorithms you'll write can be found in the lecture slides and textbook. Remember that a search node must contain not only a state but also the information necessary to reconstruct the path (plan) which gets to that state.
Important note: All of your search functions need to return a list of actions that will lead the agent from the start to the goal. These actions all have to be legal moves (valid directions, no moving through walls).
Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* differ only in the details of how the fringe is managed. So, concentrate on getting DFS right and the rest should be relatively straightforward. Indeed, one possible implementation requires only a single generic search method which is configured with an algorithm-specific queuing strategy. (Your implementation need not be of this form to receive full credit).
Hint: Make sure to check out the
Question 1 (2 points) Implement the depth-first search (DFS) algorithm in the
Your code should quickly find a solution for:
python pacman.py -l tinyMaze -p SearchAgent
python pacman.py -l mediumMaze -p SearchAgent
python pacman.py -l bigMaze -z .5 -p SearchAgentThe Pacman board will show an overlay of the states explored, and the order in which they were explored (brighter red means earlier exploration). Is the exploration order what you would have expected? Does Pacman actually go to all the explored squares on his way to the goal?
Hint: If you use a
Question 2 (1 point) Implement the breadth-first search (BFS) algorithm in the
Does BFS find a least cost solution? If not, check your implementation.
Hint: If Pacman moves too slowly for you, try the option
Note: If you've written your search code generically, your code should work equally well for the eight-puzzle search problem (textbook section 3.2) without any changes.
Varying the Cost FunctionWhile BFS will find a fewest-actions path to the goal, we might want to find paths that are "best" in other senses. Consider
Question 3 (2 points) Implement the uniform-cost graph search algorithm in
Note: You should get very low and very high path costs for the
Note 2: The cost functions are based on the horizontal position of the agent, NOT the contents of the maze.
Question 4 (3 points) Implement A* graph search in the empty function
You can test your A* implementation on the original problem of finding a path through a maze to a fixed position using the Manhattan distance heuristic (implemented already as
python pacman.py -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=manhattanHeuristicYou should see that A* finds the optimal solution slightly faster than uniform cost search (about 549 vs. 620 search nodes expanded in our implementation, but ties in priority may make your numbers differ slightly). What happens on
Finding All the Corners
The real power of A* will only be apparent with a more challenging search problem. Now, it's time to formulate a new problem and design a heuristic for it.
In corner mazes, there are four dots, one in each corner. Our new search problem is to find the shortest path through the maze that touches all four corners (whether the maze actually has food there or not). Note that for some mazes like tinyCorners, the shortest path does not always go to the closest food first! Hint: the shortest path through
Question 5 (2 points) Implement the
To receive full credit, you need to define an abstract state representation that does not encode irrelevant information (like the position of ghosts, where extra food is, etc.). In particular, do not use a Pacman
Hint: The only parts of the game state you need to reference in your implementation are the starting Pacman position and the location of the four corners.
Our implementation of
Question 6 (3 points) Implement a non-trivial, consistent heuristic for the
Admissibility vs. Consistency: Remember, heuristics are just functions that take search states and return numbers that estimate the cost to a nearest goal. More effective heuristics will return values closer to the actual goal costs. To be admissible, the heuristic values must be lower bounds on the actual shortest path cost to the nearest goal (and non-negative). To be consistent, it must additionally hold that if an action has cost c, then taking that action can only cause a drop in heuristic of at most c.
Remember that admissibility isn't enough to guarantee correctness in graph search -- you need the stronger condition of consistency. However, admissible heuristics are usually also consistent, especially if they are derived from problem relaxations. Therefore it is usually easiest to start out by brainstorming admissible heuristics. Once you have an admissible heuristic that works well, you can check whether it is indeed consistent, too. The only way to guarantee consistency is with a proof. However, inconsistency can often be detected by verifying that for each node you expand, its successor nodes are equal or higher in in f-value. Moreover, if UCS and A* ever return paths of different lengths, your heuristic is inconsistent. This stuff is tricky! If you need help, don't hesitate to ask the course staff.
Non-Trivial Heuristics: The trivial heuristics are the ones that return zero everywhere (UCS) and the heuristic which computes the true completion cost. The former won't save you any time, while the latter will timeout the autograder. You want a heuristic which reduces total compute time, though for this assignment the autograder will only check node counts (aside from enforcing a reasonable time limit).
Additionally, any heuristic should always be non-negative, and should return a value of 0 at every goal state (technically this is a requirement for admissibility!). We will deduct 1 point for any heuristic that returns negative values, or doesn't behave properly at goal states.
Eating All The DotsNow we'll solve a hard search problem: eating all the Pacman food in as few steps as possible. For this, we'll need a new search problem definition which formalizes the food-clearing problem:
python pacman.py -l testSearch -p AStarFoodSearchAgent
You should find that UCS starts to slow down even for the seemingly simple
Question 7 (5 points) Fill in
Remember: If your heuristic is inconsistent, you will receive no credit, so be careful! Can you solve
We will deduct 1 point for any heuristic that returns negative values, or does not return 0 at every goal state.
Sometimes, even with A* and a good heuristic, finding the optimal path through all the dots is hard. In these cases, we'd still like to find a reasonably good path, quickly. In this section, you'll write an agent that always greedily eats the closest dot.
Question 8 (2 points) Implement the function
Hint: The quickest way to complete
Mini Contest (up to 3 points extra credit) Implement an
We will time your agent using the no graphics option
Here's a glossary of the key objects in the code base related to search problems, for your reference: