Project 1 Searchin' in the Pac-Man World

CSE 473 Project 1: Searchin' in the Pac-Man World

CSE 473 Project 1
Searchin' in the Pac-Man World
(100 points)
Pac-man's got them searchin' blues
Searchin' for dots when there ain't no clues
Introduction
In this project, your Pac-Man agent will find paths through its maze world, both to reach a
particular location and to collect food efficiently. You will build general search algorithms and
apply them to Pac-Man scenarios.
This is a somewhat long project with lots of components, so start early!
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. You can
download all the code and supporting files (including this description) as a zip archive.
Files you'll edit:
search.py Where all of your search algorithms will reside.
searchAgents.py Where all of your search-based agents will reside.
Files you might want to look at:
pacman.py The main file that runs Pac-Man games. This file describes a Pac-Man
GameState type, which you use in this project.
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game.py The logic behind how the Pac-Man world works. This file describes
several supporting types like AgentState, Agent, Direction, and Grid.
util.py Useful data structures for implementing search algorithms.
Supporting files you can ignore:
graphicsDisplay.py Graphics for Pac-Man
graphicsUtils.py Support for Pac-Man graphics
textDisplay.py ASCII graphics for Pac-Man
ghostAgents.py Agents to control ghosts
keyboardAgents.py Keyboard interfaces to control Pac-Man
layout.py Code for reading layout files and storing their contents
What to submit: You will fill in portions of search.py and searchAgents.py during the
assignment. You should submit these two files (only) to the CSE 473 Dropbox.
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. We trust you all to submit your own work only; please don't let us down. If
you do, the department may pursue the strongest consequences available.
Getting Help: You are not alone! Feel free to use the class discussion board to discuss or get
clarifications on homework-related issues. If you find yourself stuck on something, go to office
hours or email the course staff for help. 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 to see how it
behaves.
Welcome to Pac-Man
After downloading the code (search.zip), unzipping it and changing to the search directory, you
should be able to play a game of Pac-Man by typing the following at the command line:
Note: Make sure you are running a recent version of Python (2.5 or later). If you get error
messages regarding python-tk, use your package manager to install python-tk, or see this page
for more detailed instructions.
Pac-Man lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this
world efficiently will be Pac-Man's first step in mastering its domain.
The simplest agent in searchAgents.py is called the GoWestAgent, which always goes West (a
trivial reflex agent). This agent can occasionally win:
But, things get ugly for this agent when turning is required:
python pacman.py
python pacman.py --layout testMaze --pacman GoWestAgent
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If pacman gets stuck, you can exit the game by typing CTRL-c into your terminal. Soon, your
agent will solve not only tinyMaze, but any maze you want. Note that pacman.py supports a
number of options that can each be expressed in a long way (e.g., --layout) or a short way
(e.g., -l). You can see the list of all options and their default values via:
Also, 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 bash
commands.txt.
Finding a Fixed Food Dot using Search Algorithms
In searchAgents.py, you'll find a fully implemented SearchAgent, which plans out a path through
Pac-Man's world and then executes that path step-by-step. The search algorithms for formulating
a plan are not implemented -- that's your job. As you work through the following questions, you
might need to refer to this glossary of objects in the code. First, test that the SearchAgent is
working correctly by running:
The command above tells the SearchAgent to use tinyMazeSearch as its search algorithm, which
is implemented in search.py. Pac-Man should navigate the maze successfully.
Now it's time to write full-fledged generic search functions to help Pac-Man 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 is to use 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 Stack, Queue and PriorityQueue types provided to you in
util.py!
Question 1 (10 points) Implement the depth-first search (DFS) algorithm in the
depthFirstSearch function in search.py. To make your algorithm complete, write the graph
search version of DFS, which avoids expanding any already visited states (R&N 3ed Section 3.3,
Figure 3.7).
Your code should quickly find a solution for:
The Pac-Man 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 Pac-Man actually go to all the explored squares on its way to the goal?
Hint: If you use a Stack as your data structure, the solution found by your DFS algorithm for
python pacman.py --layout tinyMaze --pacman GoWestAgent
python pacman.py -h
python pacman.py -l tinyMaze -p SearchAgent -a
fn=tinyMazeSearch
python pacman.py -l tinyMaze -p SearchAgent
python pacman.py -l mediumMaze -p SearchAgent
python pacman.py -l bigMaze -z .5 -p SearchAgent
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mediumMaze should have a length of 130 (provided you push successors onto the fringe in the
order provided by getSuccessors; you might get 244 if you push them in the reverse order). Is
this a least cost solution? If not, think about what depth-first search is doing wrong.
Question 2 (10 points) Implement the breadth-first search (BFS) algorithm in the
breadthFirstSearch function in search.py. Again, write a graph search algorithm that avoids
expanding any already visited states. Test your code the same way you did for depth-first search.
Does BFS find a least cost solution? If not, check your implementation.
Hint: If Pac-Man moves too slowly for you, try the option --frameTime 0.
Note: If you've written your search code generically, your code should work equally well for the
eight-puzzle search problem (R&N 3ed Section 3.2, Figure 3.4) without any changes.
Varying the Cost Function
While BFS will find a fewest-actions path to the goal, we might want to find paths that are "best"
in other senses. Consider mediumDottedMaze and mediumScaryMaze. By changing the cost
function, we can encourage Pac-Man to find different paths. For example, we can charge more for
dangerous steps in ghost-ridden areas or less for steps in food-rich areas, and a rational Pac-Man
agent should adjust its behavior in response.
Question 3 (10 points) Implement the uniform-cost search (UCS) algorithm in the
uniformCostSearch function in search.py. We encourage you to look through util.py for some
data structures that may be useful in your implementation. You should now observe successful
behavior in all three of the following layouts, where the agents below are all UCS agents that
differ only in the cost function they use (the agents and cost functions are written for you):
Note: You should get very low and very high path costs for the StayEastSearchAgent and
StayWestSearchAgent respectively, due to their exponential cost functions (see searchAgents.py
for details).
A* search
Question 4 (15 points) Implement A* graph search in the empty function aStarSearch in
search.py. A* takes a heuristic function as an argument. Heuristics take two arguments: a state
in the search problem (the main argument), and the problem itself (for reference information).
The nullHeuristic heuristic function in search.py is a trivial example.
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
manhattanHeuristic in searchAgents.py).
You should see that A* finds the optimal solution slightly faster than uniform cost search (about
python pacman.py -l mediumMaze -p SearchAgent -a fn=bfs
python pacman.py -l bigMaze -p SearchAgent -a fn=bfs -z .5
python eightpuzzle.py
python pacman.py -l mediumMaze -p SearchAgent -a fn=ucs
python pacman.py -l mediumDottedMaze -p StayEastSearchAgent
python pacman.py -l mediumScaryMaze -p StayWestSearchAgent
python pacman.py -l bigMaze -z .5 -p SearchAgent -a
fn=astar,heuristic=manhattanHeuristic
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549 vs. 620 search nodes expanded in our implementation, but ties in priority may make your
numbers differ slightly). What happens on openMaze for the various search strategies?
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 tinyCorners takes 28 steps.
Question 5 (10 points) Implement the CornersProblem search problem in searchAgents.py.
You will need to choose a state representation that encodes all the information necessary to
detect whether all four corners have been reached. Now, your search agent should solve:
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 Pac-Man GameState as a search state. Your code will be very, very slow if you do (and also
wrong).
Hint: The only parts of the game state you need to reference in your implementation are the
starting Pac-Man position and the location of the four corners.
Our implementation of breadthFirstSearch expands just under 2000 search nodes on
mediumCorners. However, heuristics (used with A* search) can reduce the amount of searching
required.
Question 6 (15 points) Implement a heuristic for the CornersProblem in cornersHeuristic.
Grading: inadmissible heuristics will get no credit. 5 points for any admissible heuristic. 5 points
for expanding fewer than 1600 nodes. 5 points for expanding fewer than 1200 nodes. Expand
fewer than 800, and you're doing great!
Hint: Remember, heuristic functions just return numbers, which, to be admissible, must be lower
bounds on the actual shortest path cost to the nearest goal.
Note: AStarCornersAgent is a shortcut for -p SearchAgent -a
fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic.
Eating All The Dots
Now we'll solve a hard search problem: eating all the Pac-Man food in as few steps as possible.
For this, we'll need a new search problem definition which formalizes the food-clearing problem:
FoodSearchProblem in searchAgents.py (implemented for you). A solution is defined to be a
path that collects all of the food in the Pac-Man world. For the present project, solutions do not
take into account any ghosts or power pellets; solutions only depend on the placement of walls,
regular food and Pac-Man. (Of course ghosts can ruin the execution of a solution! We'll get to that
in the next project.) If you have written your general search methods correctly, A* with a null
heuristic (equivalent to uniform-cost search) should quickly find an optimal solution to testSearch
with no code change on your part (total cost of 7).
AStarFoodSearchAgent -p SearchAgent -a
python pacman.py -l tinyCorners -p SearchAgent -a
fn=bfs,prob=CornersProblem
python pacman.py -l mediumCorners -p SearchAgent -a
fn=bfs,prob=CornersProblem
python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5
python pacman.py -l testSearch -p AStarFoodSearchAgent
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Note: is a shortcut for
fn=astar,prob=FoodSearchProblem,heuristic=foodHeuristic.
You should find that UCS starts to slow down even for the seemingly simple tinySearch. As a
reference, our implementation takes 2.5 seconds to find a path of length 27 after expanding 4902
search nodes.
Question 7 (20 points) Fill in foodHeuristic in searchAgents.py with a consistent heuristic for
the FoodSearchProblem. Try your agent on the trickySearch board:
Our UCS agent finds the optimal solution in about 13 seconds, exploring over 16,000 nodes. If
your heuristic is admissible, you will receive the following score, depending on how many nodes
your heuristic expands.
Fewer nodes than: Points
15000 5
12000 15
9000 20 (medium hard)
7000 +5 extra credit (hard)
If your heuristic is inadmissible, you will receive no credit, so be careful! Think through
admissibility carefully, as inadmissible heuristics may manage to produce fast searches and even
optimal paths. Can you solve mediumSearch in a short time? If so, we're either very, very
impressed, or your heuristic is inadmissible.
Admissibility vs. Consistency? Technically, admissibility isn't enough to guarantee correctness in
graph search -- you need the stronger condition of consistency. For a heuristic to be consistent, it
must hold that if an action has cost c, then taking that action can only cause a drop in heuristic
of at most c. If your heuristic is not only admissible, but also consistent, you will receive 5 points
extra credit.
Almost always, admissible heuristics are also consistent, especially if they are derived from
problem relaxations. Therefore it is probably 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. Inconsistency can sometimes be detected by verifying that your returned
solutions are non-decreasing in f-value. Morevoer, if UCS and A* ever return paths of different
lengths, your heuristic is inconsistent.
Suboptimal Search
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 eats the closest dot. ClosestDotSearchAgent is implemented for you
in searchAgents.py, but it's missing a key function that finds a path to the closest dot.
Question 8 (10 points) Implement the function findPathToClosestDot in searchAgents.py.
Our agent solves this maze (suboptimally!) in under a second with a path cost of 350:
Hint: The quickest way to complete findPathToClosestDot is to fill in the
AnyFoodSearchProblem, which is missing its goal test. Then, solve that problem with an
appropriate search function. The solution should be very short!
Your ClosestDotSearchAgent won't always find the shortest possible path through the maze. (If
you don't understand why, ask a TA!) In fact, you can do better if you try.
Mini Contest (10 points extra credit) Implement an ApproximateSearchAgent in
searchAgents.py that finds a short path through the bigSearch layout. Students who find the
shortest path using no more than 30 seconds of computation will receive 10 extra credit points.
python pacman.py -l trickySearch -p AStarFoodSearchAgent
python pacman.py -l bigSearch -p ClosestDotSearchAgent -z .5
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We will time your agent using the no graphics option -q, and it must complete in under 30
seconds on our grading machines. Please describe what your agent is doing in a comment! We
reserve the right to give additional extra credit to creative solutions, even if they don't work that
well. Don't hard-code the path, of course.
Object Glossary
Here's a glossary of the key objects in the code base related to search problems, for your
reference:
SearchProblem (search.py)
A SearchProblem is an abstract object that represents the state space, successor function,
costs, and goal state of a problem. You will interact with any SearchProblem only through
the methods defined at the top of search.py
PositionSearchProblem (searchAgents.py)
A specific type of SearchProblem that you will be working with --- it corresponds to
searching for a single food dot in a maze.
CornersProblem (searchAgents.py)
A specific type of SearchProblem that you will define --- it corresponds to searching for a
path through all four corners of a maze.
FoodSearchProblem (searchAgents.py)
A specific type of SearchProblem that you will be working with --- it corresponds to
searching for a way to eat all the food dots in a maze.
Search Function
A search function is a function which takes an instance of SearchProblem as a parameter,
runs some algorithm, and returns a sequence of actions that lead to a goal. Example of
search functions are depthFirstSearch and breadthFirstSearch, which you have to write.
You are provided tinyMazeSearch which is a very bad search function that only works
correctly on tinyMaze
SearchAgent
SearchAgent is is a class which implements an Agent (an object that interacts with the
world) and does its planning through a search function. The SearchAgent first uses the
search function provided to make a plan of actions to take to reach the goal state, and
then executes the actions one at a time.
python pacman.py -l bigSearch -p ApproximateSearchAgent -z .5
-q