Project 1: Search in Pacman
{width="400px"} All those colored walls,
Mazes give Pacman the blues,
So teach him to search.
Introduction
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. 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 Pacman games. This file describes a Pacman GameState type, which you use in this project.
game.py
The logic behind how the Pacman 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 Pacman
graphicsUtils.py
Support for Pacman graphics
textDisplay.py
ASCII graphics for Pacman
ghostAgents.py
Agents to control ghosts
keyboardAgents.py
Keyboard interfaces to control Pacman
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) along with a partners.txt
file. Type submit p1
to
submit your code. Here are directions for
submitting and setting up your
account.
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 Pacman
After downloading the code (search.zip), unzipping it and changing to the search directory, you should be able to play a game of Pacman by typing the following at the command line:
python pacman.py
Note: if you get error messages regarding python-tk, use your package manager to install python-tk, or see this page for more detailed instructions. Pacman 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 GoWestAgent
, which always goes West (a trivial reflex
agent). This agent can occasionally win:
python pacman.py --layout testMaze --pacman GoWestAgent
But, things get ugly for this agent when turning is required:
python pacman.py --layout tinyMaze --pacman GoWestAgent
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:
python pacman.py -h
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 Pacman’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:
python pacman.py -l tinyMaze -p SearchAgent -a fn=tinyMazeSearch
The command above tells the SearchAgent
to use tinyMazeSearch
as its
search algorithm, which is implemented in search.py
. Pacman should
navigate the maze successfully.
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 Stack, Queue
and PriorityQueue
types provided to you in util.py
!
Question 1 (2 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 (textbook section 3.5).
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 SearchAgent
The 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 Stack
as your data structure, the solution found
by your DFS algorithm for 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 (1 point) 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.
python pacman.py -l mediumMaze -p SearchAgent -a fn=bfs
python pacman.py -l bigMaze -p SearchAgent -a fn=bfs -z .5
Does BFS find a least cost solution? If not, check your implementation.
Hint: If Pacman 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 (textbook section 3.2) without any changes.
python eightpuzzle.py
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
Pacman 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 Pacman agent should adjust its behavior in
response.
Question 3 (2 points) Implement the uniform-cost graph search
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):
python pacman.py -l mediumMaze -p SearchAgent -a fn=ucs
python pacman.py -l mediumDottedMaze -p StayEastSearchAgent
python pacman.py -l mediumScaryMaze -p StayWestSearchAgent
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 (3 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
).
python pacman.py -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=manhattanHeuristic
You 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 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 (2 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:
python pacman.py -l tinyCorners -p SearchAgent -a fn=bfs,prob=CornersProblem
python pacman.py -l mediumCorners -p SearchAgent -a fn=bfs,prob=CornersProblem
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 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 Pacman 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 (3 points) Implement a non-trivial, consistent
heuristic for the CornersProblem
in cornersHeuristic
. Grading:
inconsistent heuristics will get no credit. 1 point for any
non-trivial consistent heuristic. 1 point for expanding fewer than 1600
nodes. 1 point for expanding fewer than 1200 nodes. Expand fewer than
800, and you’re doing great!
python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5
Note: AStarCornersAgent
is a shortcut for
-p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic
.
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. Morevoer, 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 Dots
Now 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:
FoodSearchProblem
in searchAgents.py
(implemented for you). A
solution is defined to be a path that collects all of the food in the
Pacman 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 Pacman. (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).
python pacman.py -l testSearch -p AStarFoodSearchAgent
Note: AStarFoodSearchAgent
is a shortcut for
-p SearchAgent -a 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 (5 points) Fill in foodHeuristic
in searchAgents.py
with a consistent heuristic for the FoodSearchProblem
. Try your agent
on the trickySearch
board:
python pacman.py -l trickySearch -p AStarFoodSearchAgent
Our UCS agent finds the optimal solution in about 13 seconds, exploring over 16,000 nodes. Any non-trivial consistent heuristic will receive 1 point. You will also receive the following additional points, depending on how few nodes your heuristic expands.
Fewer nodes than: Points
15000 1 12000 2 9000 3 (medium) 7000 4 (hard)
Remember: If your heuristic is inconsistent, you will receive no
credit, so be careful! Can you solve mediumSearch
in a short time? If
so, we’re either very, very impressed, or your heuristic is
inconsistent.
We will deduct 1 point for any heuristic that returns negative values, or does not return 0 at every goal state.
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 greedily 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 (2 points) Implement the function
findPathToClosestDot
in searchAgents.py
. Our agent solves this maze
(suboptimally!) in under a second with a path cost of 350:
python pacman.py -l bigSearch -p ClosestDotSearchAgent -z .5
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 GSI!) In
fact, you can do better if you try.
Mini Contest (2 points extra credit) Implement an
ApproximateSearchAgent
in searchAgents.py
that finds a short path
through the bigSearch
layout. The three teams that find the shortest
path using no more than 30 seconds of computation will receive 2 extra
credit points and an in-class demonstration of their brilliant Pacman
agents.
python pacman.py -l bigSearch -p ApproximateSearchAgent -z .5 -q
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]{#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 pellet 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 pellets 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 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.