Project 2: Multi-Agent Search
The goal of this project is to help you better understand multiagent search problems and adversarial search algorithms.
Figure 1: Pacman, now with ghosts. Minimax, Expectimax, Evaluation.
In this project, you will design agents for the classic version of Pacman,
including ghosts. Along the way, you will implement both minimax and
expectimax search and try your hand at evaluation function design.
The code base has not changed much from the previous project, but please
start with a fresh installation, rather than intermingling files from project 1.
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 as a zip archive in the folder VE492 Projects on Canvas.
Files to Edit and Submit: You will fill in portions of multiAgents.py
during the assignment. Please do not change the other files in this distribution or submit any of our original files other than these files.
Files you’ll edit:
multiAgents.py Where all of your multi-agent search agents will
Files you might want to look at:
The main file that runs Pacman games. This file
describes a Pacman GameState type, which you
use in this project.
The logic behind how the Pacman world works.
This file describes several supporting types like
AgentState, Agent, Direction, and Grid.
Useful data structures for implementing search
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
Code for reading layout files and storing their
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 online judge’s judgements – 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, but also codes found on internet, 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 and the discussion forum on
Piazza 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.
Discussion: Please be careful not to post spoilers.
Welcome to Multi-Agent Pacman
After downloading the code (P2.zip), unzipping it, and changing to the directory, you should be able to play a game of Pacman by typing the following
at the command line:
and using the arrow keys to move. Now, run the provided ReflexAgent in
python pacman.py -p ReflexAgent
Note that it plays quite poorly even on simple layouts:
python pacman.py -p ReflexAgent -l testClassic
Inspect its code (in multiAgents.py) and make sure you understand what
Question 1 (4 points): Reflex Agent
Improve the ReflexAgent in multiAgents.py to play respectably. The provided reflex agent code provides some helpful examples of methods that query
the GameState for information. A capable reflex agent will have to consider
both food locations and ghost locations to perform well. Your agent should
easily and reliably clear the testClassic layout:
python pacman.py -p ReflexAgent -l testClassic
Try out your reflex agent on the default mediumClassic layout with one
ghost or two (and animation off to speed up the display):
python pacman.py –frameTime 0 -p ReflexAgent -k 1
python pacman.py –frameTime 0 -p ReflexAgent -k 2
How does your agent fare? It will likely often die with 2 ghosts on the default
board, unless your evaluation function is quite good.
Note: Remember that newFood has the function asList()
Note: As features, try the reciprocal of important values (such as distance
to food) rather than just the values themselves.
Note: The evaluation function you’re writing is evaluating state-action pairs;
in later parts of the project, you’ll be evaluating states.
Note: You may find it useful to view the internal contents of various objects
for debugging. You can do this by printing the objects’ string representations.
For example, you can print newGhostStates with print(newGhostStates).
Options: Default ghosts are random; you can also play for fun with slightly
smarter directional ghosts using -g DirectionalGhost. If the randomness
is preventing you from telling whether your agent is improving, you can use
-f to run with a fixed random seed (same random choices every game). You
can also play multiple games in a row with -n. Turn off graphics with -q to
run lots of games quickly.
Grading: We will run your agent on the openClassic layout 10 times. You
will receive full points if your agent’s average score is greater than 1000.
Don’t spend too much time on this question, though, as the meat of the
project lies ahead.
Question 2 (5 points): Minimax
Now you will write an adversarial search agent in the provided MinimaxAgent
class stub in multiAgents.py. Your minimax agent should work with any
number of ghosts, so you’ll have to write an algorithm that is slightly more
general than what you’ve previously seen in lecture. In particular, your
minimax tree will have multiple min layers (one for each ghost) for every
Your code should also expand the game tree to an arbitrary depth. Score the
leaves of your minimax tree with the supplied self.evaluationFunction,
which defaults to scoreEvaluationFunction. MinimaxAgent extends
MultiAgentSearchAgent, which gives access to self.depth and
self.evaluationFunction. Make sure your minimax code makes reference
to these two variables where appropriate as these variables are populated in
response to command line options.
Important: A single search ply is considered to be one Pacman move and all
the ghosts’ responses, so depth 2 search will involve Pacman and each ghost
moving two times.
Grading: We will be checking your code to determine whether it explores the
correct number of game states. This is the only reliable way to detect some
very subtle bugs in implementations of minimax.
Hints and Observations
• Hint: Implement the algorithm recursively using helper function(s).
• The correct implementation of minimax will lead to Pacman losing the
game in some tests. This is not a problem: as it is correct behaviour,
it will pass the tests.
• The evaluation function for the Pacman test in this part is already written (self.evaluationFunction). You shouldn’t change this function,
but recognize that now we’re evaluating states rather than actions, as
we were for the reflex agent. Look-ahead agents evaluate future states
whereas reflex agents evaluate actions from the current state.
• The minimax values of the initial state in the minimaxClassic layout
are 9, 8, 7, -492 for depths 1, 2, 3 and 4 respectively. Note that your
minimax agent will often win (665/1000 games for us) despite the dire
prediction of depth 4 minimax.
python pacman.py -p MinimaxAgent -l minimaxClassic -a\
• Pacman is always agent 0, and the agents move in order of increasing
• All states in minimax should be GameStates, either passed in to getAction
or generated via GameState.generateSuccessor. In this project, you
will not be abstracting to simplified states.
• On larger boards such as openClassic and mediumClassic (the default), you’ll find Pacman to be good at not dying, but quite bad at
winning. He’ll often thrash around without making progress. He might
even thrash around right next to a dot without eating it because he
doesn’t know where he’d go after eating that dot. Don’t worry if you
see this behavior, question 5 will clean up all of these issues.
• When Pacman believes that his death is unavoidable, he will try to
end the game as soon as possible because of the constant penalty for
living. Sometimes, this is the wrong thing to do with random ghosts,
but minimax agents always assume the worst:
python pacman.py -p MinimaxAgent -l trappedClassic -a\
Make sure you understand why Pacman rushes the closest ghost in this case.
Question 3 (5 points): Alpha-Beta Pruning
Make a new agent that uses alpha-beta pruning to more efficiently explore
the minimax tree, in AlphaBetaAgent. Again, your algorithm will be slightly
more general than the pseudocode from lecture, so part of the challenge is
to extend the alpha-beta pruning logic appropriately to multiple minimizer
You should see a speed-up (perhaps depth 3 alpha-beta will run as fast as
depth 2 minimax) Ideally, depth 3 on smallClassic should run in just a few
seconds per move or faster.
python pacman.py -p AlphaBetaAgent -a depth=3 -l smallClassic
The AlphaBetaAgent minimax values should be identical to the MinimaxAgent
minimax values, although the actions it selects can vary because of different tie-breaking behavior Again, the minimax values of the initial state in
the minimaxClassic layout are 9, 8, 7 and -492 for depths 1, 2, 3 and 4
Grading: Because we check your code to determine whether it explores the
correct number of states, it is important that you perform alpha-beta pruning
without reordering children. In other words, successor states should always
be processed in the order returned by GameState.getLegalActions. Again,
do not call GameState.generateSuccessor more than necessary.
The pseudo-code below represents the algorithm you should implement for
Question 4 (5 points): Expectimax
Minimax and alpha-beta are great, but they both assume that you are playing against an adversary who makes optimal decisions. As anyone who has
ever won tic-tac-toe can tell you, this is not always the case. In this question you will implement the ExpectimaxAgent, which is useful for modeling
probabilistic behavior of agents who may make suboptimal choices.
As with the search and constraint satisfaction problems covered so far in this
class, the beauty of these algorithms is their general applicability.
Random ghosts are of course not optimal minimax agents, and so modeling
them with minimax search may not be appropriate. ExpectimaxAgent, will
no longer take the min over all ghost actions, but the expectation according
to your agent’s model of how the ghosts act. To simplify your code, assume
you will only be running against an adversary which chooses amongst their
getLegalActions uniformly at random.
To see how the ExpectimaxAgent behaves in Pacman, run:
python pacman.py -p ExpectimaxAgent -l minimaxClassic -a depth=3
You should now observe a more cavalier approach in close quarters with
ghosts. In particular, if Pacman perceives that he could be trapped but
might escape to grab a few more pieces of food, he’ll at least try. Investigate
the results of these two scenarios:
python pacman.py -p AlphaBetaAgent -l trappedClassic -a depth=3\
-q -n 10
python pacman.py -p ExpectimaxAgent -l trappedClassic -a depth=3\
-q -n 10
You should find that your ExpectimaxAgent wins about half the time, while
your AlphaBetaAgent always loses. Make sure you understand why the behavior here differs from the minimax case.
The correct implementation of expectimax will lead to Pacman losing some
of the tests. This is not a problem: as it is correct behaviour, it will pass the
Question 5 (6 points): Evaluation Function
Write a better evaluation function for pacman in the provided function
betterEvaluationFunction. The evaluation function should evaluate states,
rather than actions like your reflex agent evaluation function did. You may
use any tools at your disposal for evaluation, including your search code from
the last project. With depth 2 search, your evaluation function should clear
the smallClassic layout with one random ghost more than half the time and
still run at a reasonable rate (to get full credit, Pacman should be averaging
around 1000 points when he’s winning).
Grading: OJ will run your agent on the smallClassic layout 10 times. We
will assign points to your evaluation function in the following way:
• Win at least once without timing out the OJ
• Winning all 10 times.
• An average score of at least 1000
• Take on average less than 30 seconds on OJ
Submission and Due Date
Submit it to online judge, see the announcement later.