Project 2: Multi-Agent Pac-Man Solution





In this project, you will design agents for the classic version of Pac-Man, including ghosts. Along the way, you will implement both minimax and expectimax search and try your hand at evaluation function design.

The code for this project is available as a zip file on eCommons

Key files to read Where all of your multi-agent search agents will reside. The main file that runs Pac-Man games. This file also describes a Pac-Man GameState type, which you will use extensively in this project The logic behind how the Pac-Man world works. This file describes several supporting types like AgentState, Agent, Direction, and Grid. Useful data structures for implementing search algorithms.
Files you can ignore Graphics for Pac-Man Support for Pac-Man graphics ASCII graphics for Pac-Man Agents to control ghosts Keyboard interfaces to control Pac-Man Code for reading layout files and storing their contents


What to submit: You will fill in portions of during the assignment. You may also submit supporting files (like, etc.) that you use in your code. Please do not change the other files in this distribution or submit any of our original files other than Directions for submission will be like the other assignments, and are given in the instructions file under ‘resources’ in eCommons.

How/Where to submit:

You should submit the file (and other supporting files) with your code and comments on the CMPS140 autograder server:

Your submission should be placed in a Zip archive titled On Unix systems, you can zip your solution with the following command:


If you have supporting files (,, etc.) you can Zip them by adding the names of those files as additional arguments:

zip …

Evaluation: Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. For all programming assignments, we will grade you on both correctness and style. Here’s a description of each category and the value that will be assigned: Correctness (20 points or 25 points): This is the portion of the grade we derive from the auto-grader. Note that the auto-grader assigns partial credit to solutions that are correct but do not perform as well (based on some specified criteria) as the best-proposed solution to date. This is the core of the assignment. Documentation/Style (5 points): Additionally, we will assign 5 points based on the detail of your comments for sections of code that you edit.

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, use the discussion boards or go to office hours. We want these projects to be rewarding and instructional, not frustrating and demoralizing.

Forums: Post your questions (but not project solutions) on Piazza.

Collaboration Policy You can collaborate, but you still need to do the final work independently, turn in your own code, and you are responsible for understanding every line written and submitted.

Running code on the UCSC Unix Servers: In order to run the Pac-Man code on the Unix servers, you must first make sure you have an Xwindow server installed on your local machine. For Mac OS X, you will want to install XQuartz ( For Windows, we recommend installing Xming and follow this installation guide, Once you have an Xwindow server installed, you must ssh with the -X flag to enable graphics forwarding, as follows:

ssh -X

To verify that you have installed the Xserver correctly and the graphics forwarding is turned on, run the following command for a graphics demonstration:



Multi-Agent Pac-Man

First, play a game of classic Pac-Man:


Now, run the provided ReflexAgent in

python -p ReflexAgent

Note that it plays quite poorly even on simple layouts:

python -p ReflexAgent -l testClassic

Inspect its code (in and make sure you understand what it’s doing.

Question 1 (3 points)  Improve the ReflexAgent in 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 -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 –frameTime 0 -p ReflexAgent -k 1

python –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: you can never have more ghosts than the layout permits.

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.

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.

The autograder will check that your agent can rapidly clear the openClassic layout ten times without dying more than twice or thrashing around infinitely (i.e. repeatedly moving back and forth between two positions, making no progress).

python -p ReflexAgent -l openClassic -n 10 -q

Don’t spend too much time on this question, though, as the meat of the project lies ahead.

Question 2 (5 points) Now you will write an adversarial search agent in the provided MinimaxAgentclass stub in 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 appears in the textbook. In particular, your minimax tree will have multiple min layers (one for each ghost) for every max layer.

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 MultiAgentAgent, 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 Pac-Man move and all the ghosts’ responses, so depth 2 search will involve Pac-Man and each ghost moving two times.

Hints and Observations

  • The evaluation function in this part is already written (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 -p MinimaxAgent -l minimaxClassic -a depth=4

  • To increase the search depth achievable by your agent, remove the STOP action from Pac-Man’s list of possible actions. Depth 2 should be pretty quick, but depth 3 or 4 will be slow. Don’t worry, the next question will speed up the search somewhat.
  • Pac-Man is always agent 0, and the agents move in order of increasing agent index.
  • All states in minimax should be GameStates, either passed in to getAction or generated via 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 Pac-Man 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 Pac-Man 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 -p MinimaxAgent -l trappedClassic -a depth=3

Make sure you understand why Pac-Man rushes the closest ghost in this case.

Question 3 (3 points) 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 pseudo-code in the textbook, so part of the challenge is to extend the alpha-beta pruning logic appropriately to multiple minimizer agents.

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 -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 respectively.

Question 4 (3 points) Random ghosts are of course not optimal minimax agents, and so modeling them with minimax search may not be appropriate. Fill in ExpectimaxAgent, where your agent agent 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 RandomGhost ghosts, which choose amongst their getLegalActions uniformly at random.

You should now observe a more cavalier approach in close quarters with ghosts. In particular, if Pac-Man 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 -p AlphaBetaAgent -l trappedClassic -a depth=3 -q -n 10

python -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.

Question 5 (6 points) Write a better evaluation function for pacman in the provided functionbetterEvaluationFunction. 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 two random ghosts more than half the time and still run at a reasonable rate (to get full credit, Pac-Man should be averaging around 1000 points when he’s winning).

python -l smallClassic -p ExpectimaxAgent -a evalFn=better -q -n 10

Document your evaluation function! We’re very curious about what great ideas you have, so don’t be shy. We reserve the right to reward bonus points for clever solutions and show demonstrations in class.

Hints and Observations

  • As for your reflex agent evaluation function, you may want to use the reciprocal of important values (such as distance to food) rather than the values themselves.
  • One way you might want to write your evaluation function is to use a linear combination of features. That is, compute values for features about the state that you think are important, and then combine those features by multiplying them by different values and adding the results together. You might decide what to multiply each feature by based on how important you think it is.

Mini Contest (3 points extra credit) Pac-Man’s been doing well so far, but things are about to get a bit more challenging. This time, we’ll pit Pac-Man against smarter foes in a trickier maze. In particular, the ghosts will actively chase Pac-Man instead of wandering around randomly, and the maze features more twists and dead-ends, but also extra pellets to give Pac-Man a fighting chance. You’re free to have Pac-Man use any search procedure, search depth, and evaluation function you like. The only limit is that games can last a maximum of 3 minutes (with graphics off), so be sure to use your computation wisely. We’ll run the contest with the following command:

python -l contestClassic -p ContestAgent -g DirectionalGhost -q -n 10

The three students with the highest score (details: we run 10 games, games longer than 3 minutes get score 0, lowest and highest 2 scores discarded, the rest averaged) will receive 3, 2, and 1 extra credit points respectively and can look on with pride as their Pac-Man agents are shown off in class. Be sure to document what your agent is doing, as we may award additional extra credit to creative solutions even if they’re not in the top 3.

Project 2 is done. Go Pac-Man!


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