Project 1: Search in Pac-Man

Project 1: Search in Pac-Man
All those colored walls,
Mazes give Pac-Man the blues,
So teach him to search.
Introduction
In this project, your Pac-Man 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 Pac-Man 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 as a zip archive from the Canvas page. Note that in order to display the pretty graphics, the
easiest options are either run the code in the MCS computer lab or install python on your own computer.
The latter option is recommended as it will make your life easier in the long run.
Files you will edit:
search.py Where all of your search algorithms will reside
searchAgents.py Where all of your search based agents will reside.
Files you will 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.
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
graphicUtils.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
Getting Started
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:
python pacman.py
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.
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 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. 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 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 (R&N 3ed Section 3.3, Figure 3.7).
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 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 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 (2 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 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.
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 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 (3 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 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 (3 points) Implement a heuristic for the CornersProblem in cornersHeuristic. Grading: inadmissible heuristics will get no credit. 1 point for any admissible 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
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).
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 (3 + 1 points) Fill in foodHeuristic in searchAgents.py with an admissible and 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. If your heuristic
is admissible, you will receive the following score, depending on how many nodes your heuristic expands.
Fewer nodes than: Points
15000 1
12000 2
9000 3 (hard)
7000 +1 extra credit (very 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 1 additional point for this question.
Almost always, admissible heuristics are also consistent, especially if they are derived from problem relaxations. Therefore it is probably easiest to start out by thinking about 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. 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!
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 (2 points) Implement the function findPathToClosestDot in searchAgents.py. Our
agent solves this maze (sub-optimally!) 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!) 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 agents 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 Pac-Man 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
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 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.