Project 1: Search

Project 1: Search 
Table of Contents
Introduction
Welcome
Q1: Depth First Search
Q2: Breadth First Search
Q3: Uniform Cost Search
Q4: A* Search
Q5: Corners Problem: Representation
Q6: Corners Problem: Heuristic
Q7: Eating All The Dots: Heuristic
Q8: Suboptimal Search
Submission
All those colored walls,
Mazes give Pacman the blues,
So teach him to search.
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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.
As in Project 0, this project includes an autograder for you to grade your
answers on your machine. This can be run with the command:
python autograder.py
See the autograder tutorial in Project 0 for more information about using the
autograder.
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 (search.zip).
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
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keyboardAgents.py Keyboard interfaces to control Pacman
layout.py Code for reading layout files and storing their contents
autograder.py Project autograder
testParser.py Parses autograder test and solution files
testClasses.py General autograding test classes
test_cases/ Directory containing the test cases for each question
searchTestClasses.py Project 1 specific autograding test classes
Files to Edit and Submit: You will fill in portions of search.py and
searchAgents.py during the assignment. You should submit these files with
your code and comments. Please do not change the other files in this
distribution or submit any of our original files other than these files.
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 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 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 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 Pacman
After downloading the code ( search.zip (https://inst.eecs.berkeley.edu
/~cs188/fa18/assets/files/search.zip) ), unzipping it, and changing to the
directory, you should be able to play a game of Pacman by typing the following
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at the command line:
python pacman.py
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 .
Question 1 (3 points): Finding a Fixed Food Dot using
Depth First Search
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 find it useful to
refer to the object glossary (the second to last tab in the navigation bar above).
First, test that the SearchAgent is working correctly by running:
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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. 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).
Important note: Make sure to use the Stack , Queue and PriorityQueue data
structures provided to you in util.py ! These data structure implementations
have particular properties which are required for compatibility with the
autograder.
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).
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.
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
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successors onto the fringe in the order provided by getSuccessors; you might
get 246 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 (3 points): Breadth First Search
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 without any changes.
python eightpuzzle.py
Question 3 (3 points): 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.
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):
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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).
Question 4 (3 points): A* search
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?
Question 5 (3 points): 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.
Note: Make sure to complete Question 2 before working on Question 5, because
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Question 5 builds upon your answer for Question 2.
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): Corners Problem: Heuristic
Note: Make sure to complete Question 4 before working on Question 6, because
Question 6 builds upon your answer for Question 4.
Implement a non-trivial, consistent heuristic for the CornersProblem in
cornersHeuristic .
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
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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. Moreover, if UCS and A* ever return paths of different lengths,
your heuristic is inconsistent. This stuff is tricky!
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).
Grading: Your heuristic must be a non-trivial non-negative consistent heuristic
to receive any points. Make sure that your heuristic returns 0 at every goal
state and never returns a negative value. Depending on how few nodes your
heuristic expands, you'll be graded:
Number of nodes expanded Grade
more than 2000 0/3
at most 2000 1/3
at most 1600 2/3
at most 1200 3/3
Remember: If your heuristic is inconsistent, you will receive no credit, so be
careful!
Question 7 (4 points): 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
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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 5057 search nodes.
Note: Make sure to complete Question 4 before working on Question 7, because
Question 7 builds upon your answer for Question 4.
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 non-negative consistent heuristic will receive 1 point. Make sure
that your heuristic returns 0 at every goal state and never returns a negative
value. Depending on how few nodes your heuristic expands, you'll get
additional points:
Number of nodes expanded Grade
more than 15000 1/4
at most 15000 2/4
at most 12000 3/4
at most 9000 4/4 (full credit; medium)
at most 7000 5/4 (optional extra credit; 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.
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Question 8 (3 points): 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.
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. Make sure you understand why and try to come up with a
small example where repeatedly going to the closest dot does not result in
finding the shortest path for eating all the dots.
Submission
In order to submit your project, please upload the following files to Canvas:
search.py and searchAgents.py . Please do not upload the files in a zip file or a
directory.
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