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COMP7404 - Assignment 1
This assignment is based on materials by http://ai.berkeley.edu.
Introduction
In this part of the assignment, you will build informed, uninformed and local search algorithms
and apply them to Pacman and the 8-Queens problem.
Like in Assignment 0, this project includes an autograder for you to mark your answers. This
can be run with the command
python autograder.py
See the autograder tutorial in Assignment 0 for more information about using the autograder.
Important: The assignments in this course have been tested with python 3.6.10. Install
and activate this version as follows.
>>> conda create -n py36 python=3.6 anaconda
>>> conda activate py36
>>> python
Python 3.6.10 |Anaconda, Inc.| (default, May 7 2020, 19:46:08) [MSC v.1916
64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
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.
Related Files
Files you'll edit and submit
File Description
search.py Where all of your search algorithms will reside
searchAgents.py Where all of your search-based agents will reside
solveEightQueens.py Where all you local search algorithms go
Files you might want to look at
File Description
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
File Description
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
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 Autograding test classes
Requirements
Files to Edit and Submit: You will fill in portions of search.py, searchAgents.py and
solveEightQueens.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 may wreak havoc on the
autograder.
Academic Dishonesty: We will be checking your code against other submissions in the class
and from the 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, please submit
questions to the forum.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 Forum: Please be careful not to post spoilers. Please don't post any code that is
directly related to the assignments. However you are welcome and encouraged to discuss
general ideas.
Submission: Submit your code search.py, searchAgents.py, solveEightQueens.py as
a1_ID.zip file to moodle (ID is your university number).
You will get zero mark if
● you submit the wrong files
● you copy another student's answer
● your zip file's name does not follow the format a1_ID.zip
● Your zip uses any other file format than ZIP
● your program contains an infinite loop
Check your files before the submission.
Welcome to Pacman
Playing Pacman with the keyboard
After downloading the code, 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.
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.
A predefined simple agent
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
Pacman options
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. Below I list some of the most useful options in this
assignment.
Usage:
USAGE: python pacman.py
EXAMPLES: (1) python pacman.py
- starts an interactive game
(2) python pacman.py --layout smallClassic --zoom 2
- starts an interactive game on a smaller board, zoomed in
Options:
-h, --help show this help message and exit
-l LAYOUT_FILE, --layout=LAYOUT_FILE
the LAYOUT_FILE from which to load the map layout
[Default: mediumClassic]
-p TYPE, --pacman=TYPE
the agent TYPE in the pacmanAgents module to use
[Default: KeyboardAgent]
-z ZOOM, --zoom=ZOOM Zoom the size of the graphics window [Default: 1.0]
-a AGENTARGS, --agentArgs=AGENTARGS
Comma separated values sent to agent. e.g.
"opt1=val1,opt2,opt3=val3"
--frameTime=FRAMETIME
Time to delay between frames; <0 means keyboard
[Default: 0.1]
Different kinds of layout
In the layouts/ directory, you can find multiple predefined layouts. You can set the --layout
option to one of the following layout (please do not include .lay).
bigCorners.lay contestClassic.lay mediumMaze.lay openClassic.lay
smallSafeSearch.lay tinyMaze.lay bigMaze.lay contoursMaze.lay
mediumSafeSearch.lay openMaze.lay smallSearch.lay tinySafeSearch.lay
bigSafeSearch.lay greedySearch.lay mediumScaryMaze.lay openSearch.lay
testClassic.lay tinySearch.lay bigSearch.lay mediumClassic.lay
mediumSearch.lay originalClassic.lay testMaze.lay trappedClassic.lay
boxSearch.lay mediumCorners.lay minimaxClassic.lay smallClassic.lay
testSearch.lay trickyClassic.lay capsuleClassic.lay mediumDottedMaze.lay
oddSearch.lay smallMaze.lay tinyCorners.lay trickySearch.lay
Exit the Game
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.
Also, all of the commands that appear in this assignment also appear in commands.txt, for
easy copying and pasting.
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 find it useful to refer to the object glossary. Here's a glossary of the key
objects in the code 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 (search.py)
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 (searchAgents.py)
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.
Next, 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!
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 1: 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 2: 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 frontier 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).
Question 1 (2 points): Depth First Search
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 -a fn=dfs
python pacman.py -l mediumMaze -p SearchAgent # -a fn=dfs can be omitted,
default option
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 frontier 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 (2 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.
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 (2 points): Varying the Cost Function
(Uniform Cost Search)
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):
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 (2 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?
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): Representation for Corners
Problem
Note: Make sure to complete Question 2 before working on Question 5, because 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 (2 points): Heuristics for Corners
Problem
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 in
searchAgent.py.
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. 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 Marks
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!
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) sho mal 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 a bit even for the seemingly simple tinySearch.
As a reference, our implementation takes 0.7 seconds to find a path of length 27 after
expanding 5057 search nodes.
Question 7 (4 points): Food Heuristic
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 3 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)
at most 7000 5/4 (optional extra credit)
Remember: If your heuristic is inconsistent, you will receive no credit, so be careful!
Question 8 (6 points): Local Search
Reference: Artificial Intelligence: A Modern Approach (3rd Edition) P120-124
The 8-Queens problem places eight chess queens on an 8×8 chessboard such that no two
queens attack each other. Thus, a solution requires that no two queens share the same row,
column, or diagonal.
In this question you will implement a simple local search method. Read the code of the class
SolveEightQueens in the file solveEightQueens.py. The solve method of this class will call
the helper function search to solve the 8-Queens problem by iteratively changing the location of
a selected queen on the board. Type
python solveEightQueens.py -l
to generate the 8-Queens problem shown in the lecture. The following output should appear
iteration 0
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . q . . . .
q . . . q . . .
. q . . . q . q
. . q . . . q .
. . . . . . . .
*** Method not implemented: getNumberOfAttacks at line 115 of
solveEightQueens.py
Implement getBetterBoard
Next, implement the method getBetterBoard in solveEightQueens.py. A correct
implementation will return a tuple consisting of a better 8-Queen configuration, its corresponding
number of attacking queens and the selected row and column. The method should return the
best 8-Queen configuration obtained by moving a single queen along its column.
Important: Please move a single queen along its column at each iteration to pass the
autograder.
There are a number of correct outputs for the example above. Here is one (just the first 3
iterations are shown):
python solveEightQueens.py -l
iteration 0
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . q . . . .
q . . . q . . .
. q . . . q . q
. . q . . . q .
. . . . . . . .
# attacks: 17
18 12 14 13 13 12 14 14
14 16 13 15 12 14 12 16
14 12 18 13 15 12 14 14
15 14 14 q 13 16 13 16
q 14 17 15 q 14 16 16
17 q 16 18 15 q 15 q
18 14 q 15 15 14 q 16
14 14 13 17 12 14 12 18
iteration 1
. . . . . . . .
. . . . q . . .
. . . . . . . .
. . . q . . . .
q . . . . . . .
. q . . . q . q
. . q . . . q .
. . . . . . . .
# attacks: 12
13 7 10 10 13 9 10 9
11 11 10 12 q 11 9 11
10 7 13 10 15 9 9 9
11 9 11 q 13 11 10 11
q 9 12 10 17 9 11 11
14 q 12 13 15 q 11 q
14 9 q 11 15 10 q 11
10 8 9 13 12 10 8 12
iteration 2
. q . . . . . .
. . . . q . . .
. . . . . . . .
. . . q . . . .
q . . . . . . .
. . . . . q . q
. . q . . . q .
. . . . . . . .
# attacks: 7
10 q 7 7 9 6 5 6
8 11 7 8 q 6 4 7
6 7 9 7 9 5 4 5
7 9 7 q 9 7 5 7
q 9 7 6 12 6 6 7
9 12 7 8 9 q 6 q
9 9 q 7 10 6 q 8
6 8 5 8 7 6 3 8
iteration 3
...
Once you are confident that both your implementations of getBetterBoard and
getNumberOfAttacks are correct, you may attempt solving a larger number of 8-Queens
problems that are randomly generated.
python solveEightQueens.py -n 100 -q
Solved: 11 / 100
However, the current algorithm stops if it reaches a plateau where the best successor has the
same value as the current state. Starting from a randomly generated 8-queen state, hill-climbing
search can only solve 11% of the problem instances. One common solution is to allow a certain
number of consecutive sideways moves. For example, we could allow up to 100 consecutive
moves in the 8-queens problem. Hopefully, this will raise the success rate of local search.
Modify the stop criterion
Modify the stop criterion in the current algorithm to allow up to 100 consecutive moves even
though the best successor has the same value as the current state. The algorithm should stop
immediately if there is no attack between the queens.
After modification, you can run the above command again to check whether the success rate
will rise.
Important note: The autograder for this question will randomly generate 30 problem instances,
and your program should at least solve 25 of them to get this credit.
Acknowledgments
This work is based on previous work by John DeNero and Dan Klein et al. of berkeley.edu

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