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日期:2020-10-22 10:45

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 <options>

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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