AI berkeley solution pdf

CSL302– Artificial Intelligence L ab 1

D ue on 27/1/2016 11.55pm Ins truc tions : Upload to your moodle account one z ip file containing the following. P leas e do not s ubmit hardcopy of your s olutions . In cas e moodle is not acces s ible email the z ip file to the ins tructor at ckn@ iitrpr.ac.in. L ate s ubmis sion is not allowed without prior approval of the ins tructor. Y ou are expected to follow the honor code of the cours e while doing this homework. 1. T his lab s hould be attempted individually. 2. A neatly formatted P D F document with your ans wers for each of the ques tions in the homework. Y ou can us e latex, MS word or any other s oftware to create the P D F . 
 3. Include a separate folder named as ‘code’ containing the scripts for the homework along with the neces s ary data files . 4. Include a R E AD ME file explaining how to execute the s cripts . 
 5. Name the Z IP file us ing the following convention rollnumberhwnumber.z ip

S earc h in P ac man In this as s ignment, you will be experimenting with different AI s earch techniques that w e dis cus s ed in the clas s in a P acman environment. T his is part of the P acman projects developed at UC B erkeley [1]. T he P acman agent needs to find paths through the maz e world, both to reach a location and to collect food efficiently. Y ou are provided with a s tarter code for this project. T he code cons is ts of s everal P ython files , s ome of which you will need to read and unders tand to complete the as s ignment, and s ome of which you can ignore. F iles you will edit search.py

where all your s earch algorithms will res ide.

searchAgents.py where all your s earch-bas ed agents will res ide. F iles you m ig ht want to look at:

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Pacman.py T he main file that runs P acman games . T his file des cribes a P acman G ameS tate type, which you us e in this project game.py T he logic behind how the P acman world works . T his file des cribes s everal s upporting types like AgentS tate, Agent, D irection, and G rid. Us eful data s tructures for implementing s earch algorithms

Util.py F iles you c an ig nore

graphicsDisplay.py

G raphics for P acman

graphicsUtils.py S upport for P acman graphics textDisplay.py

AS C II graphics for P acman

ghostAgents.py

Agents to control ghos ts

keyboardAgents.py layout.py

K eyboard interfaces to control P acman

C ode for reading layout files and s toring their contents

autograder.py

P roject autograder

testParser.py

P ars es autograder tes t and s olution files

testClasses.py

G eneral autograding tes t clas s es

test_cases/

D irectory containing the tes t cas es for each ques tion

searchTestClasses.py

P roject 1 s pecific autograding tes t clas s es

T he z ip file als o includes an autograder s cript for you to grade your ans wers on your machine. T his can be run with the command: Python autograder.py Y ou mus t only include search.py and searchAgents.py as part of the final lab s ubmis s ion. Y our code mus t be well commented. P leas e do not change the other files or s ubmit other files .

Welc ome to P ac man After downloading the code (l1.z ip), unz ipping it, and changing to the directory, you s hould be able to play a game of P acman by typing the following at the command line: python pacman.py P acman lives in a s hiny blue world of twis ting corridors and tas ty round treats . Navigating this world efficiently will be P acman's firs t s tep in mas tering his domain. T he s imples t agent in searchAgents.py is called the GoWestAgent, which always goes W es t (a trivial reflex agent). T his agent can occas ionally win: python pacman.py --layout testMaze --pacman GoWestAgent 2

B ut, things get ugly for this agent when turning is required:

python pacman.py --layout tinyMaze --pacman GoWestAgent If P acman gets s tuck, you can exit the game by typing C T R L -c into your terminal. S oon, your agent will s olve not only tinyMaze, but any maz e you want. Note that pacman.py s upports s everal options that can each be expres s ed in a long way (e.g., --layout) or a s hort way (e.g., -l). Y ou can s ee the lis t of all options and their default values via: python pacman.py -h Als o, all the commands that appear in this project als o appear in commands.txt, for eas y copying and pas ting. In UNIX /Mac O S X , you can even run all thes e commands in order with bash commands.txt. Note: if you get error mes s ages regarding T kinter, s ee this page.

Ques tion 1 (5 points ): F inding a F ix ed F ood D ot us ing D epth F irs t S earc h In searchAgents.py, you'll find a fully implemented SearchAgent, which plans a path through P acman's world and then executes that path s tep-by-s tep. T he s earch algorithms for formulating a plan are not implemented -- that's your job. F irs t, tes t that the SearchAgent is working correctly by running: python pacman.py -l tinyMaze -p SearchAgent -a fn=tinyMazeSearch T he command above tells the SearchAgent to us e tinyMazeSearch as its s earch algorithm, which is implemented in search.py. P acman s hould navigate the maz e s ucces s fully. Now it's time to write full-fledged generic s earch functions to help P acman plan routes ! R emember that a s earch node mus t contain not only a s tate but als o the information neces s ary to recons truct the path (plan) which gets to that s tate. Im portantnote:Allyour search functions need to return a listof actions thatw illlead the agent from the start to the goal. These actions m ust be legal m oves (valid directions, no m oving through w alls). Im portant note: M ake sure to use the Stack, Queue and PriorityQueue data structures provided to you in util.py! These data structure im plem entations have properties w hich are required forcom patibility w ith the autograder.

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Implement the depth-firs t s earch (D F S ) algorithm in the depthFirstSearch function in search.py. T o make your algorithm complete, write the graph s earch vers ion of D F S , which avoids expanding any already vis ited s tates . Y our code s hould quickly find a s olution for: python pacman.py -l tinyMaze -p SearchAgent python pacman.py -l mediumMaze -p SearchAgent python pacman.py -l bigMaze -z .5 -p SearchAgent T he P acman board will s how an overlay of the s tates explored, and the order in which they were explored (brighter red means earlier exploration). Is the exploration order what you would have expected? D oes P acman go to all the explored s quares on his way to the goal? H int: If you us e a S tack as your data s tructure, the s olution found by your D F S algorithm for mediumMaze s hould have a length of 130 (provided you pus h s ucces s ors onto the fringe in the order provided by getSuccessors; you might get 246 if you pus h them in the revers e order). Is this a leas t cos t s olution? If not, think about what depth-firs t s earch is doing wrong.

Ques tion 2 (5 points ): B readth F irs t S earc h Implement the breadth-firs t s earch (B F S ) algorithm in the breadthFirstSearch function in search.py. Again, write a graph s earch algorithm that avoids expanding any already vis ited s tates . T es t your code the s ame way you did for depth-firs t s earch. python pacman.py -l mediumMaze -p SearchAgent -a fn=bfs python pacman.py -l bigMaze -p SearchAgent -a fn=bfs -z .5 D oes B F S find a leas t cos t s olution? If not, check your implementation. H int:If P acman moves too s lowly for you, try the option --frameTime 0. N ote:If you've written your s earch code generically, your code s hould work equally well for the eight-puz z le s earch problem without any changes . python eightpuzzle.py

Ques tion 3 (5 points ): Varying the C os t F unc tion While B F S will find a fewes t-actions path to the goal, we might want to find paths that are "bes t" in other s ens es . C ons ider mediumDottedMaze and mediumScaryMaze. B y changing the cos t function, we can encourage P acman to find different paths . F or example, we can charge more for dangerous s teps in ghos t-ridden areas or les s for s teps in food-rich areas , and a rational P acman agent s hould adjus t its behavior in res pons e. 4

Implement the uniform-cos t graph s earch algorithm in the uniformCostSearch function in search.py. W e encourage you to look through util.py for s ome data s tructures that may be us eful in your implementation. Y ou s hould now obs erve s ucces s ful behavior in all three of the following layouts , where the agents below are all UC S agents that differ only in the cos t function they us e (the agents and cos t 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: Y ou s hould get very low and very high path cos ts for the StayEastSearchAgent and StayWestSearchAgent res pectively, due to their exponential cos t functions (s ee searchAgents.py for details ).

Ques tion 4 (6 points ): A * s earc h Implement A * graph s earch in the empty function aStarSearch in search.py. A* takes a heuris tic function as an argument. H euris tics take two arguments : a s tate in the s earch problem (the main argument), and the problem its elf (for reference information). T he nullHeuristic heuris tic function in search.py is a trivial example. Y ou can tes t your A* implementation on the original problem of finding a path through a maz e to a fixed pos ition us ing the Manhattan dis tance heuris tic (implemented already as manhattanHeuristic in searchAgents.py). python pacman.py -l bigMaze -z .5 -p SearchAgent -a fn=astar,heuristic=manhattanHeuristic Y ou s hould s ee that A* finds the optimal s olution s lightly fas ter than uniform cos t s earch (about 549 vs . 620 s earch nodes expanded in our implementation, but ties in priority may make your numbers differ s lightly). W hat happens on openMaze for the various s earch s trategies ?

Ques tion 5 (6 points ): F inding A ll the C orners T he real power of A* will only be apparent with a more challenging s earch problem. Now, it's time to formulate a new problem and des ign a heuris tic for it.

In corner maz es , there are four dots , one in each corner. O ur new s earch problem is to find the s hortes t path through the maz e that touches all four corners (whether the maz e has food there or not). Note that for s ome maz es like tinyCorners, the s hortes t path does not always go to the clos es t food firs t! Hint: the s hortes t path through tinyCorners takes 28 s teps .

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N ote: Make s ure to complete Ques tion 2 before working on Q ues tion 5, becaus e Q ues tion 5 builds upon your ans wer for Q ues tion 2. Implement the CornersProblem s earch problem in searchAgents.py. Y ou will need to choos e a s tate repres entation that encodes all the information neces s ary to detect whether all four corners have been reached. N ow, your s earch agent s hould s olve: python pacman.py -l tinyCorners -p SearchAgent -a fn=bfs,prob=CornersProblem python pacman.py -l mediumCorners -p SearchAgent -a fn=bfs,prob=CornersProblem T o receive full credit, you need to define an abs tract s tate repres entation that does not encode irrelevant information (like the pos ition of ghos ts , where extra food is , etc.). D o not us e a P acman GameState as a s earch s tate. Y our code will be very, very s low if you do (and wrong). H int: T he only parts of the game s tate you need to reference in your implementation are the s tarting P acman pos ition and the location of the four corners . O ur implementation of breadthFirstSearch expands jus t under 2000 s earch nodes on mediumCorners. H owever, heuris tics (us ed with A* s earch) can reduce the amount of s earching required.

Ques tion 6 (6 points ): C orn ers P roblem : H euris tic N ote: Make s ure to complete Ques tion 4 before working on Q ues tion 6, becaus e Q ues tion 6 builds upon your ans wer for Q ues tion 4. Implement a non-trivial, cons is tent heuris tic for the CornersProblem in cornersHeuristic. python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5 Note: AStarCornersAgent is a s hortcut for -p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic. Admis s ibility vs . C ons is tency: R emember, heuris tics are jus t functions that take s earch s tates and return numbers that es timate the cos t to a neares t goal. More effective heuris tics will return values clos er to the actual goal cos ts . T o be admis s ible, the heuris tic values mus t be lower bounds on the actual s hortes t path cos t to the neares t goal (and non-negative). T o be cons is tent, it mus t additionally hold that if an action has cos t c, then taking that action can only caus e a drop-in heuris tic of at mos t c. R emember that admis s ibility is n't enough to guarantee correctnes s in graph s earch -- you need the s tronger condition of cons is tency. H owever, admis s ible heuris tics are us ually als o cons is tent, es pecially if they are derived from problem relaxations . T herefore it is us ually eas ies t to s tart out by brains torming admis s ible heuris tics . O nce you have an admis s ible heuris tic that 6

works well, you can check whether it is indeed cons is tent, too. T he only way to guarantee cons is tency is with a proof. H owever, incons is tency can often be detected by verifying that for each node you expand, its s ucces s or nodes are equal or higher in in f-value. Moreover, if UC S and A* ever return paths of different lengths , your heuris tic is incons is tent. T his s tuff is tricky! N on-TrivialH euristics:T he trivial heuris tics are the ones that return z ero everywhere (UC S ) and the heuris tic which computes the true completion cos t. T he former won't s ave you any time, while the latter will timeout the autograder. Y ou want a heuris tic which reduces total compute time, though for this as s ignment the autograder will only check node counts (as ide from enforcing a reas onable time limit). G rading: Y our heuris tic mus t be a non-trivial non-negative cons is tent heuris tic to receive any points . Make s ure that your heuris tic returns 0 at every goal s tate and never returns a negative value. D epending on how few nodes your heuris tic expands , you'll be graded: Number of nodes expanded G rade More than 2000 2 At mos t 2000 3 At mos t 1600 4 At mos t 1200 5 R emember: If your heuris tic is incons is tent, you will receive no credit, s o be careful!

Ques tion 7 (6 points ): E ating A ll T he D ots Now we'll s olve a hard s earch problem: eating all the P acman food in as few s teps as pos s ible. F or this , we'll need a new s earch problem definition which formaliz es the food-clearing problem: FoodSearchProblem in searchAgents.py (implemented for you). A s olution is defined to be a path that collects all the food in the P acman world. F or the pres ent project, s olutions do not cons ider any ghos ts or power pellets ; s olutions only depend on the placement of walls , regular food and P acman. (O f cours e ghos ts can ruin the execution of a s olution! W e'll get to that in the next project.) If you have written your general s earch methods correctly, A* with a null heuris tic (equivalent to uniform-cos t s earch) s hould quickly find an optimal s olution to testSearch with no c ode change on your part (total cos t of 7). python pacman.py -l testSearch -p AStarFoodSearchAgent Note: AStarFoodSearchAgent is a s hortcut for -p SearchAgent fn=astar,prob=FoodSearchProblem,heuristic=foodHeuristic.

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Y ou s hould find that UC S s tarts to s low down even for the s eemingly s imple tinySearch. As a reference, our implementation takes 2.5 s econds to find a path of length 27 after expanding 5057 s earch nodes . N ote: Make s ure to complete Ques tion 4 before working on Q ues tion 7, becaus e Q ues tion 7 builds upon your ans wer for Q ues tion 4.

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F ill in foodHeuristic in searchAgents.py with a cons is tent heuris tic FoodSearchProblem. T ry your agent on the trickySearch board:

for the

python pacman.py -l trickySearch -p AStarFoodSearchAgent O ur UC S agent finds the optimal s olution in about 13 s econds , exploring over 16,000 nodes . Any non-trivial non-negative cons is tent heuris tic will receive 1 point. Make s ure that your heuris tic returns 0 at every goal s tate and never returns a negative value. D epending on how few nodes your heuris tic expands , you'll get additional points : Number of nodes expanded More than 15000 At mos t 15000 At mos t 12000 At mos t 9000 At mos t 7000

G rade 1 3 4 5 6

R emember: If your heuris tic is incons is tent, you will receive no credit, s o be careful! C an you s olve mediumSearch in a s hort time? If s o, we're either very, very impres s ed, or your heuris tic is incons is tent.

Ques tion 8 (6 points ): S uboptim al S earc h S ometimes , even with A* and a good heuris tic, finding the optimal path through all the dots is hard. In thes e cas es , we'd s till like to find a reas onably good path, quickly. In this s ection, you'll write an agent that always greedily eats the clos es t dot. ClosestDotSearchAgent is implemented for you in s earchAgents .py, but it's mis s ing a key function that finds a path to the clos es t dot. Implement the function findPathToClosestDot in searchAgents.py. O ur agent s olves this maz e (s uboptimally!) in under a s ec ond with a path cos t of 350:

python pacman.py -l bigSearch -p ClosestDotSearchAgent -z .5 H int: T he quickes t way to complete findPathToClosestDot is to fill in the AnyFoodSearchProblem, which is mis s ing its goal tes t. T hen, s olve that problem with an appropriate s earch function. T he s olution s hould be very s hort! Y our ClosestDotSearchAgent won't always find the s hortes t pos s ible path through the maz e. Make s ure you unders tand why and try to come up with a s mall example where repeatedly going to the clos es t dot does not res ult in finding the s hortes t path for eating all the dots .

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S ubm is s ion Include a neatly formatted pdf document that des cribes your heuris tics , and other obs ervations while implementing the lab.

R eference [1] http://ai.berkeley.edu/project_overview.html

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