Assignment 1
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.
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 (4th Edition) P111 - 112
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 getNumberOfAttacks
It is time to write some code. Implement the function getNumberOfAttacks in the file solveEightQueens.py. This function should return the number of attacks of the current board (self.squareArray). The data type of the return value should be int.
Once you are done with your implementation you can try to run the following command again.
python solveEightQueens.py -l
You should see the following output.
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
*** Method not implemented: getBetterBoard at line 107 of solveEightQueens.py
At this time, you may also try to run the first autograder for question 8 as follows.
python autograder.py -q q8_1
You should see the following output.
Question q8_1
=============
*** PASS: test_cases\q8_1\num_of_attack1.test
*** solution: 17
*** PASS: test_cases\q8_1\num_of_attack2.test
*** solution: 12
*** PASS: test_cases\q8_1\num_of_attack3.test
*** solution: 7
*** PASS: test_cases\q8_1\num_of_attack4.test
*** solution: 0
### Question q8_1: 2/2 ###
Finished at 12:54:37
Provisional grades
==================
Question q8_1: 2/2
------------------
Total: 2/2
Next, we will implement the getBetterBoard function so that we can get out of this state.
Implement getBetterBoard
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 (one of) the best 8-Queen states obtained by moving a single queen along its column. A best 8-Queen state has the smallest number of attacks. In the example above you can see that we have multiple best states for this start state.
Important: Please only move a single queen along its column at each iteration.
Once you are done with your implementation, you may try to run the following command again. Note that there are a number of correct outputs for this example (depending on which of the best states you select). Here is one that we obtained (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
...
Note that you may not be able to find a solution for this particular start state. For our implementation, the program will output the following.
Solved: 0/1
Why can’t we find a solution? It is because our implementation is a greedy local search algorithm that just grabs a good neighbor state. We might get stuck for any of the following reasons:
· Local optima: i.e., every move of a single queen result in a worst situation
· Ridge, i.e., a sequence of local optima that is very difficult for greedy algorithms to navigate
· Plateau, i.e., flat area in the state space. It could be a flat local optima or a shoulder from which progress is possible.
However, you may attempt solving a larger number of 8-Queens problems (here we try 1000) that are randomly generated as follows.
python solveEightQueens.py -n 1000 -q
Solved: 146 / 1000
Starting from a randomly generated 8-queen state, hill-climbing search can solve 14% of the problem instances. Not bad considering the huge search space of 8^8 = 17 million states.
At this stage, you may try to pass the second autograder for this question as follows.
python autograder.py -q q8_2
To increase the success rate of our local search algorithm we will next try to allow a certain number of consecutive sideways moves, i.e., keep going when reaching a plateau in the hope that the plateau is really a shoulder. For example, we could allow up to 100 consecutive moves in the 8-queens problem. 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 you are done you may try to pass the third autograder for this question as follows.
python autograder.py -q q8_3
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