Homework 1: Search in Pac-Man (10%)

Learning Objectives

In this assignment, you will

• implement various search algorithms from psuedocode
• create a reasonable search heuristic for A*

Introduction

Your Pac-Man agent will find paths through his maze world, both to reach a particular location and to collect food efficiently. You will build general search algorithms and apply them to Pac-Man scenarios.

This homework includes an autograder for you to grade your answers on your machine. This can be run with the command:

python autograder.py

See more on using the autograder, run python autograder.py -h

The code for this homework consists of several Python files, some of which you will need to read and understand in order to complete the assignment, and some of which you can ignore. You are provided all the code and supporting files in the zip of this assignment.

Files you'll edit:
search.py	Where all of your search algorithms will reside.
searchAgents.py	Where all of your search-based agents will reside.
Files you might want to look at:
pacman.py	The main file that runs Pac-Man games. This file describes a Pac-Man GameState type, which you use in this homework.
game.py	The logic behind how the Pac-Man world works. This file describes several supporting types like AgentState, Agent, Direction, and Grid.
util.py	Useful data structures for implementing search algorithms.
Supporting files you can ignore:
graphicsDisplay.py	Graphics for Pac-Man
graphicsUtils.py	Support for Pac-Man graphics
textDisplay.py	ASCII graphics for Pac-Man
ghostAgents.py	Agents to control ghosts
keyboardAgents.py	Keyboard interfaces to control Pac-Man
layout.py	Code for reading layout files and storing their contents
autograder.py	Homework 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	HW 1 specific autograding test classes

Files to Edit and Submit: You will fill in portions of search.py and searchAgents.py during the assignment. You should submit these files with your code and comments in .zip files. 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, using the same autograder and test cases you are provided with. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder. You should ensure your code passes all the test cases before submitting the solution, as we will not give any points for any questions if not all the test cases for it pass. However, the correctness of your implementation -- not the autograder's judgements -- will be the final judge of your score. Even if your code passes the autograder, we reserve the right to check it for mistakes in implementation, though this should only be a problem if your code takes too long or you disregarded announcements regarding the homework.

Collaboration: You are allowed to collaborate in pairs on this homework Please make sure both of your names are in the zip file name and that you are in a group together for the assignment on Blackboard.

Academic Dishonesty: We will be checking your code against other submissions in the class for logical redundancy. If you copy someone else/another pair's code and submit it with minor changes, we will know. We trust you all to submit your own work only; please don't let us down. Likewise, do not attempt to write your code specifically to pass the autograder's tests. Either copying or trying to cheat the autograder will be considered violations of the student honor code.

Getting Help: You are not alone! If you find yourself stuck on something, contact the course staff for help. Office hours and Slack are there for your support; please use them. If you can't make our office hours, let us know and we will schedule more. We want these homeworks to be rewarding and instructional, not frustrating and demoralizing. But, we don't know when or how to help unless you ask.

Welcome to Pac-Man

After unzipping the code and changing to its directory, you should be able to play a game of Pac-Man by typing the following at the command line:

python pacman.py

Pac-Man lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this world efficiently will be Pac-Man's first step in mastering his domain.

The simplest agent in searchAgents.py is called the GoWestAgent, which always goes West (a trivial reflex agent). This agent can occasionally win:

python pacman.py --layout testMaze --pacman GoWestAgent

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

python pacman.py --layout tinyMaze --pacman GoWestAgent

If Pac-Man gets stuck, you can exit the game by typing CTRL-c into your terminal.

Soon, your agent will solve not only tinyMaze, but any maze you want.

Note that pacman.py supports a number of options that can each be expressed in a long way (e.g., --layout) or a short way (e.g., -l). You can see the list of all options and their default values via:

python pacman.py -h

Also, all of the commands that appear in this homework also appear in commands.txt, for easy copying and pasting. In UNIX/Mac OS X, you can even run all these commands in order with bash commands.txt.

Object Glossary

Here's a glossary of the key objects in the code base 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

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

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.

Finding a Fixed Food Dot using Search Algorithms

In searchAgents.py, you'll find a fully implemented SearchAgent, which plans out a path through Pac-Man's world and then executes that path step-by-step. The search algorithms for formulating a plan are not implemented -- that's your job. As you work through the following questions, you might find it useful to refer to the object glossary (the second to last tab in the navigation bar above).

First, test that the SearchAgent is working correctly by running:

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. Pac-Man should navigate the maze successfully.

Now it's time to write full-fledged generic search functions to help Pac-Man plan routes! Pseudocode for the search algorithms you'll write can be found in the lecture slides. Remember that a search node must contain not only a state but also the information necessary to reconstruct the path (plan) which gets to that state.

Important note: All of your search functions need to return a list of actions that will lead the agent from the start to the goal. These actions all have to be legal moves (valid directions, no moving through walls).

Important note: Make sure to use the Stack, Queue and PriorityQueue data structures provided to you in util.py! These data structure implementations have particular properties which are required for compatibility with the autograder.

Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* differ only in the details of how the fringe is managed. So, concentrate on getting DFS right and the rest should be relatively straightforward. Indeed, one possible implementation requires only a single generic search method which is configured with an algorithm-specific queuing strategy. (Your implementation need not be of this form to receive full credit).

Question 1 (2 points)

Implement the depth-first search (DFS) algorithm in the depthFirstSearch function in search.py. To make your algorithm complete, write the graph search version of DFS, which avoids expanding any already visited states.

Your code should quickly find a solution for:

python pacman.py -l tinyMaze -p SearchAgent

python pacman.py -l mediumMaze -p SearchAgent

python pacman.py -l bigMaze -z .5 -p SearchAgent

The Pac-Man 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 Pac-Man 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 fringe in the order provided by getSuccessors; you might get 246 if you push them in the reverse order). Is this a least cost solution? If not, think about what depth-first search is doing wrong.

Question 2 (2 points)

Implement the breadth-first search (BFS) algorithm in the breadthFirstSearch function in search.py. Again, write a graph search algorithm that avoids expanding any already visited states. Test your code the same way you did for depth-first search.

python pacman.py -l mediumMaze -p SearchAgent -a fn=bfs

python pacman.py -l bigMaze -p SearchAgent -a fn=bfs -z .5

Does BFS find a least cost solution? If not, check your implementation.

Hint: If Pac-Man moves too slowly for you, try the option --frameTime 0.

Note: If you've written your search code generically, your code should work equally well for the eight-puzzle search problem without any changes.

python eightpuzzle.py

Varying the Cost Function

While BFS will find a fewest-actions path to the goal, we might want to find paths that are "best" in other senses. Consider mediumDottedMaze and mediumScaryMaze.

By changing the cost function, we can encourage Pac-Man 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 Pac-Man agent should adjust its behavior in response.

Question 3 (2 points)

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).

A* search

Question 4 (3 points)

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)

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 Pac-Man 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 Pac-Man position and the location of the four corners.

Our implementation of breadthFirstSearch expands just under 2000 search nodes on mediumCorners. However, heuristics (used with A* search) can reduce the amount of searching required.

Question 6 (3 points)

Note: Make sure to complete Question 4 before working on Question 6, because Question 6 builds upon your answer for Question 4.

Implement a non-trivial, consistent heuristic for the CornersProblem in cornersHeuristic.

python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5

Note: AStarCornersAgent is a shortcut for

-p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic.

Admissibility vs. Consistency: Remember, heuristics are just functions that take search states and return numbers that estimate the cost to a nearest goal. More effective heuristics will return values closer to the actual goal costs. To be admissible, the heuristic values must be lower bounds on the actual shortest path cost to the nearest goal (and non-negative). To be consistent, it must additionally hold that if an action has cost c, then taking that action can only 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 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).

Note: You cannot use the mazeDistance function for this question.

Grading: Your heuristic must be a non-trivial non-negative consistent heuristic to receive any points. Make sure that your heuristic returns 0 at every goal state and never returns a negative value. Depending on how few nodes your heuristic expands, you'll be graded:

Number of nodes expanded	Grade
more than 2000	0/3
at most 2000	1/3
at most 1600	2/3
at most 1200	3/3

Remember: If your heuristic is inconsistent, you will receive no credit, so be careful!

Eating All The Dots

Now we'll solve a hard search problem: eating all the Pac-Man 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 Pac-Man world. For the present homework, solutions do not take into account any ghosts or power pellets; solutions only depend on the placement of walls, regular food and Pac-Man. (Of course ghosts can ruin the execution of a solution! We'll get to that in the next homework.) If you have written your general search methods correctly, A* with a null heuristic (equivalent to uniform-cost search) should quickly find an optimal solution to testSearch with no code change on your part (total cost of 7).

python pacman.py -l testSearch -p AStarFoodSearchAgent

Note: AStarFoodSearchAgent is a shortcut for -p SearchAgent -a fn=astar,prob=FoodSearchProblem,heuristic=foodHeuristic.

You should find that UCS starts to slow down even for the seemingly simple tinySearch. As a reference, our implementation takes 2.5 seconds to find a path of length 27 after expanding 5057 search nodes.

Question 7 (4 points)

Note: Make sure to complete Question 4 before working on Question 7, because Question 7 builds upon your answer for Question 4.

Fill in foodHeuristic in searchAgents.py with a consistent heuristic for the FoodSearchProblem. Try your agent on the trickySearch board:

python pacman.py -l trickySearch -p AStarFoodSearchAgent

Our UCS agent finds the optimal solution in about 13 seconds, exploring over 16,000 nodes.

Any non-trivial non-negative consistent heuristic will receive 1 point. Make sure that your heuristic returns 0 at every goal state and never returns a negative value. Depending on how few nodes your heuristic expands, you'll get additional points:

Number of nodes expanded	Grade
more than 15000	1/4
at most 15000	2/4
at most 12000	3/4
at most 9000	4/4 (full credit; medium)
at most 7000	5/4 (optional extra credit; hard)

Remember: If your heuristic is inconsistent, you will receive no credit, so be careful! Can you solve mediumSearch in a short time? If so, we're either very, very impressed, or your heuristic is inconsistent.

Again, you cannot use the mazeDistance function for this question.

Suboptimal Search

Sometimes, even with A* and a good heuristic, finding the optimal path through all the dots is hard. In these cases, we'd still like to find a reasonably good path, quickly. In this section, you'll write an agent that always greedily eats the closest dot. ClosestDotSearchAgent is implemented for you in searchAgents.py, but it's missing a key function that finds a path to the closest dot.

Question 8 (2 points)

Implement the function findPathToClosestDot in searchAgents.py. Our agent solves this maze (suboptimally!) in under a second with a path cost of 350:

python pacman.py -l bigSearch -p ClosestDotSearchAgent -z .5 

Hint: The quickest way to complete findPathToClosestDot is to fill in the AnyFoodSearchProblem, which is missing its goal test. Then, solve that problem with an appropriate search function. The solution should be very short!

Your ClosestDotSearchAgent won't always find the shortest possible path through the maze. Make sure you understand why and try to come up with a small example where repeatedly going to the closest dot does not result in finding the shortest path for eating all the dots.

Mini Contest (up to 2 points extra credit)

Implement an ApproximateSearchAgent in searchAgents.py that finds a short path through the bigSearch layout. If your agent finds a solution of cost at most 290 receive you 1 point extra credit. If the cost is at most 280 you receive 2 points extra credit. The three individuals that find the shortest path using no more than 30 seconds of computation will receive an in-class demonstration of their brilliant Pac-Man agents.

python pacman.py -l bigSearch -p ApproximateSearchAgent -z .5 -q 

We will time your agent using the no graphics option -q, and it must complete in under 30 seconds on our grading machines. Please describe what your agent is doing in a comment! Don't hard-code the path, of course.

There is a mazeDistance helper function that you can use if you need to. This function finds the distance between two coordinates, accounting for walls.

What to Submit

Zip only the files you altered for this assignment as a .zip named with the first letter of your first name, your last name, and homework number (example: lmartin_hw1.zip) and submit it on Blackboard before the due date. If you are submitting as a pair, please label the file with both of your last names and the homework number (example: martin_ayanzadeh_hw1.zip).
Submission link

Important: Please re-download your submission and ensure all files run as intended. We will not entertain regrade requests for submitting the wrong files.