CS 444 Artificial Intelligence
PA1: Search
Learning Objectives
After completing this activity, students should be able to:- Construct uniformed (BFS, DFS, IDS) and informed (A*) search algorithms
python autograder.py
Partners
This assignment may be completed individually or in pairs. If you are doing this in pairs, you must notify me at the beginning of the project. My expectation for pairs is that both members are actively involved, and take full responsibility for all aspects of the project. In other words, I expect that you are either sitting or virtually together to work, and not that you are splitting up tasks to be completed separately. If both members of the group are not able to fully explain the code to me, then this does not meet this expectation.Provided Files
Download this zip archive search.zip which contains all the code and supporting files. 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.Files you will 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 Pacman games. This file describes a Pacman GameState type, which you use in this project. |
game.py | Useful data structures for implementing search algorithms. |
util.py | The logic behind how the Pacman world works. This file describes several supporting types like AgentState, Agent, Direction, and Grid. |
Support files you can ignore: | |
graphicsDisplay.py | Graphics for pacman |
graphicsUtils.py | Support for pacman graphics |
textDisplay.py | ASCII graphics for pacman |
ghostAgents.py | Agents to support the ghosts |
keyboardAgents.py | Keyboard interfaces to control pacman |
layout.py | Code for reading layout files and storing their content |
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 | Project 1 specific autograding test classes |
Submission and Policies
You will submit the filessearch.py
and searchAgents.py
to
Autolab in a zip file named PA_01.zip.
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 will wreak havoc on the autograder. However, the correctness of your implementation – not the autograder’s judgements – will be the final judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.
Academic Dishonesty: Your code will be checked against other submissions in the class for logical redundancy. If you copy someone else’s code and submit it with minor changes, it will be detected. These cheat detectors are quite hard to fool, so please don’t try. We trust you all to submit your own team's work; please don’t let us down.
Getting Help: You are not alone! If you find yourself stuck on something, contact me. Office hours and Piazza discussion forum are there for your support; please use them. If you can’t make office hours, let me know and I will schedule a meeting with you. I want these projects to be rewarding and instructional, not frustrating and demoralizing. But, I don’t know when or how to help unless you ask.
Running Pacman
After download the code (search.zip), unzipping it, and changing to the search directory (created via unzip), you should be able to play a game of pacman. Make sure your python environment is configured (see resources) and then enter 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.
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 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.
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 project 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.
Question 1: Finding a Fixed Food Dot using Depth First Search (3 points)
>
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.
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. Pacman should navigate the maze successfully.
Now it’s time to write full-fledged generic search functions to help Pacman 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).
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 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 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: Breadth First Search (3 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.
Does BFS find a least cost solution? If not, check your implementation.
Hint: If Pacman 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 pacman.py -l mediumMaze -p SearchAgent -a fn=bfs
python pacman.py -l bigMaze -z .5 -p SearchAgent
Question 3: Varying the Cost Function(3 points)
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: A* Search(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?
Question 5: Finding All the Corners (3 points)
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.
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: Corners Problem: Heuristic (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 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 | Grade |
more than 2000 | 0/3 |
at most 2000 | 1/3 |
at most 1600 | 2/3 |
at most 1200 | 3/3 |
Question 7: Eating all the Dots (4 points)
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) 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.
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 |
at most 7000 | 5/4 (optional extra credit) |
Question 8: Suboptimal Search (3 points)
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.
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.
Submission
You can test all your code prior to submission by runnning:python autograder.py
Submit your two files in a single zip named
PA_01.zip
to Autolab
under PA 1.