This assignment is due Wednesday, 2/4/09 at 11:59 pm

All those colored walls,

Mazes give Pacman the blues,

So teach him to search.

In this project, your Pacman 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 Pacman scenarios.

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. You can download all the code and supporting files (including this description) as a zip archive.

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 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: | |

`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 |

**What to submit:** You will fill in portions of `search.py`

and `searchAgents.py`

during the assignment. You should submit these two files (only) along with a `partners.txt`

file. Type `submit p1`

to submit your code. Here are directions for submitting and setting up your account.

**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 output -- 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:** We will be checking your code against other submissions in the class 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, contact the course staff for help. Office hours, section, and the newsgroup 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 projects to be rewarding and instructional, not frustrating and demoralizing. But, we don't know when or how to help unless you ask. One more piece of advice: if you don't know what a variable is, print it out.

python pacman.pyPacman 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 GoWestAgentBut, things get ugly for this agent when turning is required:

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

`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 -hSoon, your agent will solve not only

`tinyMaze`

, but any maze you want.
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`

.
`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 selecting a plan are not implemented -- that's your job. As you work through the following questions, you might need to refer to this glossary of objects in the code.
First, test that the `SearchAgent`

is working correctly by running:
python pacman.py -l tinyMaze -p SearchAgent -a fn=tinyMazeSearchThe 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 and textbook. Remember that a search node must contain not only a state but also the information necessary to reconstruct the path (plan) 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).

*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).

*Hint:* Make sure to check out the `Stack, Queue`

and `PriorityQueue`

types provided to you in `util.py`

!

* Question 1 (2 points) * Implement the depth-first search (DFS) algorithm in the

`depthFirstSearch`

function in `search.py`

. To make your algorithm 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 SearchAgentThe 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 244 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 (1 point) * 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 .5Does BFS find a least cost solution? If not, check your implementation.

*Hint:* If Pacman moves to 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 (textbook section 3.2) without any changes.

python eightpuzzle.py

`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.
* Question 3 (2 points) * Implement the uniform-cost graph search algorithm in
the

`uniformCostSearch`

function in `search.py`

. 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 (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 argument: 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=manhattanHeuristicYou should see that A* finds the optimal solution slightly faster than uniform cost search (549 vs. 620 search nodes expanded in our implementation). What happens on

`openMaze`

for the various search strategies?
The real power of A* will only be apparent with a more challenging search problem. Now, it's time to formulate a new search 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. 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) * 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=CornersProblemTo receive full credit, you need to define an abstract state representation that

`GameState`

as a search state. Your code will be very, very slow if you do.
*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.

Heuristics can reduce the amount of searching required. Our implementation of `breadthFirstSearch`

expands just under 2000 search nodes on mediumCorners.

* Question 6 (3 points) * Implement a heuristic for the

`CornersProblem`

in `cornersHeuristic`

. Grading: inadmissible heuristics will get python pacman.py -l mediumCorners -p AStarCornersAgent -z 0.5

*Hint:* Remember, heuristic functions just return numbers, which, to be admissible, must be lower bounds on the actual shortest path cost to the nearest goal.

*Note:* `AStarCornersAgent`

is a shortcut for `-p SearchAgent -a fn=aStarSearch,prob=CornersProblem,heuristic=cornersHeuristic`

.

`FoodSearchProblem`

in `searchAgents.py`

(implemented for you). A solution is a path that collects all of the food in the Pacman world. Such a solution will not change if there are ghosts or power pellets in the game; it only depends on the placement of walls, food and Pacman, though of course ghosts can ruin the execution of a solution! If you have written your general search methods correctly, `A*`

with a null heuristic (equivalent to uniform-cost search) should quickly find optimal an 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 4902 search nodes.

* Question 7 (5 points) * Fill in

`foodHeuristic`

in `searchAgents.py`

with an `FoodSearchProblem`

. Try your agent on the `trickySearch`

board:
python pacman.py -l trickySearch -p AStarFoodSearchAgentOur UCS agent finds the optimal solution in about 13 seconds, exploring over 16,000 nodes. As long as your heuristic is admissible, you will receive the following score.

Fewer nodes than: | Points |
---|---|

15500 | 2 |

13500 | 3 |

11500 | 4 |

10000 | 5 |

Inadmissible heuristics will receive at most 2 points. Think through admissibility carefully, as inadmissible heuristics may manage to produce fast searches and optimal paths. Can you solve `mediumSearch`

in a short time? If so, we're either very, very impressed, or your heuristic is inadmissible. If UCS and A* ever return paths of different lengths, your heuristic is inadmissible. This stuff is tricky. If you need help, don't hesitate to ask a GSI!

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 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 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.

Your `ClosestDotSearchAgent`

won't always find the shortest possible path through the maze. (If you don't understand why, ask a GSI!) In fact, you can do better if you try.

* Mini Contest (2 points extra credit)* Implement an

`ApproximateSearchAgent`

in `searchAgents.py`

that finds a short path through the `bigSearch`

layout. The three teams that find the shortest path in under 30 seconds of computation will receive 2 extra credit points and an in-class demonstration of their brilliant Pacman.
python pacman.py -l bigSearch -p ApproximateSearchAgent -z .5 -qWe will time your agent using the no graphics option

`-q`

, and it must complete in under 30 seconds. Please describe what your agent is doing in a comment! We reserve the right to give additional extra credit to creative solutions, even if they don't work that well. Don't hard-code the path, of course.
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 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.