Project 1: Search in Pac-Man Solution

All those colored walls,




Mazes give Pac-Man the blues,




So teach him to search.




Introduction




In this project, your Pac-Man agent will nd paths through his maze world, both to reach a particular location and to collect food e ciently. You will build general search algorithms and apply them to Pac-Man scenarios.




The code for this project consists of several Python les, 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 les as a zip archive from the Canvas page. Note that in order to display the pretty graphics, the easiest options are either run the code in the MCS computer lab or install python on your own computer. The latter option is recommended as it will make your life easier in the long run.




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 will want to look at:




pacman.py The main le that runs Pac-Man games. This le describes a Pac-Man GameState type, which you use in this project.




game.py The logic behind how the Pac-Man world works. This le describes several supporting types like AgentState, Agent, Direction, and Grid.




util.py Useful data structures for implementing search algorithms.




Supporting les you can ignore:




graphicsDisplay.py Graphics for Pac-Man




graphicUtils.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 les and storing their contents




Getting Started




After downloading the code (search.zip), unzipping it and changing to the search directory, you should be able to play a game of Pac-Man by typing the following at the command line:




python pacman.py




Note: Make sure you are running a recent version of Python (2.5 or later). If you get error messages regarding python-tk, use your package manager to install python-tk.




Pac-Man lives in a shiny blue world of twisting corridors and tasty round treats. Navigating this world e ciently will be Pac-Man’s rst step in mastering his domain.




The simplest agent in searchAgents.py is called the GoWestAgent, which always goes West (a trivial re ex 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.




Finding a Fixed Food Dot using Search Algorithms




In searchAgents.py, you’ll nd 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 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=tinyMazeSearch



The command above tells the SearchAgent to use tinyMazeSearch as its search algorithm, which is imple-mented in search.py. Pac-Man should navigate the maze successfully.




Now it’s time to write full- edged generic search functions to help Pac-Man 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) 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).




Hint: Each algorithm is very similar. Algorithms for DFS, BFS, UCS, and A* di er only in the details of how the fringe is managed. So, concentrate on getting DFS right and the rest should be relatively straightfor-ward. Indeed, one possible implementation requires only a single generic search method which is con gured with an algorithm-speci c 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- rst 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 (R&N 3ed Section 3.3, Figure 3.7).




Your code should quickly nd 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 medium-Maze 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- rst search is doing wrong.




Question 2 (2 point) Implement the breadth- rst 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- rst 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 nd 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 (R&N 3ed Section 3.2, Figure 3.4) without any changes.




python eightpuzzle.py




Varying the Cost Function




While BFS will nd a fewest-actions path to the goal, we might want to nd paths that are \best" in other senses. Consider mediumDottedMaze and mediumScaryMaze. By changing the cost function, we can encour-age Pac-Man to nd di erent 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 (3 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 di er 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 prob-lem (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 nding a path through a maze to a xed posi-tion 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* nds 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 di er 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 nd 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 rst! 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=CornersProblem




To receive full credit, you need to de ne 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) Implement a heuristic for the CornersProblem in cornersHeuristic. Grad-ing: inadmissible heuristics will get no credit. 1 point for any admissible heuristic. 1 point for expanding fewer than 1600 nodes. 1 point for expanding fewer than 1200 nodes. Expand fewer than 800, and you’re doing great!







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




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 de nition which formalizes the food-clearing problem: FoodSearchProblem in searchAgents.py (implemented for you). A solution is de ned to be a path that collects all of the food in the Pac-Man 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 Pac-Man. (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 nd 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 nd that UCS starts to slow down even for the seemingly simple tinySearch. As a reference, our implementation takes 2.5 seconds to nd a path of length 27 after expanding 4902 search nodes.




Question 7 (3 + 1 points) Fill in foodHeuristic in searchAgents.py with an admissible and consistent heuristic for the FoodSearchProblem. Try your agent on the trickySearch board:




python pacman.py -l trickySearch -p AStarFoodSearchAgent




Our UCS agent nds the optimal solution in about 13 seconds, exploring over 16,000 nodes. If your heuristic is admissible, you will receive the following score, depending on how many nodes your heuristic expands.




Fewer nodes than:
Points




15000
1




12000
2




9000
3 (hard)




7000
+1 extra credit (very hard)







If your heuristic is inadmissible, you will receive no credit, so be careful! Think through admissibility carefully, as inadmissible heuristics may manage to produce fast searches and even optimal paths. Can you solve mediumSearch in a short time? If so, we’re either very, very impressed, or your heuristic is inadmissible.




Admissibility vs. Consistency? Technically, admissibility isn’t enough to guarantee correctness in graph search { you need the stronger condition of consistency. For a heuristic to be consistent, it must hold that if an action has cost c, then taking that action can only cause a drop in heuristic of at most c. If your heuristic is not only admissible, but also consistent, you will receive 1 additional point for this question.




Almost always, admissible heuristics are also consistent, especially if they are derived from problem relax-ations. Therefore it is probably easiest to start out by thinking about admissible heuristics. Once you have an admissible heuristic that works well, you can check whether it is indeed consistent, too. Inconsistency can sometimes be detected by verifying that your returned solutions are non-decreasing in f-value. Moreover, if UCS and A* ever return paths of di erent lengths, your heuristic is inconsistent. This stu is tricky. If you need help, don’t hesitate to ask!




Suboptimal Search




Sometimes, even with A* and a good heuristic, nding the optimal path through all the dots is hard. In these cases, we’d still like to nd 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 nds a path to the closest dot.




Question 8 (2 points) Implement the function findPathToClosestDot in searchAgents.py. Our agent solves this maze (sub-optimally!) 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 ll 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 nd the shortest possible path through the maze. (If you don’t understand why, ask!) In fact, you can do better if you try.




Mini Contest (2 points extra credit) Implement an ApproximateSearchAgent in searchAgents.py that nds a short path through the bigSearch layout. The agents that nd the shortest path using no more than 30 seconds of computation will receive 2 extra credit points and 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! We reserve the right to give addi-tional extra credit to creative solutions, even if they don’t work that well. Don’t hard-code the path, of course.




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 de ned at the top of search.py




PositionSearchProblem (searchAgents.py)




A speci c type of SearchProblem that you will be working with | it corresponds to searching for a single pellet in a maze.




CornersProblem (searchAgents.py)




A speci c type of SearchProblem that you will de ne | it corresponds to searching for a path through all four corners of a maze.




FoodSearchProblem (searchAgents.py)




A speci c 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 algo-rithm, 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 rst 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.