This assignment covers state-space search in single-agent, deterministic environments. Later we will consider multi-agent search in environments with stochastic dynamics. We start by introducing a framework for the classical theory of problem solving. Then we examine heuristic search. This assignment is quite substantial, and that's one reason it is divided into two parts.

Along with various Python files, you'll be submitting two separate report files, one called BlindSearches.pdf (that you create in Part 1) and one called HeuristicSearches.pdf (that you create in Part 2).

This part is about basic problem formulation and basic search algorithms.

Although both Part 1 and Part 2 are due on Monday, January 22, there is an option to submit your solution for Part 1 early and receive a 5-point bonus. To get the bonus, submit your Part 1 files by 11:59 PM on Wednesday, January 17, to GradeScope, and don't overwrite it with a submission after the early-bird deadline. If you do submit early, you retain the right to resubmit Part 1 later, but the bonus will not accrue in that case.

1. First, download the starter code for this assignment. Unzip it with a utility such as Windows Compressed Folders, etc.

In the given formulation files, pay particular attention to how the State class is defined and how the operators are established. We will be talking about this code in class.

python Int_Solv_Client.py TowersOfHanoi 3

(a) Run the interactive solving client and by trying different operators solve the problem of getting all the humans and robots across the river. (b) Examine the formulation code, and focus most of your attention on the can_move method, which implements the preconditions for all the operators of this formulation. (c) In this method, there are five lines of code containing "return False". Explain what is going on in the 4th one of these lines. Put your answer into your Part 1 Report file ("BlindSearches.pdf") under the heading "Part 1 Step 4 (c)."

9. The starter-code file UCS.py, provides an implemention of the Uniform-Cost Search algorithm. This file also provides you with an implementation of a special kind of priority queue which supports not only the standard insert and delete_min operations, but also a method called contains, which returns True if a given element is in the priority queue. It also allows accessing and updating the priority value of any element in the priority queue. See the documentation for more information. This priority queue is not just adequate for implementing Uniform-Cost Search, but is particularly helpful in implementing the A* Search algorithm.
The main difference between Breadth-First Search and Uniform-Cost Search (UCS) is that UCS works with problem formulations that have different costs associated with different moves. In terms of graph search, there are edge costs, and they are not necessarily assumed to be all equal to 1 as they essentially are in Breadth-First Search.

The starter code includes a new problem formulation for you to use with UCS; it's the French Cities network in which the problem is to find a shortest route from the initial-state city to the goal-state city. These are, by default, RENNES and AVIGNON. (These could easily be changed by editing the formulation file's line defining STARTING_CITY, etc.) This formulation is in the file FranceWithCosts.py.
The State class in this formulation file has a method edge_distance(s2), which is used to get the edge cost from the current state to s2. You'll be setting up the UCS.py program to use these cost values to determine the cost of the lowest-cost path from the starting state to any newly reached state.
When the UCS algorithm reaches a goal state, it produces a backtrace of "backlinks" (sometimes called predecessor links) to represent the actual lowest-cost path from the start state to the goal state found. The file UCS.py includes a method runUCS.

For the default initial state and goal state, the results are

['Rennes', 'Nantes', 'Limoges', 'Lyon', 'Avignon']

1041.0

Page 184 in the reading shows the state space for this problem, with the distances on the graph edges. When you run the code you should get a solution path of 4 edges (5 cities) and total distance 1041: [’Rennes’, ’Nantes’, ’Limoges’, ’Lyon’, ’Avignon’]. It might be formatted differently in the printout. The map is also shown below:

Map showing French cities (which serve as the states of this problem) and distance values on roads (represented as graph edges) between them.

Implement an A* search program, putting your code into the starting template file AStar.py. You may wish to cut and paste from the UCS.py file, since most of the implementation will be identical.

Develop your A* program to work with the heuristic function defined in the file FranceWithDXHeuristic.py. Your program will be operated as follows:

python AStar.py FranceWithDXHeuristic

Here are some hints about how to modify UCS.py to implement A*. Change the names of the file and the algorithm in the code and the comments. After the code that imports the Problem, assign self.h = Problem.h, so that you can call the heuristic function easily in your algorithm. Within the search algorithm, any time UCS uses gs or new_g as a priority value, you should compute f (or call it fs or new_f, depending on the context), and use the f value as the priority.

When checking the CLOSED list, don't necessarily delete the new state if the same city is already on CLOSED, but look at the priority, and if the new state has a lowever priority value, delete the state on CLOSED and put the new one on OPEN.

Make sure that the first five CAPITALIZED variables in class AStar get assigned the values they need (as described in the corresponding comments), so that you can receive credit on autograder tests. These include self.COUNT through self.TOTAL_COST. The solution path should be set as the value of self.PATH, and it must be a list of strings, such as ['Rennes', 'Nantes', 'Limoges', 'Lyon', 'Avignon']. Also, be sure to assign proper values in the dictionary for self.g.

Try to solve some instances of the Eight Puzzle using UCS.py. There is a default instance you should try first. You can do it with the command line:

python UCS.py EightPuzzle

python UCS.py EightPuzzle '[[3, 1, 2], [4, 5, 0], [6, 7, 8]]'

python UCS.py puzzle_rotate_2

Example puzzles to try:

# Puzzle A. (should be very fast)
python UCS.py EightPuzzle '[[3,0,1],[6,4,2],[7,8,5]]'

# Puzzle B. (should not take long)
python UCS.py EightPuzzle '[[3,1,2],[6,8,7],[5,4,0]]'

# Puzzle C. (May take a few minutes)
python UCS.py EightPuzzle '[[4,5,0],[1,2,8],[3,7,6]]'

# Puzzle D. (May take several minutes)
python UCS.py EightPuzzle '[[0,8,2],[1,7,4],[3,6,5]]'

# Test with Puzzle A:
python AStar.py EightPuzzleWithHamming '[[3,0,1],[6,4,2],[7,8,5]]'

You'll be turning in a report for this part of the assignment in addition to your code (see below). Create a section of your report called "Heuristics for the Eight Puzzle". Compare the performance of these heuristics on each of the example puzzles (given above). For each puzzle-heuristic pair, report (a) whether the puzzle was successfully solved, (b) length of the solution path found, in number of edges, (c) total cost of the path found, (d) number of states expanded, and (d) MAX_OPEN_LENGTH. Put this information into the table, described below.

The table should have a row for each puzzle instance and heuristic (e.g., "(Puzzle A, Hamming)", and columns for the following: puzzle instance permutation (e.g., [3,0,1,6,4,2,7,8,5]; this flattened list is OK here), success (yes/no), count of expanded nodes, aborted (yes/no). If it takes more than 5 minutes to solve a particular problem with a particular heuristic then note that; you may abort such runs. You are welcome to use the format for your report: shown in the starter-code file named HeuristicSearches-template.txt.

Here are some ideas to keep in mind for this assignment. The problem format we are using not only permits the "manual solving" that you do with the Interactive Solving Client. It also permits automatic solving, such as with DFS, and BFS. Thus it is important that you follow the problem structure correctly. Certain methods are required in the State class, including __init__, __eq__, __hash__, __str__, and copy. The operators must have the correct structure, as well. The nice thing about the Interactive Solving Client is that it provides a pretty good means to test whether your formulation will be OK.

Even if you are familiar with Python, there may be some constructs in the formulation files that you are not familiar with. You can read up on list comprehensions (p.31 of the first reading) and lambda expressions (pp. 47-52 of that reading). We'll also cover them in class.

Parts of your code will be graded by an autograder. To do this, your files will be imported as modules by the autograder. Your search should not automatically start running when the module is imported. The starter template file AStar.py comes with some code at the end of the file that takes care of this. This code is: "if __name__ == '__main__' " which avoids running the search automatically if it is being imported, but still runs it automatically if it is the main program. The autograder will be comparing the solutions and statistics found by your code with expected solutions, by calling functions in your code and examining the values of certain variables in your code. These variables are generally already in place for you in the starter code UCS.py. So you should not rename variables like self.PATH or any of the other variables written with all CAPITAL letters.

Each of your Python files should begin with a multiline string (more details are shown below.)

Follow reasonable commenting practice in your code. The comments in the starter code can serve as examples of the commenting style that we consider appropriate.

For Part 1, turn in the following files to GradeScope:

Farmer_Fox.py
FFCG-log.txt
ItrBFS.py
BlindSearches.pdf

For Part 2, turn in the following files to GradeScope:

partnership-retrospective.txt
AStar.py
EightPuzzleWithHamming.py
EightPuzzleWithManhattan.py
HeuristicSearches.pdf

Each of the Python files should start with a multiline comment in the following format with your own information rather than the sample information given here.

'''Farmer_Fox.py
by John Nathan Smith and Emily Doe
UWNetIDs: jnsmith25, emilydoe24
Student numbers: 2576543, 2483119

Assignment 2, Part 1, in CSE 415, Winter 2024
 
This file contains my (or our) problem formulation for the problem of
the Farmer, Fox, Chicken, and Grain.
'''

The turn-in method is via file uploads to GradeScope. Be sure to upload your Part 1 files to the A2-Part-1 assignment, and upload your Part 2 files to the A2-Part-2 assignment. We expect to grade this assignment semi-automatically, and having files in the wrong places might lead to unnecessary losses in points.

If needed, updates and corrections will be posted here, and/or in ED.