# Homework 1 3D Travelling-Salesman Problem (TSP)

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CSCI-561 – Foundations of Artificial Intelligence Homework 1
1. Project Description
This is a programming assignment in which you will apply AI search/optimization techniques
to a 3D Travelling-Salesman Problem (TSP) such as the one shown in Figure 1. Conceptually
speaking, the space of traveling is a set of “cities” located on some grid points with (x, y, z)
locations in which your AI agent has to travel. Your agent can travel from any city to any city
and the distance between two cities can be calculated as the Euclidean distance between
the two grid locations.
Figure 1: Traveling-Salesman Problem in 3D Space.
Your programming task is as follows. XYZ is a student at USC who has to run some errands
across campus. The student starts from his house location, travels around USC to complete the
errands, and returns home, or else the student will have to sleep on the streets :). Given is a list
of 3D coordinates where each coordinate points to a location within the USC campus (the z
coordinate represents the floor of the building located at (x, y)). The problem is that the student
is lazy, and does not want to walk a lot. Being a Computer Science student, XYZ notices that this
problem resembles Traveling Salesman Problem (TSP), and wants to tackle this problem using
one of the concepts he studied in CSCI-561 i.e Genetic Algorithm.
TSP is defined as given a list of cities/locations, the person has to go to all the locations exactly
once, return back to the starting point, and cover the minimum distance as a whole.
The student is happy that he studied this class and knows that by using Genetic Algorithm the
student will be able to find the optimal path. But he forgot how the Genetic Algorithm works.
Now, you being a good friend of XYZ and a current student of CSCI-561 during Fall 2022, have to
distance, visit every location exactly once, and return back to the start location. The shorter the
path distance, the better your agent is.
All homework material is checked vigorously for dishonesty using several methods. All detected
violations of academic honesty are forwarded to the Office of Student Judicial Affairs. To be safe
you are urged to err on the side of caution. Do not copy work from another student or off the
web. Keep in mind that sanctions for dishonesty are reflected in your permanent record and can
negatively impact your future success. As a general guide:
Do not copy code or written material from another student. Even single lines of code
should not be copied.
Do not collaborate on this assignment. The assignment is to be solved individually.
Do not copy code off the web. This is easier to detect than you may think.
Do not share any custom test cases you may create to check your program’s behavior in
more complex scenarios than the simplistic ones considered below.
Do not copy code from past students. We keep copies of past work to check for this.
Even though this problem differs from those of previous years, do not try to copy from
homework of previous years.
Do not ask on piazza how to implement some function for this homework, or how to
calculate something needed for this homework.
Do not post code on piazza asking whether or not it is correct. This is a violation of
Do not post test cases on piazza asking for what the correct solution should be.
Do ask the professor or TAs if you are unsure about whether certain actions constitute
dishonesty. It is better to be safe than sorry.
3. Assignment Terminologies
Location: A location is represented as a combination of 3D coordinate points, x, y, and z as
shown in the figure above. For example: (10, 0, 30) represents a city with x= 10, y = 0, z= 30.
Path: A list of locations that your agent will visit only once and return to the starting location.
For example: We have 3 locations A, B, C (each represented with 3D coordinates), then a valid
path for this would be [A -> B -> C -> A]. Note that the path is a loop and has the starting
location (A) as the final endpoint.
Grading for this assignment consists of 2 parts:
Part A – Optimality with respect to TA’s agent (60%)
We will run your search agent on the set of hidden test/grading cases to get the corresponding
shortest paths. We will then use your path to calculate the path cost to grade your agent using
the following criteria:
● Your score for a test case = (TA’s agent shortest path cost)/(your-path cost)
● If your path cost < TA’s agent path cost, we will give you full marks i.e 1 for that test case
● Sum up all the scores obtained in the above point and convert it to 60%.
Part B – Quality of your solution (40%)
This section will test the quality of your agent and differentiate amongst the agents developed
by other students. Students need to research and come up with ways they can improve their
Genetic Algorithm.
The path scores obtained in Part A (above) will be ranked against other students’ agents.
Rank-based scores will be calculated for the student’s agent which contributes to 40% of the
Student’s score = 40 * (1 − (𝑟𝑎𝑛𝑘/𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠))
5. Tips for Implementation
The students can read through the following material in this section and use it as
suggestions for their implementation.
NOTE: This section doesn’t list the entire working of the genetic algorithm and is in no way
mandated to follow exactly. These can be used as starting points for your assignment. You
a. Initial Population:
i. You will need to create the initial population and you can do it using the
following way:
CreateInitialPopulation(size, cities): Arguments defined below:
Size: An integer representing the size of the list (initial_population) which
needs to be returned.
Cities: A list of cities where a city is represented in 3d coordinates (x,y,z)
Return Value: returns a list of paths (a permutation of cities) of size = size
Students need to implement this function which creates paths randomly
or with some heuristic chosen by you.
b. Parent Selection:
i. In a genetic algorithm, parent selection is an important step. The method
your agent implements to select a parent will determine the optimality of
CreateMatingPool(population, RankList): Arguments defined below:
Population: A list of paths from which the mating pool is to be created
RankList: A list of tuples of index and fitness scores sorted in descending
order.
Return Value: A list of populations selected for mating (List contains
paths)
Function Definition: This function defines the best fit individuals and
selects them for breeding. You will implement a Roulette wheel-based
selection (reference link) which is a widely used and most efficient
method for selecting parents. Make sure to assign the appropriate
probabilities to the parents for roulette-wheel selection.
c. Crossover:
i. Crossover(Parent1, Parent2, Start_index, End_index): Arguments are as
follows:
Parent1: First argument of the function: A list containing the random
sequence of cities for the salesman to follow
Parent2: Second argument of the function: A list containing the random
sequence of cities for the salesman to follow
Start_index: Start index of the SUBARRAY to be chosen from parent 1
End_index: End index of the SUBARRAY to be chosen from parent 1
Return Value: Return child after performing the crossover (also a list
containing a valid sequence of cities)
Function Definition: In this function, students are asked to implement a
two-point crossover. Choose the subarray from Parent1 starting at
start_index and ending at end_index. Choose the rest of the sequence
from Parent 2. For example: if Start_index = 1 and End_Index = 3, then
the child created should look like the following:
Parent-1: 1,2,3,4,5
Parent-2: 5,4,3,2,1
Start_index = 1
End_Index = 3
Resulting Parent 1 subarray from Start_index to End_index = 2,3,4
Your function should return the child as:
=> Child: 5,2,3,4,1
Note: For TSP, the child follows the constraints of each city is only visited
once. So, any conflicts after copying the substring from parent 1, and the
rest of the sequence from parent 2 should be resolved by your function.
For example:
Parent-1: 1,2,3,4,5
Parent-2: 5,2,3,1,4
Start_index = 1
End_Index = 3
Resulting Parent 1 substring from Start_index to End_index = 2,3,4
Your function should return the child as:
=> Child: 5,2,3,4,1
Steps to resolve conflict:
● Copied subarray from parent-1 = 2,3,4
● Rest of the subarray from parent-2 = 5, . . .,4
● Resulting child list = 5,2,3,4,4
● Since the child doesn’t follow the TSP constraint (city 4 is coming
twice), we replace the last 4 from parent-2 with the missing city,
i.e. city 1.
6. Input and Output
Your program will be run in a directory on Vocareum that contains the following input file. Your
program should output the output file in the same directory.
Input: The file input.txt in the current directory of your program will be formatted as follows:
● 1st line: A strictly positive 32-bit integer N, indicating the number of “city” locations in
the 3D space.
● Next N lines: Each line is a city coordinate represented by three non-negative 32-bit
integers separated by one space character, for the grid location of the city.
Output: Report your path of traveling the cities, that is N locations of the city. For example:
● N+1 lines: Each line has three non-negative 32-bit integers separated by one space
character indicating the city visited in order.
● Note: Your path ends at the start city, hence you will have N+1 lines.
For example, if there are five cities, then the output path would be:
60 103 97 // the location of the 1st city visited
61 103 97
62 103 97
63 103 97
64 103 97 // the location of the Nth city visited
60 103 97 // the location of the start city
To assist your programming, you will be provided with some sample inputs and outputs (see
below). Please understand that the goal of these samples is to check that you can correctly parse
the problem definitions and generate a correctly formatted output. The samples are very simple,
and it should not be assumed that if your program works on the samples it would definitely work
make sure that your program will work correctly on any valid input. You are encouraged to design
and try your own test cases to check how your program would behave in some complex special
cases that you might think of. Since each homework is checked via an automated A.I. script,
your output should match the specified format exactly. Failure to do so will most certainly cost
some points. The output format is simple, and examples are provided. You should upload and
test your code on vocareum.com at their terminal window which is a Linux-like environment.
Please make sure you test your program at the terminal window at vocareum.com before you
click the submit button there. You can submit as many times as you like, and the last submission
7. Notes and Hints
– You may use any of the following programming languages: C++, Java, Python3, but
Python may be the preferred language to use in today’s large-scale AI program
applications.
– Please name your program “homework.xxx” where ‘xxx’ is the extension for the
programming language you choose (“py” for python, “cpp” for C++, and “java” for Java).
If you are using C++11, then the name of your file should be “homework11.cpp” and if
you are using python3 then the name of your file should be “homework3.py”. Please use
the programming languages mentioned above for this homework.
– If you are using python, then make a note that the highest version of Python that is
offered is Python 3.7.5, hence the walrus operator and other features of the higher
version of python are not supported. JAVA
– Try first to fully understand the genetic algorithm before developing your own code.
– To allow us to grade the whole class in a reasonable amount of time, your program will
be killed after some time (e.g. it takes too long to return or appears stuck on a given test
case. In this situation, you will get 0 points on the ongoing test case no matter if the
output is generated or not. We will make sure that the time limit for a given test or
grading case (or class) is sufficient and long enough for solving the case for correct
algorithm implementation.
– The time limit is the total combined CPU time as measured by the Unix time command.
This command measures pure computation time used by your program, and discards
time taken by the operating system, disk I/O, program loading, etc. Beware that it
and use 400% CPU for 10 seconds, this will count as using 40 seconds of allocated time).
– There is no limit on the input size, the number of cities, and any other 32-bit integer
specified above. However, we will seriously consider the complexity of each test case.
You should take care of the data structures used in your algorithms so that the program
returns in a bounded time. Additional information may be posted on Piazza if necessary.
– If several optimal solutions exist, then any of them will count as correct.
– There may be a lot of Q&A on Piazza. Please always search for relevant questions before
posting a new one. Duplicate questions make everyone’s lives harder.
– Only submit the source code files (in .java, .py or .cpp) and helper files (if any, in .json or
.txt). All other files should be excluded.
password” for the first time login. You should have been enrolled in this course on
Piazza so that we can invite you again.
– You can submit your homework code (by clicking the “submit” button on Vocareum) as
many times as you want. Only the latest submission will be considered for grading. After
the initial deadline, the submission window will still be open for 5 days. However, a late
penalty will be applied as 20% per day if your latest submission is later than the initial
– Every time you click the “submit” button, you can view your submission report to see if
your code works. The grading report will be released after the due date of the project.
– You don’t have to keep the page open on Vocareum while the scripts are running.
– Every time you click the “submit” button on Vocareum, your submitted agent will be run
and tested by our AI script on a number of test cases and the results will be reported to
you in the submission report which you can read and examine. You may use these
reports for debugging and improving your agent. Notice that these are “test cases”, and
and may not be available to your search agent before the grading process begins.
– It’s highly suggested to reserve some time for submission and testing on Vocareum
because you may come across some technical issues if this is the first time to use it.
Anyway, don’t wait until the last minute!
– Be careful and avoid multiple submissions of large files to Vocareum. Vocareum does not
allow students to delete old submissions, and in the past, students have run out of space
and been unable to use Vocareum until we got in touch with support and asked them to
delete files.
command-line argument. It should read a text file called “input.txt” in the current directory that
contains a problem definition. It should create and write a file “output.txt” with your solution in
the same current directory. The format for input.txt and output.txt is specified as in section 5.
The end-of-line character is LF (since vocareum is a Unix system and follows the Unix
convention).
– Create an input.txt file and delete any old output.txt file.
– Check the correctness of your program’s output.txt file.
– For Section 4, Part A, there will be 40 test cases divided into four classes: Class1 (easy),
10 cases; Class2 (medium), 10 cases; Class3 (hard), 10 cases; and Class4 (complex), 10
cases.
– We will make sure that the time limit for a given test or grading case (or class) is
sufficient and long enough for solving the case for correct algorithm implementation.
– Class 1 (easy): < 60 seconds
– Class 2 (medium): < 75 seconds
– Class 3 (hard): < 120 seconds
– Class 4 (complex): < 200 seconds
Time limits are uniformly measured by Vocareum (instead of anyone’s local machine).
They are typically determined by a standard algorithm implementation that has been
tested thoroughly, and we ensure that these time limits
are typically very generous.
Note that if your code can’t be compiled, or somehow fails to load and parse input.txt, or writes
an incorrectly formatted output.txt, or no output.txt at all, or OuTpUt.TxT, you will get zero
points. Anything you write to stdout or stderr will be ignored and is ok to leave in the code you
submit (but it will likely slow you down). Please test your program on Vocareum’s terminal
window with the provided sample files to avoid any problems.
9. Example Input and Output
The students need to understand the format in which the input.txt is given and the format of the
output.txt that is needed from them. Post your queries on Piazza if you have any.
Example 1:
=========input.txt==========
3
158 147 135
56 24 160
162 194 104
==========================
=========output.txt=========
162 194 104
158 147 135
56 24 160
162 194 104
==========================
Example 2:
=========input.txt==========
5
59 170 117
113 152 44
174 135 162
11 36 174
177 32 24
==========================
=========output.txt=========
11 36 174
174 135 162
177 32 24
113 152 44
59 170 117
11 36 174
==========================
Example 3:
=========input.txt==========
7
199 173 30
120 199 34
144 39 130
137 199 93
153 196 97
175 53 76
173 101 186
==========================
=========output.txt=========
120 199 34
199 173 30
175 53 76
144 39 130
173 101 186
153 196 97
137 199 93
120 199 34
==========================

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