COMP3411/9814 Artificial Intelligence
Term 1, 2022
Assignment 1 – Search and Constraint Solving
Due: Friday 11 March, 10:00 pm
Marks: 20% of final assessment for COMP3411/9814 Artificial Intelligence
Part 1 - Search
Question 1: Search Algorithms for the 15-Puzzle
In this question you will construct a table showing the number of states expanded
when the 15-puzzle is solved, from various starting positions, using four different
searches:
(i) Uniform Cost Search (with Dijkstra’s Algorithm)
(ii) Iterative Deepening Search
(iii) ASearch (using the Manhattan Distance heuristic)
(iv) Iterative Deepening A Search
Go to theWebCMS. Under “Assignments” you will find Prolog Search Code
“prolog_search.zip”. Unzip the file and change directory to prolog search, e.g.
unzip prolog_search.zip
cd prolog_search
Start prolog and load puzzle15.pl and ucsdijkstra.pl by typing
[puzzle15].
[ucsdijkstra].
Then invoke the search for the specified start10 position by typing
start10(Pos),solve(Pos,Sol,G,N),showsol(Sol).
When the answer comes back, just hit Enter/Return. This version of Uniform Cost
Search (UCS) uses Dijkstra’s algorithm which is memory efficient, but is designed to
return only one answer. Note that the length of the path is returned as G, and the total
number of states expanded during the search is returned as N.
a) Draw up a table with four rows and five columns. Label the rows as UCS, IDS, A*
and IDA*, and the columns as start10, start12, start20, start30
and start40. Run each of the following algorithms on each of the 5 start states:
(I)
[ucsdijkstra]
(II)
[ideepsearch]
(III)
[astar]
(IV)
[idastar]
In each case, record in your table the number of nodes generated during the search.
If the algorithm runs out of memory, just write “Mem” in your table. If the code
runs for five minutes without producing out- put, terminate the process by typing
Control-C and then “a”, and write “Time” in your table. Note that you will need
to re-start prolog each time you switch to a different search.
b) Briefly discuss the efficiency of these four algorithms (including both time and
memory usage).
Question 2: Heuristic Path Search for 15-Puzzle
In this question you will be exploring an Iterative Deepening version of the Heuristic
Path Search algorithm discussed in the Week 2 Tutorial. Draw up a table in the
following format:
The top row of the table has been filled in for you (to save you from running some
rather long computations).
(a) Run [greedy] for start50, start60 and start64, and record the values returned for G
and N in the last row of your table (using the Manhattan Distance heuristic defined
in puzzle15.pl).
(b) Now copy idastar.pl to a new file heuristic.pl and modify the code of this new file
so that it uses an Iterative Deepening version of the Heuristic Path Search algorithm
discussed in the Weak 3 Tutorial Exercise, with w = 1.2 .
In your submitted document, briefly show the section of code that was changed, and
the replacement code.
© Run [heuristic] on start50, start60 and start64 and record the values of G and N in
your table. Now modify your code so that the value of w is 1.4, 1.6 ; in each case,
run the algorithm on the same three start states and record the values of G and N in
your table.
(d) Briefly discuss the tradeoff between speed and quality of solution for these five
algorithms.
In each case, record in your table the number of nodes generated dur-
ing the search. If the algorithm runs out of memory, just write “Mem”
in your table. If the code runs for five minutes without producing out-
put, terminate the process by typing Control-C and then “a”, and write
“Time” in your table. Note that you will need to re-start prolog each
time you switch to a different search.
(b) Briefly discuss the efficiency of these four algorithms (including both time
and memory usage).
Question 2: Heuristic Path Search for 15-Puzzle (2 marks)
In this question you will be exploring an Iterative Deepening version of the
Heuristic Path Search algorithm discussed in the Week 4 Tutorial. Draw up
a table in the following format:
start50
start60
start64
IDA∗
50
14642512
60
321252368
64
1209086782
1.2
1.4
1.6
Greedy
The top row of the table has been filled in for you (to save you from running
some rather long computations).
(a) Run [greedy] for start50, start60 and start64, and record the values
returned for G and N in the last row of your table (using the Manhattan
Distance heuristic defined in puzzle15.pl).
(b) Now copy idastar.pl to a new file heuristic.pl and modify the code of
this new file so that it uses an Iterative Deepening version of the Heuristic
Path Search algorithm discussed in the Week 4 Tutorial Exercise, with
w = 1.2 .
In your submitted document, briefly show the section of code that was
changed, and the replacement code.
© Run [heuristic] on start50, start60 and start64 and record the
values of G and N in your table. Now modify your code so that the value
of w is 1.4, 1.6 ; in each case, run the algorithm on the same three start
states and record the values of G and N in your table.
(d) Briefly discuss the tradeoff between speed and quality of solution for
these five algorithms.
2
Part 2 - Constraint Solving
Question 1: Arc Consistency
Consider a scheduling problem, similar to the one discussed in lectures, where there are
five variables A, B, C, D, and E, each with domain {1, 2, 3, 4}. Suppose the constraints
are: E − A is even, C ̸= D, C > E, C ̸= A, B > D, D > E, B > C.
Show how arc consistency can be used to solve this problem. To do this you need to
• draw the constraint graph,
• show which elements of a domain are deleted at each step, and which arc is
responsible for removing the element,
• show explicitly the constraint graph after arc consistency has stopped.
• show how splitting domains can be used to solve this problem. Include all arc
consistency steps.
Question 2: Variable Elimination
Consider the constraint graph, below, with named binary constraints. r1 is a relation on
A and B, which we can write as r1(A, B), and similarly for the other relations. Consider
solving this network using VE.
(a) Suppose you were to eliminate variable A. Which constraints are removed? A
constraint is created on which variables? (You can call this r11).
(b) Suppose you were to subsequently eliminate B (i.e., after eliminating A). Which
relations are removed? A constraint is created on which variables?
30
4. Reasoning With Constraints
A
r1
B
D
r3
r2
r6
r4
r7
r5
C
E
F
G
r8
r9
r10
Figure 4.3: Abstract constraint network
Sample Exam Questions
Exercise 4.14 Why would a local search algorithm choose something other than the
neighboring variable-value pair that is the best according to its heuristic?
Submitting your assignment
Your submission will consist of a single PDF file assign1.pdf which should contain the
results of your search experiments in part 1 and the answers to the questions in part 2.
To hand in, log in to a School of CSE Linux workstation or server, make sure that your
files are in the current working directory, and use the Unix command:
% give cs3411 assign1 assign1.pdf
Please make sure your code works on CSE’s Linux machines and generates no
warnings. Remove all test code from your submission. Make sure you have named
your predicates correctly.
You can submit as many times as you like - later submissions will overwrite earlier
ones. Once give has been enabled, you can check that your submission has been
received by using one of these commands:
The submission deadline is Friday 11 March, 10:00 pm.
10% penalty will be applied to the (maximum) mark for every 24 hours late after the
deadline.
Questions relating to the project can be posted to the forums on the course Web site.
If you have a question that has not already been answered on the forum, you can email
it to [email protected]
Plagiarism Policy
Group submissions are not allowed. Your program must be entirely your own work.
Plagiarism detection software will be used to compare all submissions pairwise
(including submissions for any similar projects from previous years) and serious
penalties will be applied, particularly in the case of repeat offences.
DO NOT COPY FROM OTHERS. DO NOT ALLOW ANYONE TO SEE YOUR
CODE
Please refer to the UNSW Policy on Academic Honesty and Plagiarism if you require
further clarification on this matter.