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日期:2020-06-27 10:45

COMP9414: Artificial Intelligence

Assignment 1: Fuzzy Scheduling

Due Date: Week 5, Friday, July 3, 11:59 p.m.

Value: 15%

This assignment concerns developing optimal solutions to a scheduling problem inspired by the

scenario of a manufacturing plant that has to fulfil multiple customer orders with varying deadlines,

but where there may be constraints on tasks and on relationships between tasks. Any number

of tasks can be scheduled at the same time, but it is possible that some tasks cannot be finished

before their deadline. A task finishing late is acceptable, however incurs a cost, which for this

assignment is a simple (dollar) amount per hour that the task is late.

A fuzzy scheduling problem in this scenario is specified by ignoring orders and giving a number

of tasks, each with a fixed duration in hours. Each task must start and finish on the same day,

within working hours (9am to 5pm). In addition, there can be constraints both on single tasks

and between two tasks. One type of constraint is that a task can have a deadline, which can be

“hard” (the deadline must be met in any valid schedule) or “soft” (the task may be finished late

– though still at or before 5pm – but with a “cost” per hour for missing the deadline). The aim

is to develop an overall schedule for all the tasks (in a single week) that minimizes the total cost

of all the tasks that finish late, provided that all the hard constraints on tasks are satisfied.

More technically, this assignment is an example of a constraint optimization problem, a problem

that has constraints like a standard Constraint Satisfaction Problem (CSP), but also a cost associated

with each solution. For this assignment, you will implement a greedy algorithm to find

optimal solutions to fuzzy scheduling problems that are specified and read in from a file. However,

unlike the greedy search algorithm described in the lectures on search, this greedy algorithm has

the property that it is guaranteed to find an optimal solution for any problem (if a solution exists).

You must use the AIPython code for constraint satisfaction and search to develop a greedy search

method that uses costs to guide the search, as in heuristic search. The search will use a priority

queue ordered by the values of the heuristic function that give a cost for each node in the search.

The heuristic function for use in this assignment is defined below. The nodes in the search

are CSPs, i.e. each state is a CSP with variables, domains and the same constraints (and a cost

estimate). The transitions in the state space implement domain splitting subject to arc consistency.

A goal state is an assignment of values to all variables that satisfies all the constraints.

A CSP for this assignment is a set of variables representing tasks, binary constraints on pairs

of tasks, and unary constraints (hard or soft) on tasks. The domains are all the working hours

in one week, and a task duration is in hours. Days are represented (in the input and output)

as strings ‘mon’, ‘tue’, ‘wed’, ‘thu’ and ‘fri’, and times are represented as strings ‘9am’, ‘10am’,

‘11am’, ‘12pm’, ‘1pm’, ‘2pm’, ‘3pm’, ‘4pm’ and ‘5pm’. The only possible values for the start and

end times of a task are combinations of such days and times, e.g. ‘mon 9am’. Each task name is

a string (with no spaces), and the only soft constraints are the soft deadline constraints.

The possible input (tasks and constraints) are as follows:

# binary constraints

constraint, ht1i before ht2i # t1 ends when or before t2 starts

constraint, ht1i after ht2i # t1 starts after or when t2 ends

constraint, ht1i same-day ht2i # t1 and t2 are scheduled on the same day

constraint, ht1i starts-at ht2i # t1 starts exactly when t2 ends

# hard domain constraints

domain, hti hdayi # t starts on given day at any time

domain, hti htimei # t starts at given time on any day

domain, hti starts-before hdayi htimei # at or before given time

domain, hti starts-after hdayi htimei # at or after given time

domain, hti ends-before hdayi htimei # at or before given time

domain, hti ends-after hdayi htimei # at or after given time

domain, hti starts-in hdayi htimei-hdayi htimei # day-time range

domain, hti ends-in hdayi htimei-hdayi htimei # day-time range

domain, hti starts-before htimei # at or after time on any day

domain, hti ends-before htimei # at or before time on any day

domain, hti starts-after htimei # at or after time on any day

domain, hti ends-after htimei # at or after time on any day

# soft deadline constraints

domain, hti ends-by hdayi htimei hcosti # cost per hour of missing deadline

# tasks with name and duration

task, hnamei hdurationi

To define the cost of a solution (that may only partially satisfy the soft deadline constraints), add

the costs associated with violating the soft constraints over all tasks. Let V be the set of variables

(representing tasks) and C be the set of all soft deadline constraints. Suppose such a constraint c

with deadline (dc, tc) and penalty cost costc applies to variable v, and let (dv, tv) be the end day

and time of v in a solution S. For example, costc might be 100 and (dv, tv) might be (mon, 5pm)

while the deadline (dc, tc) is (mon, 3pm); the cost of this variable assignment is 200.

Define the delay δ((d1, t1),(d2, t2)) to be the number of hours that (d1, t1) is after (d2, t2) if this is

positive, and 0 otherwise, where a full day counts as 24 hours. Then, where cv is the soft deadline

constraint applying to variable v:

cost(S) = P

cv∈C

costcv ? δ((dv, tv),(dcv

, tcv

))

Heuristic

In this assignment, you will implement greedy search using a priority queue to order nodes based

on a heuristic function h. This function must take an arbitrary CSP and return an estimate of the

distance from any state S to a solution. So, in contrast to a solution, each variable v is associated

with a set of possible values (the current domain).

The heuristic estimates the cost of the best possible solution reachable from a given state S by

assuming each variable can be assigned the value that minimizes the cost of the soft deadline

constraint applying to that variable. The heuristic function adds these minimal costs over the set

of all variables, similar to calculating the cost of a solution cost(S) above. Let S be a CSP with

variables V and let the domain of v, written dom(v), be a set of end days and times for v. Then,

where the summation is over all soft deadline constraints cv as above:

h(S) = P

cv∈C min(dv,tv )∈dom(v) costcv ? δ((dv, tv),(dcv

, tcv

))

Implementation

Put all your code in one Python file called fuzzyScheduler.py. You may (in one or two cases)

copy code from AIPython to fuzzyScheduler.py and modify that code, but do not copy large

amounts of AIPython code. Instead, in preference, write classes in fuzzyScheduler.py that

extend the AIPython classes.

Use the Python code for generic search algorithms in searchGeneric.py. This code includes a

class Searcher with a method search that implements depth-first search using a list (treated

as a stack) to solve any search problem (as defined in searchProblem.py). For this assignment,

modify the AStarSearcher class that extends Searcher and makes use of a priority queue to store

the frontier of the search. Order the nodes in the priority queue based on the cost of the nodes

calculated using the heuristic function.

Use the Python code in cspProblem.py, which defines a CSP with variables, domains and constraints.

Add costs to CSPs by extending this class to include a cost and a heuristic function h to

calculate the cost. Also use the code in cspConsistency.py. This code implements the transitions

in the state space necessary to solve the CSP. The code includes a class Search with AC from CSP

that calls a method for domain splitting. Every time a CSP problem is split, the resulting CSPs

are made arc consistent (if possible). Rather than extending this class, you may prefer to write

a new class Search with AC from Cost CSP that has the same methods but implements domain

splitting over constraint optimization problems.

You should submit your fuzzyScheduler.py and any other files from AIPython needed to run

your program (see below). The code in fuzzyScheduler.py will be run in the same directory

as the AIPython files that you submit. Your program should read input from a file passed as an

argument and print output to standard output.

Sample Input

All input will be a sequence of lines defining a number of tasks, binary constraints and domain

constraints, in that order. Comment lines (starting with a ‘#’ character) may also appear in the

file, and your program should be able to process and discard such lines. All input files can be

assumed to be of the correct format – there is no need for any error checking of the input file.

Below is an example of the input form and meaning. Note that you will have to submit at least

three input test files with your assignment. These test files should include one or more comments

to specify what scenario is being tested.

# two tasks with two binary constraints and soft deadlines

task, t1 3

task, t2 4

# two binary constraints

constraint, t1 before t2

constraint, t1 same-day t2

# domain constraint

domain, t2 mon

# soft deadlines

domain, t1 ends-by mon 3pm 10

domain, t2 ends-by mon 3pm 10

Sample Output

Print the output to standard output as a series of lines, giving the start day and time for each task

(in the order the tasks were defined). If the problem has no solution, print ‘No solution’. When

there are multiple optimal solutions, your program should produce one of them. Important: For

auto-marking, make sure there are no extra spaces at the ends of lines, and no extra line at the

end of the output. Set all display options in the AIPython code to 0.

The output corresponding to the above input is as follows:

t1:mon 9am

t2:mon 12pm

cost:10

Submission

? Submit all your files using the following command (this includes relevant AIPython code):

give cs9414 ass1 fuzzyScheduler.py search*.py csp*.py display.py *.txt

? Your submission should include:

– Your .py source file(s) including any AIPython files needed to run your code

– A series of .txt files (at least three) that you have used as input files to test your system

(each including comments to indicate the scenarios tested), and the corresponding .txt

output files (call these input1.txt, output1.txt, input2.txt, output2.txt, etc.);

submit only valid input test files

? When your files are submitted, a test will be done to ensure that your Python files run on

the CSE machine (take note of any error messages printed out)

? Check that your submission has been received using the command:

9414 classrun -check ass1

Assessment

Marks for this assignment are allocated as follows:

? Correctness (auto-marked): 10 marks

? Programming style: 5 marks

Late penalty: 3 marks per day or part-day late off the mark obtainable for up to 3

(calendar) days after the due date.

Assessment Criteria

? Correctness: Assessed on valid input tests as follows (where the input file can have any

name, not just input1.txt, so read the file name from sys.argv[1]):

python3 fuzzyScheduler.py input1.txt > output1.txt

? Programming style: Understandable class and variable names, easy to understand code,

good reuse of AIPython code, adequate comments, suitable test files

Plagiarism

Remember that ALL work submitted for this assignment must be your own work and no code

sharing or copying is allowed. You may use code from the Internet only with suitable attribution

of the source in your program. Do not use public code repositories. All submitted assignments will

be run through plagiarism detection software to detect similarities to other submissions, including

from past years. You should carefully read the UNSW policy on academic integrity and plagiarism

(linked from the course web page), noting, in particular, that collusion (working together on an

assignment, or sharing parts of assignment solutions) is a form of plagiarism. There is also a new

plagiarism policy starting this term with more severe penalties.


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