Andrea Rendl PhD thesis

241 Pages·2010·2.57 MB·English

EFFECTIVE COMPILATION OF CONSTRAINT MODELS
Andrea Rendl
A Thesis Submitted for the Degree of PhD
at the
University of St. Andrews
2010
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Effective Compilation of Constraint
Models
A thesis submitted to the
UNIVERSITY OF ST ANDREWS
for the degree of
DOCTOR OF PHILOSOPHY
by
Andrea Rendl
SchoolofComputerScience
UniversityofStAndrews
January2010

A
BSTRACT
ConstraintProgrammingisapowerfultechniqueforsolvinglarge-scalecombinatorial(op-
timisation) problems. However, it is often inaccessible to users without expert knowledge
in the area, precluding the wide-spread use of Constraint Programming techniques. This
thesisaddressesthisissueinthreemaincontributions.
First, we propose a simple ‘model-and-solve’ approach, consisting of a framework where
the user formulates a solver-independent problem model, which is then automatically tai-
lored to the input format of a selected constraint solver (a process similar to compiling a
high-level modelling language to machine code). The solver is then executed on the in-
put, solver, and solutions (if they exist) are returned to the user. This allows the user to
formulateconstraintmodelswithoutrequiringanyparticularbackgroundknowledgeofthe
respective solver and its solving technique. Furthermore, since the framework can target
severalsolvers,theusercanexploredifferenttypesofsolvers.
Second,weextendthetailoringprocesswithmodeloptimisationsthatcancompensatefora
wideselectionofpoormodellingchoicesthatnovices(andexperts)inConstraintProgram-
ming often make and hence result in redundancies. The elimination of these redundancies
by the proposed optimisation techniques can result in solving time speedups of over an
order of magnitude, in both naive and expert models. Furthermore, the optimisations are
particularlylight-weight,addingnegligibleoverheadtotheoveralltranslationprocess.
The third contribution is the implementation of this framework in the tool TAILOR, that
currentlytranslates2differentsolver-independentmodellinglanguagesto3differentsolver
formats and is freely available online. It performs almost all optimisation techniques that
areproposedinthisthesisanddemonstratesitssignificanceinourempiricalanalysis.
In summary, this thesis presents a framework that facilitates modelling for both experts
and novices: problems can be formulated in a clear, high-level fashion, without requiring
anyparticularbackgroundknowledgeaboutconstraintsolversandtheirsolvingtechniques,
while (sometimes naturally occurring) redundancies in the model are eliminated for prac-
tically no additional cost, improving the respective model in solving performance by up to
anorderofmagnitude.

I, Andrea Rendl, hereby certify that this thesis, which is approximately 78,500 words in
length, has been written by me, that it is the record of work carried out by me, and that it
hasnotbeensubmittedinanypreviousapplicationforahigherdegree.
date signatureofcandidate
I was admitted as a research student in September 2006 and as a candidate for the degree
ofDoctorofPhilosophyinSeptember2006;thehigherstudyforwhichthisisarecordwas
carriedoutintheUniversityofStAndrewsbetween2006and2009.
date signatureofcandidate
I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regu-
lationsappropriatefor thedegreeofDoctorof PhilosophyintheUniversity ofStAndrews
andthatthecandidateisqualifiedtosubmitthisthesisinapplicationforthatdegree.
date signatureofsupervisor
In submitting this thesis to the University of St. Andrews I understand that I am giving
permission for it to be made available for use in accordance with the regulations of the
University Library for the time being in force, subject to any copyright vested in the work
not being affected thereby. We also understand that the title and the abstract will be pub-
lished, and that a copy of the work may be made and supplied to any bona fide library or
research worker, that my thesis will be electronically accessible for personal or research
use unless exepmt by award of an embargo as requested below, and that the library has the
righttomigratemythesisintonewelectronicformsasrequiredtoensurecontinuedaccess
tothethesis. Wehaveobtainedanythird-partycopyrightpermissionsthatmayberequired
in order t oallow such access and migration, or have requested the appropriate embargo
below.
The following is an agreed request by the candidate and the supervisor regarding the elec-
tronicpublicationofthisthesis:
Access to Printed copy and electronic publication of thesis through the University of St
Andrews.
date signatureofcandidate

A
CKNOWLEDGEMENT
I want to thank my main supervisor, Ian Miguel, who has done the best possible job in
advising me during this work. Thank you for your constant support, the vast amount of
freedom and the uncountable things I’ve learnt during the work on this thesis. Also many
thanks to my second supervisor, Ian Gent, who, in the most entertaining way, has demon-
strated how to be a good, professional and respected researcher, which has contributed a
lottothiswork. Thankyoubothforyouradviceandfriendship.
I also want to thank my colleagues at St Andrews, in particular the members of the local
constraintsgroup,AndyGrayland,PeteNightingale,NeilMoore,LarsKotthoff,ChrisJef-
ferson,andOzgurAkgunformanyinterestingdiscussions(someoftheminvolvingwork),
as well as all members of CIRCA and the School of Computer Science in St Andrews,
of which many have enriched my time during my stay. For many inspirational talks and
discussions,IwanttothankresearchersoutsideofStAndrews,inparticularPeterGregory,
AlanFrisch,MikaelLagerkvist,KarenPetrie,ChristianSchulte,BarbaraSmithandGuido
Tack.
ThisprojectwasfundedbyaDOCfFORTEscholarshipprovidedbytheAustrianAcademy
of Sciences and an EPSRC grant. Therefore, I would like to extend my gratitude to the
Austrian Academy of Sciences and EPSRC for their generous financial support that has
allowedmealotoffreedomandhencehascertainlypositivelycontributedtothisthesis.
Last, but certainly not least, I want to thank my dear friends and family, without whose
support this thesis would not have been possible. I want to thank all the members of my
family,inparticularmyparents,EvaandFranz,fortheirunconditionalsupport,theiradvice
and friendship. I also want to thank my brother Stefan and my aunt Susi for sharing many
of my experiences during this work, despite the distance. Many thanks to all my friends
from St Andrews who have made the last three years an extraordinary time. In particular,
Marion, Valentina, Tania, Sandra, Melina, Amy, Heike, Angie and Karen, as well my dear
flatmates, Ralph and Andrea, and Diego, Pascal, Fred, Alan and all the others that I have
not mentioned. Finally, I want to thank all my dear friends from Austria and Stockholm.
Youhaveallcontributedtothisthesisinyourownway.
Thankyou!

C
ONTENTS
1 Introduction 1
1.1 SolvingProblemsusingConstraintProgramming . . . . . . . . . . . . . . 2
1.1.1 ModellingConstraintSatisfactionProblems(CSPs) . . . . . . . . . 3
1.1.2 SolvingConstraintSatisfactionProblems(CSPs) . . . . . . . . . . 4
1.2 AutomatedConstraintModelling . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 ThesisStatementandContributions . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Specificationof ESSENCE! . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 ModelOptimisations . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.4 Thetool TAILOR . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.5 AddressingtheMissingLinkinAutomatedConstraintModelling . 11
1.4 ThesisStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 TheModellingLanguage ESSENCE! 15
2.1 ESSENCE! byExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 ParametersandConstants . . . . . . . . . . . . . . . . . . . . . . 23
2.2.5 DecisionVariables . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.6 ObjectiveandConstraints . . . . . . . . . . . . . . . . . . . . . . 24
2.2.7 GlobalConstraints . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.8 QuantifiedExpressions , and . . . . . . . . . . . . . . . . . 25
∀ ∃
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
!
3 TailoringProblemInstances 27
3.1 TailoringinaNutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.1 Thetailoringtool TAILOR . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Frontend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Middle-End . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.2 Flattening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.3 RepresentingSolverFeatures . . . . . . . . . . . . . . . . . . . . 41
3.4 Backend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
i