Dynamic Flexible Constraint Satisfaction and its Application to AI Planning

328 Pages·2004·10.02 MB·English

by  Ian Miguel BSC

Distinguished Dissertations
Springer-Verlag London Ltd.
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lan Miguel
Dynamic Flexible
Constraint Satisfaction
and its Application to
AI Planning
, Springer
lan Miguel, BSC, MSc, PhD
Un iversity of Yo rk
Series Editor
Professor C.]. van Rijsbergen
Department of Computing Science, University of Glasgow
British Library Cataloguing in Publication Data
Miguel,lan
Dynamic flexible constraint satisfaction and its
application to AI Planning. -(Distinguished dissertations)
l.Constraints (Artificial intelligence)
I.Titie
006.3
Library of Congress Cataloging-in-Publication Data
Miguel, lan.
Dynamic flexible constraint satisfaction and its application to AI planning / lan MigueL
p. cm. - (distinguished dissertations, ISSN 1439-9768)
Inc1udes bibliographical references.
ISBN 978-1-4471-1048-4 ISBN 978-0-85729-378-7 (eBook)
DOI 10.1007/978-0-85729-378-7
l.Constraints (Artificial intelligence) 2. CONSAT. 3. Dynamic programming. I. Title.
11. Distinguished dissertations (Springer-Verlag)
Q340.M54 2003
006.3--dc22 2003058512
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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sent to the publishers.
Distinguished Dissertations ISSN 1439-9768
http://www.springer.co.uk
© Springer-Verlag London 2004
Originally published by Springer-Verlag London Limited in 2004
Softcover reprint ofthe hardcover 1st edition 2004
The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a
specific statement, that such DImeS are exempt from the relevant laws and regulations and therefore
free for general use.
The publisher malces no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for any errors
or omissions that may be made.
Typesetting: Camera-ready by author
34/3830-543210 Printed on acid-free paper SPIN 10945292
This book is dedicated to my wifeAngela, without whoselove
and support this would not have been possible.
Preface
First, I would like to thank my principal supervisor Dr Qiang Shen for all
his help, advice and friendship throughout. Many thanks alsoto my second
supervisor Dr Peter Jarvis forhisenthusiasm, help and friendship.
I would also like to thank the other members of the Approximate and
QualitativeReasoninggroupat Edinburghwhohavealsohelpedand inspired
me.
This project has been funded by an EPSRC studentship, award num
ber 97305803. I wouldlike,therefore, to extend mygratitude to EPSRC for
supporting this work.
Many thanks to the staff at Edinburgh University for all their help and
support and forpromptly fixingany technical problems that I have had.
Mywholefamilyhavebeen both encouragingand supportive throughout
the completion of this book, for whichI am foreverindebted.
York,
April 2003 Ian Miguel
Contents
List ofFigures XV
1 Introduction. ............................................. 1
1.1 SolvingClassical CSPs .................................. 2
1.2 Applications of Classical CSP ...... ....... ...... .. .... ... 3
1.3 Limitations of ClassicalCSP ............................. 6
1.3.1 Flexible CSP 6
1.3.2 Dynamic CSP.................................... 7
1.4 Dynamic Flexible CSP .............. ....... ...... .. .... . 7
1.5 Flexible Planning: a DFCSP Application .................. 8
1.6 Structure... ................. ................. ........ . 9
1.7 Contributions and their Significance 11
2 The Constraint Satisfaction Problem 13
2.1 Constraints and Constraint Graphs ....................... 13
2.2 Tree Search Solution Techniquesfor Classical CSP.......... 16
2.2.1 Backtrack ... .......... .... ... ............... .... 17
2.2.2 Backjumping .. .. .......... .. ... ...... ........... 18
2.2.3 Conflict-Directed Backjumping ..................... 19
2.2.4 Backmarking ...... ...... .. ... ........ ......... .. 20
2.2.5 The Backmark Hybrids 21
2.2.6 Dynamic Backtracking ............................ 22
2.2.7 Relative Evaluation... .. .... ................... 23
2.3 Pre-ProcessingTechniques......... ..... ........ .. .... 23
2.3.1 Arc Consistency...'" .......... ... .... .... ....... 24
2.3.2 Improving Efficiency in Enforcing Arc Consistency. ... 25
2.3.3 Path Consistency................................. 28
2.3.4 K-Consistency ................... ................ 29
2.3.5 Practical Consistency Enforcing .................... 30
2.3.6 Directional Pre-Processing......................... 31
2.4 Hybrid Tree-search Consistency-enforcingAlgorithms 32
2.4.1 Partial Arc Consistency. .......................... 33
2.4.2 Relative Evaluation............................... 34
2.5 Heuristics. ....... ....... .. ............... ............. 35
2.6 Conflict Recording...................................... 37
X Contents
2.7 The Phase Transition in CSPs 38
2.8 Graph-Based Methods 39
2.8.1 The InvasionProcedure ........................... 40
2.8.2 The Cycle-CutsetMethod .. ... ... .... .... .. .. ..... 41
2.8.3 Non-separableComponents........................ 42
2.8.4 Tree-Clustering...... ........................... . 42
2.9 Extending the CSP Framework :. 43
2.9.1 Extending TreeSearch ...... .. .. 45
2.9.2 Solutionvia Graph Decomposition.................. 46
2.9.3 AdditiveFlexibleCSP 47
2.9.4 Priority MaximisationFlexibleCSP 51
2.10 DynamicConstraint Satisfaction . ..... . .... 55
2.10.1 Restriction/Relaxation-based Dynamic Constraint
SatisfactionProblems ............................. 56
2.10.2 Recurrent DynamicConstraint Satisfaction Problems. 58
2.10.3 Activity-based Dynamic Constraint Satisfaction
Problems........................................ 60
2.11 Summary.............................................. 62
3 Dynamic Flexible Constraint Satisfaction 65
3.1 TowardsDynamicFlexibleConstraintSatisfaction. 65
3.1.1 ConceptsofDFCSP 66
3.2 Examplesfromthe DynamicPerspective 67
3.2.1 Restriction/Relaxation-based DFCSP ............... 67
3.2.2 Recurrent DFCSP ................................ 68
3.2.3 Activity-basedDFCSP .... .. ....... .... .. .... ..... 70
3.3 ASpecific Instance ofDFCSP............................ 70
3.3.1 The FlexibleComponent- a Recap.............. .. 71
3.4 FuzzyrrDFCSP Solutionvia Branch and Bound ..... 72
3.5 FuzzyrrDFCSP Solutionvia LocalRepair. ................ 72
3.5.1 LocalChanges ................................... 73
3.5.2 FlexibleLocalChanges:AFuzzyrrDFCSP Algorithm 74
3.5.3 FLC ComplexityIssues 79
3.6 FuzzyArcConsistency.................................. 80
3.6.1 The ComplexityofFuzzyArc Consistency.... .. ..... 81
3.6.2 Pre-processingwith FuzzyArc Consistency. ......... 82
3.6.3 Hybrids .... ......... ............... ............. 82
3.6.4 The DeletionThreshold ..... ......... .... .. .. ..... 84
3.7 SolutionTechniques forother DFCSP Instances ............ 85
3.8 An Example ........................................... 86
3.8.1 SolutionofInitial Problem via Branch and Bound. ... 86
3.8.2 SolutionofInitial Problem via FLC 87
3.8.3 The Problem Changes 87
3.8.4 SolutionofUpdated Problem via Branch and Bound.. 88
3.8.5 SolutionofUpdated Problem via FLC 88
Contents XI
3.9 Summary...... ...... .... ............................ .. 89
4 An Empirical Study ofFuzzy rrDFCSPs 91
4.1 The Problems................ ... ...... ...... .. .. 91
4.2 The AlgorithmsStudied..................... ....... .. 93
4.3 Evaluation Criteria ..................................... 93
4.4 Heuristics Investigated .. ................................ 94
4.4.1 Variable Selection 94
4.4.2 Domain Element Selection......................... 95
4.4.3 Constraint CheckSelection ........................ 96
4.5 Results:3-point SatisfactionScale ........................ 96
4.6 Results:4-point Satisfaction Scale 106
4.7 Results:5-point Satisfaction Scale 114
4.8 The Utility ofDynamicInformation 122
4.9 The Utility ofthe DeletionThreshold 130
4.10 The Utility ofthe Constraint CheckOrdering Heuristic 136
4.11 The Utility ofFLC VariableSelectionHeuristics 140
4.12 The Utility ofFLC Domain Element SelectionHeuristics 148
4.13 Summary 157
5 Dynamic CSP in Domain-independent AI Planning 159
5.1 AI Planning 159
5.1.1 Constraint Satisfaction in Planning 161
5.2 An OverviewofGraphplan 161
5.2.1 The Planning Graph 163
5.2.2 Basic Plan Extraction 165
5.2.3 Memoisation 165
5.3 Viewingthe Planning Graph as a CSP 166
5.4 Plan Extraction via Dynamic Constraint Satisfaction 166
5.4.1 A HierarchicalApproach 166
5.4.2 Memoisationin the HierarchicalContext 168
5.5 The GP-rrDCSPAlgorithm ............................... 174
5.5.1 The Top-levelProcedure 174
5.5.2 The extractO Procedure 174
5.5.3 The propagateMSO Procedure 176
5.6 ComplexityIssues 177
5.7 Avoiding Irrelevant Variablesin Memosets Created by
Propagation ........... 177
5.8 Focusingthe Search. .................................... 179
5.8.1 VariableSelection 179
5.8.2 ValueSelection 180
5.8.3 Constraint CheckSelection 181
5.9 Summary 182
XII Contents
6 GP-rrDCSP: Experimental Results 185
6.1 The Logistics Domain 186
6.1.1 The RocketAProblem 186
6.1.2 The RocketBProblem 187
6.1.3 The LogisticsAProblem 189
6.1.4 The LogisticsB and LogisticsCProblems 191
6.1.5 The LogisticsDProblem 193
6.2 The Blocks-world Domain 194
6.2.1 The 12-stepProblem 194
6.2.2 The Blocks-world LargeAProblem 195
6.2.3 The Blocks-world LargeBProblem 196
6.3 The Gripper Domain 197
6.4 The MovieDomain ..................................... 199
6.5 The Grid Domain 199
6.6 Summary 199
7 Flexible Planning Problems & Flexible Graphplan 203
7.1 Background................ .. ...... ..... ............ ... 203
7.2 FlexiblePlanning Problems 205
7.2.1 Representation 205
7.2.2 The ValuablePackageProblem (Continued) 208
7.3 FlexibleGraph Expansion 210
7.3.1 Mutual Exclusivity 210
7.3.2 BasicFlexibleGraph Expansion 210
7.3.3 Limited Graph Expansion 212
7.3.4 Satisfaction Propagation During Graph Expansion 212
7.4 FlexiblePlan Extraction via rrDFCSP 213
.7.4.1 The FCSP Viewpoint , 213
7.4.2 The HierarchicalApproach Revisited 214
7.4.3 MemoisationforFlexible Plan Synthesis 215
7.4.4 The ValuablePackageProblem - SynthesisedPlans 218
7.5 The FGP Algorithm 219
7.5.1 The Top-levelProcedure 219
7.5.2 The FExtractO Procedure 220
7.5.3 ComplexityIssues " 221
7.6 Summary 222
8 FGP: Experimental Results 225
8.1 The Test Suite 225
8.2 The Test Suite: Plan Synthesis Results 227
8.2.1 The Utility of Limited Graph Expansion and
SatisfactionPropagation 229
8.3 The RescueProblem 230
8.3.1 The Shortest Plan 232
8.3.2 A FiveStep Plan................................. 232