Distributed Search by Constrained Agents: Algorithms, Performance, Communication

222 Pages·2008·4.015 MB·English

by  Amnon Meisels (auth.)

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Amnon Meisels
Distributed Search
by Constrained Agents
Algorithms, Performance,
Communication
AmnonMeisels
DepartmentofComputerScience
Ben-GurionUniversity,Beer-Sheva,Israel
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ISBN:978-1-84800-039-1 e-ISBN:978-1-84800-040-7
(cid:2)c Springer-VerlagLondonLimited2008
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permittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlybereproduced,
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The publisher makes no representation, express or implied, with regard to the accuracy of the
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Printedonacid-freepaper.
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To Sari with love
My wife and best friend
Preface
Distributed search by agents is an important topic of distributed AI and has
not been treated thoroughly as such. While the scope of work on multi-agent
systems has grown steadily over the last decade, very little of it has spilled
into distributed search. In conrast, the constraints processing community has
produced a sizable body of work on distributed constrained search. Paradoxi-
cally, a community that concentrates on search algorithms and heuristics has
created a distributed model for agents that cooperate on solving hard search
problems.Traditionally,thisfieldhasbeennamedDitributed Constraints Sat-
isfactionandlatelyalsodistributedconstraintsoptimization.Thepresentbook
attemptstopromptdeeperresponsefromtheMAScommunityandhopefully
to give rise to cooperative work on distributed search by agents. In order to
achievethishighgoal,thebookpresentsthelargebodyofworkondistributed
search by constrained agents. The presentation emphasizes many aspects of
distributed computation that connect naturally to multi-agent systems, es-
pecially measures of performance for distributed search algorithms and the
impact of delays in communication.
DistributedConstraintsSatisfactionProblems(DisCSPs)havebeenstud-
ied over the last decade, starting with the pioneering proposal by Makoto
Yokoo [18]. The first distributed search algorithm for DisCSPs - Asyn-
chronous Backtracking (ABT) - was first published in complete format in
1998 [64]. The first book on Distributed Constraints Satisfaction Problems
has appeared as early as 2000 [61]. The book includes most of Yokoo’s early
work-distributedsearchalgorithms,bothcompleteandstochastic,andsome
experimental evaluation of the algorithms. It took five more years for the ex-
tensive form of ABT, including three well-defined versions and a correctness
proof, to be published. In total, 10 years elapsed between Yokoo’s original
proposal of Asynchronous Backtracking, to the final extended form in the
AI Journal in 2005 [9]. This gives a clear demonstration of the intricacies of
distributed search algorithms, which form the heart of the field and of the
present book.
VIII Preface
In the last six years, since the year 2000, the community of researchers in
the field have had at least one yearly workshop. These activities have helped
the field mature into one of the recognized disciplines of both Constraints
Processing (CP) and Multi-Agent Systems (MAS). In fact, the yearly work-
shops have been taking place alternately within the CP conferences and the
AAMAS conferences (and the general AI conference, IJCAI). The series of
Distributed Constraints Reasoning (DCR) workshops served as the forum for
a community of more than 50 researchers worldwide and has published more
than 20 papers yearly on DisCSP.
The field of distributed constraints search now includes two main fam-
ilies of problems - Distributed Constraints Satisfaction Problems DisCSPs
and Distributed Constraints Optimization Problems (DisCOP)s. With the
rapidrateofpublishedworkonDisCSPsandDisCOPsabookisverymuch
needed, to present in detail the accumulated body of work of all researchers.
While preparing my tutorial talk for CP-2004 in Toronto, I first noticed that
a short presentation of the field must include three parts. These three parts
formthebackboneofthisbook.Thefirstandmostimportantpartintrocuces
ingreatdetailsearchalgorithmsforDisCSPsandDisCOPs.Quiteanumber
of search algorithms have been proposed in recent years for both DisCSPs
and DisCOPs and an in-depth exposition of all algorithms is long overdue.
The algorithmic part of the exposition has also grown to include ordering
heuristics. Both asynchronous heuristics and sequential ones have appeared
in the DisCSP literature in the last three years. Asynchronous heuristics are
accompaniedbyaninnovativealgorithmthatenablesABTtoincludedynamic
ordering of agents [74].
The second part of the presentation of Distributed Search by Constrained
Agents includes a comprehensive study of distributed performance measures
for all algorithms. Based on the resulting coherent and asynchronous scale of
performance,anextensiveexperimentalevaluationcanbeconstructed.Inthe
present book this part is in Chapter 10 and Chapter 11.
The third part of our presentation of current research on DisCSPs and
DisCOPs relates to their inherent distributed nature and addresses poten-
tial problems. These can relate to potential delays in communication, or to
a variety of other agent topics, such as privacy of information used during
search. This book addresses communication problems like message delays in
detail in Chapter 12 and measures the impact of delays on the performance
of families of DisCSP search algorithms in Chapter 13. The first few steps
inthedirectionofprivacypreservationhavebeentakeninthelastfouryears,
for example, investigating means of preserving privacy [10, 42]. However, this
topic is left for a later addition when more work will have accumulated.
The book starts by describing the problems and by giving motivation for
theirgreatusefulnessintoday’sdistributedworld.InordertosolveDisCSPs
one needs distributed search algorithms. The first asynchronous algorithm
in the field was introduced a decade ago by the pioneering work of Makoto
Yokoo[62,64].Theasynchronousbacktrackingalgorithm(ABT)ispresented
Preface IX
in its modern form, as in [9]. ABT continues to be a central DisCSP search
algorithm and will be used in two forms in the book, first, as a reference
for all performance evaluations of other algorithms, second, as a basis for
enhancement, regarding ordering heuristics.
The distributed nature of the search problem that is at the center of this
book makes it a natural selection for a graduate course on this topic. Dis-
tributed search algorithms that are run by all agents and find a global so-
lution can serve as a solid demonstration for distributed AI and multi-agent
systems(MAS).AshortintroductiononConstraintsSatisfactionProblemsis
needed, perhaps a bit more extensive than the one given in the first chapter.
Part of the material in this book has been presented by me in the graduate
course on Constraints Processing that I have been giving over the last four
years in both my department at Ben-Gurion University and at the computer
science department of the Open University. Emphasizing the distributed na-
ture of DisCSP algorithms I have routinely focused all final projects of the
students on my course on implementing and investigating distributed search
algorithms.
This book focuses on the main research results in distributed constraints
satisfaction and optimization over the last decade. Thus it can serve as a re-
searchassettoresearchersandtograduatestudentsthatfocusondistributed
search by agents and in particular on DisCSPs and DisCOPs. It is my hope
that this complete text can serve as a basis for a course on distributed search
in AI. I believe that the accumulated work on search by constrained agents is
an excellent algorithmic and clearcut example of the cooperation of agents in
search.
The present book is the result of six very intensive years of research with
mywonderfulgroupofgraduatestudents.Mysincerethanksgotoallofthem,
without whom the great research on Distributed Constraints would have not
been possible. My deepest thanks to my students - Amir Gershman, Arnon
Gilboa, Eliezer Kaplanski, Oz Lavee, Michael Orlov, Igor Razgon, Moshe Za-
zon,andRoieZivan.ThethesesofOz,Michael,andAmirhavealsobeenused
extensively within the text of the relevant chapters. The chapter on ADOPT
(Chapter 15) is completely taken from Amir’s thesis. The extensive study
and wonderful implementations of ADOPT by Amir have made him in my
eyes the world’s expert on the ADOPT algorithm. The contents of the out-
standing thesis of Roie Zivan (which is still not written) are present in most
of the book, from our papers on search algorithms (Chapter 6, Chapter 7),
through our work on concurrent performance measures (Chapter 10), and to
hisbriliantworkonasynchronousorderingheuristics(Chapter9).Ilookback
in appreciation on the great research road we have covered together and in
excitement on what’s yet to come.
Beer-Sheva, July 2007 Amnon Meisels
Contents
1 Introduction............................................... 1
2 Constraints Satisfaction Problems - CSPs.................. 7
2.1 Defining CSPs .......................................... 8
2.2 CSP Algorithms and Techniques........................... 10
2.3 Behavior of CSP solving algorithms........................ 13
3 Constraints Optimization Problems - COPs................ 19
3.1 Branch and Bound (BnB) ................................ 20
3.2 Branch and Bound + Arc-Consistency (BnB-AC)............ 23
3.3 Branch and Bound + AC* (BnB-AC*) ..................... 24
3.4 Phase Transition in MaxCSPs............................. 25
4 Distributed Search......................................... 27
4.1 Distributed search algorithms on DisCSPs .................. 30
4.2 Introducing Asynchronous Backtracking.................... 33
5 Asynchronous Backtracking (ABT) ........................ 37
5.1 A Complete 4-Queens Example............................ 40
5.2 The ABT Algorithm - Polynomial Storage.................. 43
5.3 Correctness of ABT...................................... 47
5.4 Improving Performance of ABT ........................... 49
6 Asynchronous Forward-Checking .......................... 53
6.1 AFC - Algorithm Description ............................ 55
6.2 Correctness of AFC...................................... 59
6.3 Improved Backtrack Method for AFC ...................... 61
7 Concurrent Dynamic Backtracking ........................ 63
7.1 4-Queens with Concurrent Search.......................... 65
7.2 The ConcBT Algorithm.................................. 67
7.2.1 A splitting of search space example .................. 72
XII Contents
7.3 Concurrent Dynamic Backtracking......................... 75
7.4 Correctness of Concurrent Search.......................... 79
8 Distributed Ordering Heuristics ........................... 83
8.1 Ordering heuristics for Synchronous Backjumping ........... 85
8.1.1 Heuristics with no additional messages ............... 85
8.1.2 Heuristics with additional network overhead .......... 86
8.2 Ordering heuristics for AFC .............................. 86
9 Asynchronous Ordering Heuristics......................... 89
9.1 Specific Asynchronous Heuristics .......................... 89
9.2 Dynamically ordered ABT................................ 91
9.3 Correctness of ABT_DO ................................ 94
9.4 A new class of asynchronous heuristics ..................... 97
9.5 Correctness of Retroactive ABT_DO......................102
10 Performance measures for distributed search ..............105
10.1 A Simple Example with Naive Methods ....................107
10.2 Dividing concurrent search into rounds ....................108
10.3 A More Complex Example for Computing NCCCs...........110
10.4 A Model for Nonconcurrent Constraints Checks .............111
10.5 The Cumulative Cost Algorithm (CCA) ....................113
10.6 Realization of the Model by the CCA Algorithm ............115
11 Experimental Evaluation of DisCSP Algorithms ..........121
11.1 Comparing Different Algorithms...........................122
11.1.1 Asynchronous forward-checking vs. ABT .............122
11.1.2 Experimental evaluation of ConcDB ................123
11.2 Empirical Evaluation of Heuristic Ordering .................125
11.2.1 Evaluation of synchronous ordering heuristics .........126
11.2.2 Evaluation of dynamically ordered ABT..............128
11.2.3 Retroactive ordering for ABT.......................133
12 The Impact of Communication - Message Delays ..........137
12.1 Simulating Delayed Messages on DisCSPs ..................139
12.1.1 Adjusting the measuring method for dynamic ordering 140
12.2 Validity of AMDS ......................................141
13 Message Delays and DisCSP Search Algorithms...........143
13.1 The Impact of Message Delays ............................145
13.2 A summary of the Impact of Message Delays ...............154
13.3 Message Delays and Dynamic Ordering.....................156