Christian Blum, Maria José Blesa Aguilera, Andrea Roli and Michael Sampels (Eds.) Hybrid ...

293 Pages·2012·5.7 MB·English

Christian Blum, Maria Jose´ Blesa Aguilera, Andrea Roli and Michael Sampels
(Eds.)
HybridMetaheuristics
StudiesinComputationalIntelligence,Volume114
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Christian Blum
Maria Jose´ Blesa Aguilera
Andrea Roli
Michael Sampels
(Eds.)
Hybrid Metaheuristics
An Emerging Approach to Optimization
123
Dr.ChristianBlum Dr.AndreaRoli
ALBCOM DEIS,CampusofCesena
Dept.LlenguatgesiSistemesInforma´tics AlmaMaterStudiorum
UniversitatPolite`cnicadeCatalunya Universita`diBologna
JordiGirona1-3Omega112, ViaVenezia52
CampusNord I-47023Cesena
E-08034Barcelona Italy
Spain [email protected]
[email protected]
Dr.MariaJose´BlesaAguilera Dr.MichaelSampels
ALBCOM IRIDIA
Dept.LlenguatgesiSistemesInforma´tics Universite´LibredeBruxelles
UniversitatPolite`cnicadeCatalunya AvenueFranklinRoosevelt50,CP194/6
JordiGirona1-3Omega213, B-1050Brussels
CampusNord Belgium
E-08034Barcelona [email protected]
Spain
[email protected]
ISBN978-3-540-78294-0 e-ISBN978-3-540-78295-7
StudiesinComputationalIntelligenceISSN1860-949X
LibraryofCongressControlNumber:2008921710
(cid:1)c 2008Springer-VerlagBerlinHeidelberg
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For my parents Maria and Dieter
(Christian Blum)
For Christian and Marc
(Mar´ıa J. Blesa)
For Elisabetta, Raffaella and Paolo
(Andrea Roli)
For Astrid, Julian and Carlotta
(Michael Sampels)
Preface
Whenfacingcomplexnewoptimizationproblems,itisverynaturaltouserules
of thumb, common sense, trial and error, which are called heuristics, in order
to find possible answers. Such approaches are, at first sight, quite different
from rigorous scientific approaches, which are usually based on characteriza-
tions, deductions, hypotheses and experiments. It is common knowledge that
many heuristic criteria and strategies, which are used to find good solutions
for particular problems, share common aspects and are often independent of
the problems themselves.
In the computer science and artificial intelligence community, the term
metaheuristic was created and is now well accepted for general techniques
which are not specific to a particular problem. Genetic and evolutionary al-
gorithms, tabu search, simulated annealing, iterated local search, ant colony
optimization, scatter search, etc. are typical representatives of this generic
term.Researchinmetaheuristicshasbeenveryactiveduringthelastdecades,
whichiseasytounderstand,whenlookingatthewidespectrumoffascinating
problemsthathavebeensuccessfullytackledandthebeautyofthetechniques,
manyoftheminspiredbynature.Eventhoughmanycombinatorialoptimiza-
tion problems are very hard to solve optimally, the quality of the results
obtained by somewhat unsophisticated metaheuristics is often impressive.
This success record has motivated researchers to focus on why a given
metaheuristic is successful, on which problem instance characteristics should
be exploited and on which problem model is best for the metaheuristic of
choice. Investigations on theoretical aspects have begun, and formal theories
of the working of metaheuristics are being developed. Questions as to which
metaheuristic isbestforagiven problemusedtobequitecommon and,more
prosaically, often led to a defensive attitude towards other metaheuristics.
Finally, it also became evident that the concentration on a single meta-
heuristic is rather restrictive for advancing the state of the art when tack-
ling both academic and practical optimization problems. Examples showed
that a skillful combination of metaheuristics with concepts originating from
other types of algorithms for optimization can lead to more efficient behavior
VIII Preface
and greater flexibility. For example, the incorporation of typical operations
research (OR) techniques, such as mathematical programming, into meta-
heuristics may be beneficial. Also, the combination of metaheuristics with
other techniques known from artificial intelligence (AI), such as constraint
programming and data mining, can be fruitful. Nowadays, such a combina-
tion of one metaheuristic with components from other metaheuristics or with
techniques from AI and OR techniques is called a hybrid metaheuristic.
The lack of a precise definition of the term hybrid metaheuristics is some-
times subject to criticism. On the contrary, we believe that this relatively
open definition is helpful, because strict borderlines between related fields of
research often block creative research directions. A vital research community
needs new ideas and creativity, not overly strict definitions and limitations.
In 2004, we founded with the First International Workshop on Hybrid
Metaheuristics (HM 2004) a series of annual workshops. These workshops
have developed into a forum for researchers who direct their work towards
hybrid algorithms that go beyond the scope of single metaheuristics. The
growing interest in these workshops is an indication that questions regarding
the proper integration of different algorithmic components and the adequate
analysis of results can now emerge from the shadows. With this backdrop,
it becomes evident that hybrid metaheuristics is now a part of experimental
science and that its strong interdisciplinarity supports cooperation between
researchers with different expertise.
In the light of the above, we feel that it is now time for a textbook on
hybrid metaheuristics, presenting the most important achievements and de-
velopments in this domain. We have invited key experts in the field to supply
chapters with the objective of providing an introduction to the themes of
hybrid metaheuristics and discussing associated theoretical aspects or appli-
cations.Wehopethat,byreadingthisbook,eitherresearchersorstudentswill
have an easy entry point to this fascinating field and will get a clear overview
of its research directions.
Barcelona, Bologna, Brussels Christian Blum
November 2007 Maria Jos´e Blesa Aguilera
Andrea Roli
Michael Sampels
Contents
Hybrid Metaheuristics: An Introduction
Christian Blum and Andrea Roli ................................... 1
Combining (Integer) Linear Programming Techniques
and Metaheuristics for Combinatorial Optimization
Gu¨nther R. Raidl and Jakob Puchinger ............................. 31
The Relation Between Complete and Incomplete Search
Steven Prestwich................................................. 63
Hybridizations of Metaheuristics With Branch & Bound
Derivates
Christian Blum, Carlos Cotta, Antonio J. Ferna´ndez, Jos´e E. Gallardo,
and Monaldo Mastrolilli .......................................... 85
Very Large-Scale Neighborhood Search: Overview and Case
Studies on Coloring Problems
Marco Chiarandini, Irina Dumitrescu, and Thomas Stu¨tzle ............117
Hybrids of Constructive Metaheuristics and Constraint
Programming: A Case Study with ACO
Bernd Meyer ....................................................151
Hybrid Metaheuristics for Packing Problems
Toshihide Ibaraki, Shinji Imahori, and Mutsunori Yagiura.............185
Hybrid Metaheuristics for Multi-objective Combinatorial
Optimization
Matthias Ehrgott and Xavier Gandibleux ............................221
Multilevel Refinement for Combinatorial Optimisation:
Boosting Metaheuristic Performance
Chris Walshaw ..................................................261
Hybrid Metaheuristics: An Introduction
Christian Blum1 and Andrea Roli2
1 ALBCOM research group
Universitat Polit`ecnica de Catalunya, Barcelona, Spain
[email protected]
2 DEIS, Campus of Cesena
Alma Mater Studiorum Universit`a di Bologna, Bologna, Italy
[email protected]
Summary. In many real life settings, high quality solutions to hard optimization
problemssuchasflightschedulingorloadbalancingintelecommunicationnetworks
arerequiredinashortamountoftime.Duetothepracticalimportanceofoptimiza-
tion problems for industry and science, many algorithms to tackle them have been
developed. One important class of such algorithms are metaheuristics. The field of
metaheuristic research has enjoyed a considerable popularity in the last decades.
In this introductory chapter we first provide a general overview on metaheuristics.
Thenweturntowardsanewandhighlysuccessfulbranchofmetaheuristicresearch,
namely the hybridization of metaheuristics with algorithmic components originat-
ingfromothertechniquesforoptimization.Thechapterendswithanoutlineofthe
remaining book chapters.
1 Introduction
In the context of combinatorial optimization (CO), algorithms can be classi-
fied as either complete or approximate algorithms. Complete algorithms are
guaranteed to find for every finite size instance of a CO problem an opti-
mal solution in bounded time (see [80, 76]). Yet, for CO problems that are
NP-hard [42], no polynomial time algorithm exists, assuming that P (cid:1)=NP.
Therefore, complete methods might need exponential computation time in
the worst-case. This often leads to computation times too high for practi-
cal purposes. In approximate methods such as metaheuristics we sacrifice the
guarantee of finding optimal solutions for the sake of getting good solutions
in a significantly reduced amount of time. Thus, the use of metaheuristics
has received more and more attention in the last 30 years. This was also the
caseincontinuousoptimization;duetootherreasons:Metaheuristicsareusu-
ally easier to implement than classical gradient-based techniques. Moreover,
metaheuristics donotrequiregradientinformation. This isconvenient forop-
timizationproblemswheretheobjectivefunctionisonlyimplicitlygiven(e.g.,
C.BlumandA.Roli:HybridMetaheuristics:AnIntroduction,StudiesinComputationalIntel-
ligence(SCI)114,1–30(2008)
www.springerlink.com (cid:1)c Springer-VerlagBerlinHeidelberg2008
2 Christian Blum and Andrea Roli
when objective function values are obtained by simulation), or where the ob-
jective function is not differentiable.
The first two decades of research on metaheuristics were characterized by
the application of rather standard metaheuristics. However, in recent years it
has become evident that the concentration on a sole metaheuristic is rather
restrictive. A skilled combination of a metaheuristic with other optimization
techniques, a so called hybrid metaheuristic, can provide a more efficient be-
havior and a higher flexibility when dealing with real-world and large-scale
problems. This can be achieved, for instance, by combining the complemen-
tary strengths of metaheuristics on one side and of complete methods such as
branch & bound techniques or mathematical programming on the other side.
In general, hybrid metaheuristic approaches can be classified as either collab-
orative combinations or integrative combinations (see [85, 86]). Collaborative
combinations are based on the exchange of information between several opti-
mizationtechniquesrunsequentially(orinparallel).Thiskindofcombination
is more related to cooperative and parallel search and we forward the inter-
estedreadertothespecificliteratureonthesubject[55,24,105,98,19,18,3].
Mostcontributionsofthisbookdealwithinterestingandrepresentativecases
of integrative combinations.
In this introductory chapter we first aim at giving an overview over some
of the most important metaheuristics. Then we deal with the hybridization
of metaheuristics with other techniques for optimization. Finally, we shortly
outline the books’ contents, with the aim of providing a general guidance to
the reader.
2 Basics
An optimization problem P can be described as a triple (S,Ω,f), where
1. S is the search space defined over a finite set of decision variables X ,
i
i = 1,...,n. In case these variables have discrete domains we deal with
discrete optimization (or combinatorial optimization), and in case of con-
tinuous domains P is called a continuous optimization problem. Mixed
variableproblemsalsoexist.Ω isasetofconstraintsamongthevariables;
2. f :S →IR+ is the objective function that assigns a positive cost value to
each element (or solution) of S.
The goal is to find a solution s ∈ S such that f(s) ≤ f(s(cid:2)), ∀ s(cid:2) ∈ S (in case
wewanttominimizetheobjectivefunction),orf(s)≥f(s(cid:2)),∀s(cid:2) ∈S (incase
the objective function must be maximized). In real-life problems the goal is
often to optimize several objective functions at the same time. This form of
optimization is labelled multi-objective optimization.
Approximate methods are generally based on two basic principles: con-
structive heuristics and local search methods.