Fractional Order Darwinian Particle Swarm Optimization: Applications and Evaluation of an Evolutionary Algorithm

82 Pages·2016·5.019 MB·English

by  Micael Couceiro, Pedram Ghamisi (auth.)

SPRINGER BRIEFS IN
APPLIED SCIENCES AND TECHNOLOGY
Micael Couceiro
Pedram Ghamisi
Fractional Order
Darwinian Particle
Swarm Optimization
Applications and
Evaluation of
an Evolutionary
Algorithm
123
SpringerBriefs in Applied Sciences
and Technology
More informations about this series at http://www.springer.com/series/8884
Micael Couceiro Pedram Ghamisi
(cid:129)
Fractional Order Darwinian
Particle Swarm Optimization
Applications and Evaluation
of an Evolutionary Algorithm
123
Micael Couceiro PedramGhamisi
Ingeniarius, Ltd. Faculty of Electrical andComputer
Mealhada Engineering
Portugal University of Iceland
Reykjavik
and Iceland
Institute of Systems andRobotics (ISR)
University of Coimbra
Coimbra
Portugal
ISSN 2191-530X ISSN 2191-5318 (electronic)
SpringerBriefs inApplied SciencesandTechnology
ISBN978-3-319-19634-3 ISBN978-3-319-19635-0 (eBook)
DOI 10.1007/978-3-319-19635-0
LibraryofCongressControlNumber:2015940427
SpringerChamHeidelbergNewYorkDordrechtLondon
©TheAuthor(s)2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor
foranyerrorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia
(www.springer.com)
Foreword
Biomimetics has been exploited in several research areas as a means to endow
artificial systems with intelligence, resilience, adaptation, and natural selection
typicallyexhibitedbylivingorganismsandbiologicalecosystems,inordertosolve
complex human problems through new technologies inspired by such biological
systems at macro-and nanoscales.
Bioinspiration has received special attention in the robotics community for the
past two decades in order to solve complex optimization problems through bioin-
spired algorithms. It has been mainly devoted to the study of robot swarms com-
prising many unsophisticated robots interacting locally with neighbor robots and
the environment, which can exhibit useful collective patterns resembling the way
swarms of biological species behave collectively to strive for survival in hostile
environments against threats and predators. However, such techniques have a
broader application range, not being confined only to swarm robotics.
One of the most well-known bioinspired optimization techniques is particle
swarm optimization (PSO), which has demonstrated remarkably high potential in
optimizationproblemswhereinconventionaloptimization techniquescannotfinda
satisfactory solution, due to nonlinearities and discontinuities. The PSO technique
consists of a number of particles whose collective dynamics, resembling a bio-
logicalecosystem,allowseffectivelyexploringthesearchspacetofindtheoptimal
solution. The Darwinian PSO (DPSO) is an evolutionary optimization algorithm
and an extension ofthe original PSOthat makes use ofDarwin’s theory of natural
selectiontoregulatetheevolutionoftheparticles andoftheircollectivedynamics,
so that complex optimization of functions exhibiting many local maxima/minima
can be successfully accomplished. The fractional order DPSO (FODPSO) incor-
poratesinDPSOthenotionoffractional-orderderivativestoattainmemoryofpast
decisions and even better convergence properties.
Thisbookisanimportantresourceforresearchersandpractitionersontheuseof
PSO and related bioinspired techniques in complex optimization problems. The
Chap.1isanexcellentintroductiontothebasicsofPSO,alongwithapresentation
of its potential applications. The Chap. 2 presents how the original PSO can be
extended to include Darwin’s survival-of-the-fittest principle and fractional
v
vi Foreword
calculus, thus presenting the DPSO and the FODPSO techniques. Chapters 3–5
illustrate how these techniques can be used to tackle three interesting case studies
effectively:curvefitting,imagesegmentation,andswarmrobotics.Iamparticularly
closetothelattercasestudy,asIhadtheprivilegeofsupervisingaPh.D.thesison
the subject by one of this book’s authors. But, nevertheless, all three case studies
are equally relevant for the reader assessing the high potential of the bioinspired
techniques addressed in the book. The final chapter summarizes conclusions and
points out future research directions on the subject.
I hope the reader can have a pleasant and fruitful reading experience with this
book as I had. Enjoy it!
February 2015 Rui P. Rocha
University of Coimbra, Portugal
Acknowledgements
The authors would like to thank Profs. Rui Paulo Pinto da Rocha, Nuno Miguel
Fonseca Ferreira, José António Tenreiro Machado, and Jón Atli Benediktsson for
their scientific and technical support.
vii
Contents
1 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 The Traditional PSO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 PSO-Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Applications: What Can We “Optimize”? . . . . . . . . . . . . . . . . . 8
1.3.1 Curve Fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Image Segmentation. . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Swarm Robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Fractional-Order Darwinian PSO. . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Fractional Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 FODPSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Benchmarking Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Case Study I: Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Traditional Optimization Methods . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Mathematical Modeling of the Putting . . . . . . . . . . . . . . . . . . . 22
3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Case Study II: Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . 31
4.1 Thresholding-Based Image Segmentation . . . . . . . . . . . . . . . . . 31
4.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ix
x Contents
4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Case Study III: Swarm Robotics. . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.1 Robotic Darwinian PSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.1.1 Fractional-Order Swarm Robots. . . . . . . . . . . . . . . . . . . 42
5.1.2 Obstacle Avoidance. . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1.3 Ensuring MANET Connectivity. . . . . . . . . . . . . . . . . . . 47
5.1.4 “Punish–Reward” Mechanism . . . . . . . . . . . . . . . . . . . . 51
5.1.5 Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.1 Numerical Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.2 Laboratory Experiments . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.1 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2 Limitations and Further Research. . . . . . . . . . . . . . . . . . . . . . . 74
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75