Table Of ContentJyotsna K. Mandal Somnath Mukhopadhyay
(cid:129)
Paramartha Dutta
Editors
Multi-Objective Optimization
Evolutionary to Hybrid Framework
123
Editors
Jyotsna K.Mandal Paramartha Dutta
University of Kalyani VisvaBharati University
Kalyani, West Bengal, India Bolpur, Santiniketan,West Bengal, India
SomnathMukhopadhyay
AssamUniversity
Silchar, Assam, India
ISBN978-981-13-1470-4 ISBN978-981-13-1471-1 (eBook)
https://doi.org/10.1007/978-981-13-1471-1
LibraryofCongressControlNumber:2018947473
©SpringerNatureSingaporePteLtd.2018
Foreword
Multi-objective optimization problems have two or more (usually conflicting)
objectives that we aim to solve simultaneously. The solution to these problems
involves finding a set of solutions (rather than only one) representing the best
possible trade-offs among the objectives, such that no objective can be improved
without worsening another. In spite of the existence of a number of mathematical
programmingtechniquesthathavebeenexplicitlydesignedtosolvemulti-objective
optimization problems, such techniques have several limitations, which has moti-
vated the use of evolutionary algorithms, giving rise to an area known as evolu-
tionary multi-objective optimization.
The first evolutionary multi-objective algorithm was published in 1985, but it
was until the late 1990s that this research area started to gain popularity. Over the
last 20 years, this discipline has given rise to a wide variety of algorithms,
methodologies and applications that span practically all areas of knowledge.
This book brings together a very interesting collection of applications of
multi-objective evolutionary algorithms and hybrid approaches in a variety of
disciplines, including bioinformatics, networking, image processing, medicine and
finance.Thisbookshouldbeofinteresttoresearchersandstudentswithorwithout
experience in evolutionary multi-objective optimization, who will certainly benefit
from the novel applications and concepts discussed in this volume.
Mexico City, México Carlos A. Coello Coello
April 2018 CINVESTAV-IPN
Editorial Preface
In our day-to-day real life, we have to take decisions on the basis of various
associatedfactors.Arrivingatadecisionbecomesevenmorechallengingifonehas
to deal with factors apparently contradictory to one another. In such a situation,
addressing one factor falls short of being meaningful without addressing the other
factors even though conflicting. The issue of multi-/many-objective framework
typically deals with an environment where we have to consider simultaneous
optimization of more than one factor/objective to arrive at a comprehensive
conclusion/inference. In such cases, we try to achieve a collection of solutions,
typically referred to as Pareto front, where a typical solution element in the front
does neither dominate nor is dominated by another.
ThiseditedbookvolumeentitledMulti-ObjectiveOptimization:Evolutionaryto
Hybrid Framework is a collection of fourteen chapters contributed by leading
researchers in the field. The chapters were initially peer-reviewed by the Editorial
Review Board members spanning over many countries across the globe. In that
sense,thepresentendeavourisaresultantofcontributionsfromseriousresearchers
in the relevant field and subsequently duly peer-reviewed by pioneer scientists.
A brief description of each of the chapters is as follows:
Chapter “Non-dominated Sorting Based Multi/Many-Objective Optimization:
Two Decades of Research and Application” gives an exhaustive analysis and
picture of non-dominated sorting-based multi-/many-objective optimization algo-
rithms proposed in the last two decades of research and application. Authors have
mentioned that for more than two decades, non-dominated sorting has been a
cornerstone in most successful multi-/many-objective optimization algorithms. In
this chapter, they have discussed the effect of non-dominated sorting in multi- and
many-objectivescenarios.Thereafter,theyhavepresentedsomeofthemostwidely
used optimization algorithms involving non-dominated sorting, where they have
discussed their extentand ubiquity across many scientificdisciplines. Finally,they
havegoneoversomeofthestate-of-the-artcombinationsofnon-dominatedsorting
with other optimization techniques.
Chapter “Mean-EntropyModel ofUncertainPortfolioSelectionProblem”deals
with the portfolio selection problem, which is a single-period invest model where
aninvestorhastoselectanddistributeavailablecapitalamongvarioussecuritiesto
achieve the target investment. Authors have proposed in this study a bi-objective
portfolio selection model, which maximizes the average return and minimizes
theinvestmentriskofthesecurities.Intheproposedmodel,theaveragereturnand
the risk are represented, respectively, by the mean and entropy of the uncertain
securities.Theexpectedvalueandthetriangularentropyoftheuncertainsecurities
are determined to represent the mean and entropy, respectively. The proposed
model is solved with two different classical multi-objective solution techniques:
(i) weighted sum method and (ii) weighted metric method. Both the techniques
generate a single compromise solution. To generate a set of non-dominated solu-
tions,fortheproblem,twodifferentmulti-objectivegeneticalgorithms(MOGAs)—
(i) non-dominated sorting genetic algorithm II (NSGA-II) and (ii) multi-objective
evolutionaryalgorithmbasedondecomposition(MOEA/D)—areused.Finally,the
performances of the MOGAs are analysed and compared based on different per-
formance metrics.
InChapter“IncorporatingGeneOntologyInformationinGeneExpressionData
Clustering Using Multiobjective Evolutionary Optimization: Application in Yeast
Cell Cycle Data”, authors have described how microarray technology has made it
possibletosimultaneouslymonitortheexpressionlevelsofalargenumberofgenes
over different experimental conditions or time points. In this chapter, authors have
presented an approach for combining experimental gene expression information
and biological information in the form of gene ontology (GO) knowledge through
multi-objective clustering. The method combines the expression-based and
GO-basedgenedissimilarities.Moreover,themethodsimultaneouslyoptimizestwo
objectivefunctions—onefromgeneexpressionpointofviewandanotherfromGO
point of view. Authors have demonstrated the performance of the proposed tech-
niqueonreal-lifegeneexpressiondatasetofyeastcellcycle.Theyhavealsostudied
here the biological relevance of the produced clusters to demonstrate the effec-
tiveness of the proposed technique.
In Chapter “Interval-Valued Goal Programming Method to Solve Patrol
Manpower Planning Problem for Road Traffic Management Using Genetic
Algorithm”, an interval-valued goal programming (IVGP) method is proposed for
modelling and solving patrolmen deployment problem in traffic control system in
an inexact environment. Here, the objective functions are to be optimized and
represented as goals by assigning target intervals for the achievement of objective
values and incorporating interval coefficients to objective parameter sets to reach
satisfactory solution in decision horizon. Authors have also defined a performance
measuring function to represent different kinds of objectives that are inherently
fractional in form in decision premises by transforming it into linear equivalent to
avoid computational difficulty with fractional objectives in course of searching
solution to the problem. After that they have converted interval arithmetic rules,
interval-valuedgoalsintogoalsasinconventionalGPtoformulatestandardmodel
of the problem. Authors have designed the executable model by an extended GP
methodology for solving the traffic control problem. They have demonstrated the
proposed approach via a case example of the metropolitan city, Kolkata, West
Bengal, in India.
InChapter“Multi-objectiveOptimizationtoImproveRobustnessinNetworks”,
authors have proposed a new approach to address the budget-constrained
multi-objective optimization problem of determining the set of new edges (of
given size) that maximally improve multiple robustness measures. Authors have
presentedtheexperimentalresultstoshowthataddingtheedgessuggestedbytheir
approach significantly improves network robustness, compared to the existing
algorithms. The networks whichthey have presentedcanmaintain high robustness
during random or targeted node attacks.
Chapter “On Joint Maximization in Energy and Spectral Efficiency in
Cooperative Cognitive Radio Networks” addresses a joint spectral efficiency
(SE)–energy efficiency (EE) optimization problem in a single secondary user (SU)
and primary user (PU) network under the constraints of sensing reliability, coop-
erative SE for primary network and transmission power constraints. Differential
evolution (DE) is explored by the authors to handle this nonlinear optimization
problem and to find the optimal set of values for the sensing duration, cooperation
andtransmissionpowerofSU.Thetrade-offbetweenEE–SEisshownthroughthe
simulation.
In Chapter “Multi-Objective Optimization Approaches in Biological Learning
System on Microarray Data”, authors have provided a comprehensive review of
variousmulti-objectiveoptimizationtechniquesusedinbiologicallearningsystems
dealing with the microarray or RNA sequence data. In this regard, the task of
designing a multi-class cancer classification system employing a multi-objective
optimization technique is addressed first. Next, they have discussed how a gene
regulatory network can be built from the perspective of multi-objective optimiza-
tion problem. The next application deals with fuzzy clustering of categorical
attributesusingamulti-objectivegeneticalgorithm.Afterthis,howmicroarraydata
can be automatically clustered using a multi-objective differential evolution is
addressed. Then, the applicability of multi-objective particle swarm optimization
techniques in identifying the gene markers is explored. The next application con-
centrates on feature selection for microarray data using a multi-objective binary
particle swarm optimization technique. Thereafter, a multi-objective optimization
approach is addressed for producing differentially coexpressed module during the
progression of the HIV disease. In addition, they have represented a comparative
studybasedontheliteraturealongwithhighlightingtheadvantagesandlimitations
ofthemethods.Finally,theyhavedepictedanewdirectiontobio-inspiredlearning
system related to multi-objective optimization.
The main goal of the Chapter “Application of Multi-Objective Optimization
Techniques in Biomedical Image Segmentation—A Study” is to give a compre-
hensive study of multi-objective optimization techniques in biomedical image
analysis problem. This study mainly focusses on the multi-objective optimization
techniquesthatcanbeusedtoanalysedigitalimages,especiallybiomedicalimages.
Here, some of the problems and challenges related to images are diagnosed and
analysed with multiple objectives. It is a comprehensive study that consolidates
some of the recent works along with future directions.
In Chapter “Feature Selection Using Multi-Objective Optimization Technique
for Supervised Cancer Classification”, a new multi-objective blended particle
swarm optimization (MOBPSO) technique is proposed for the selection of signif-
icant and informative genes from the cancer datasets. To overcome local trapping,
authors have integrated here a blended Laplacian operator. The concept is also
implemented for differential evolution, artificial bee colony, genetic algorithm and
subsequently multi-objective blended differential evolution (MOBDE),
multi-objective blended artificial bee colony (MOBABC) and multi-objective
blendedgenetic algorithm (MOBGA) toextract therelevantgenesfromthecancer
datasets.Theproposedmethodologyutilizestwoobjectivefunctionstosortoutthe
geneswhicharedifferentiallyexpressedfromclasstoclassaswellasprovidesgood
results for the classification of disease.
In Chapter “Extended Non-dominated Sorting Genetic Algorithm (ENSGA-II)
for Multi-Objective Optimization Problem in Interval Environment”, authors have
proposed an efficient algorithm for solving a multi-objective optimization problem
withintervalobjectives.Forthispurpose,theyhavedevelopedanextendedversion
of existing NSGA-II algorithm (ENSGA-II) for fixed objectives in an interval
environment with the help of interval ranking and interval metric. In this connec-
tion, they have proposed non-dominated sorting based on interval ranking,
interval-valued crowding distance and crowded tournament selection of solutions
with respect to the values of interval objectives.
In Chapter “A Comparative Study on Different Versions of Multi-Objective
Genetic Algorithm for Simultaneous Gene Selection and Sample Categorization”,
authors have studied different versions of multi-objective genetic algorithm for
simultaneousgeneselectionandsamplecategorization.Here,authorshaveselected
optimal gene subset, and sample clustering is performed simultaneously using
multi-objectivegeneticalgorithm(MOGA).Theyhaveemployeddifferentversions
ofMOGAtochoosetheoptimalgenesubset,wherethenaturalnumberofoptimal
clusters of samples is automatically obtained at the end of the process. The pro-
posedmethodsusenonlinearhybriduniformcellularautomataforgeneratinginitial
population, tournament selection strategy, two-point crossover operation and a
suitablejumpinggenemutationmechanismtomaintaindiversityinthepopulation.
They have used mutual correlation coefficient, and internal and external cluster
validation indices as objective functions to find out the non-dominated solutions.
In Chapter “A Survey on the Application of Multi-Objective Optimization
Methods in Image Segmentation”, authors have provided a comprehensive survey
on multi-objective optimization (MOO), which encompasses image segmentation
problems. Here, the segmentation models are categorized by the problem formu-
lationwithrelevantoptimizationscheme.Thesurveytheyhavedonealsoprovides
the latest direction and challenges of MOO in image segmentation procedure.
In Chapter “Bi-objective Genetic Algorithm with Rough Set Theory for
Important Gene Selection in Disease Diagnosis”, a bi-objective genetic algorithm
with rough set theory has been proposed for important gene selection in disease
diagnosis. Here, two criteria are combined, and a novel bi-objective genetic algo-
rithm is proposed for gene selection, which effectively reduces the dimensionality
ofthehugevolumeofgenedatasetwithoutsacrificinganymeaningfulinformation.
The proposed method uses nonlinear uniform hybrid cellular automata for gener-
ating initial population and a unique jumping gene mechanism for mutation to
maintain diversity in the population. It explores rough set theory and Kullback–
Leiblerdivergence methodtodefinetwoobjective functions, whichareconflicting
in nature and are used to approximate a set of Pareto optimal solutions.
Chapter“Multi-ObjectiveOptimizationandCluster-wiseRegressionAnalysisto
EstablishInput-OutputRelationshipsofaProcess”dealswithanapproachwhichis
used to establish input–output relationships of a process utilizing the concepts of
multi-objectiveoptimizationandcluster-wiseregressionanalysis.Atfirst,aninitial
Pareto front is obtained for a given process using a multi-objective optimization
technique. Then, these Pareto optimal solutions are applied to train a neuro-fuzzy
system (NFS). The training of the NFS is implemented using a meta-heuristic
optimization algorithm. Now, for generating a modified Pareto front, the trained
NFS is used in MOEA for evaluating the objective function values. In this way, a
new set of trade-off solutions is formed. These modified Pareto optimal solutions
are then clustered using a clustering algorithm. Cluster-wise regression analysis is
then carried out to determine input–output relationships of the process. These
relationshipsarefoundtobesuperiorintermsofprecisiontothoseoftheequations
obtainedusingconventionalstatisticalregressionanalysisoftheexperimentaldata.
Contributions available in the fourteen chapters, after being meticulously
reviewed, reflect some of the latest sharing of some serious researches of the
concerned field. The editors want to avail this opportunity to express their sincere
gratitude to all the contributors for their efforts in this regard without which this
editedvolumecouldhavenevercometoareality.Theeditorssincerelyfeelthatthe
success of such an effort in the form of edited volume can be academically
meaningfulonlywhenitiscapableofdrawing significantcontributions fromgood
researchers in the relevant field.
The editors also thank the reviewers who are leading researchers in the domain
for spending their time from their busy schedules to give valuable suggestions to
improve the quality of the contributed articles. Last but not least, the editors are
inclinedtoexpresstheirsincerethankstoSpringerNature,Singapore,forbeingthe
publishing partner. But for their acceptance to publish this volume would never
have been possible in the present standard.
Enjoy reading it.
Kalyani, India Jyotsna K. Mandal
Silchar, India Somnath Mukhopadhyay
Bolpur, Santiniketan, India Paramartha Dutta
Contents
Non-dominated Sorting Based Multi/Many-Objective Optimization:
Two Decades of Research and Application. . . . . . . . . . . . . . . . . . . . . . . 1
Haitham Seada and Kalyanmoy Deb
Mean-Entropy Model of Uncertain Portfolio Selection Problem. . . . . . . 25
Saibal Majumder, Samarjit Kar and Tandra Pal
Incorporating Gene Ontology Information in Gene Expression Data
Clustering Using Multiobjective Evolutionary Optimization:
Application in Yeast Cell Cycle Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Anirban Mukhopadhyay
Interval-Valued Goal Programming Method to Solve Patrol
Manpower Planning Problem for Road Traffic Management
Using Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Bijay Baran Pal
Multi-objective Optimization to Improve Robustness in Networks. . . . . 115
R. Chulaka Gunasekara, Chilukuri K. Mohan and Kishan Mehrotra
On Joint Maximization in Energy and Spectral Efficiency
in Cooperative Cognitive Radio Networks . . . . . . . . . . . . . . . . . . . . . . . 141
Santi P. Maity and Anal Paul
Multi-Objective Optimization Approaches in Biological Learning
System on Microarray Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
SauravMallik,TapasBhadra,SoumitaSeth,SanghamitraBandyopadhyay
and Jianjiao Chen
Application of Multiobjective Optimization Techniques in Biomedical
Image Segmentation—A Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Shouvik Chakraborty and Kalyani Mali
Feature Selection Using Multi-Objective Optimization Technique
for Supervised Cancer Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
P. Agarwalla and S. Mukhopadhyay
Extended Nondominated Sorting Genetic Algorithm (ENSGA-II)
for Multi-Objective Optimization Problem in Interval
Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Asoke Kumar Bhunia, Amiya Biswas and Ali Akbar Shaikh
A Comparative Study on Different Versions of Multi-Objective
Genetic Algorithm for Simultaneous Gene Selection and Sample
Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Asit Kumar Das and Sunanda Das
ASurveyontheApplicationofMulti-ObjectiveOptimizationMethods
in Image Segmentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Niladri Sekhar Datta, Himadri Sekhar Dutta, Koushik Majumder,
Sumana Chatterjee and Najir Abdul Wasim
Bi-objectiveGeneticAlgorithmwithRoughSetTheoryforImportant
Gene Selection in Disease Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Asit Kumar Das and Soumen Kumar Pati
Multi-Objective Optimization and Cluster-Wise Regression Analysis
to Establish Input–Output Relationships of a Process . . . . . . . . . . . . . . 299
Amit Kumar Das, Debasish Das and Dilip Kumar Pratihar
