49
1 INTRODUCTION
Prediction of Ship performances in calm and rough
waterisoneofthemostimportantconcernsfornaval
architects, already at the earliest design stage. From
this point of view seakeeping performanceisoneof
the most important performances in the ship hull
form optimization. It is possible to achieve
considerable improvements in terms of habit
ability,
operabilityandsurvivabilitybymeansofchangesin
hull form even when displacement and main
dimensionshavebeenfixed.
It is worth noting that for a comprehensive and
detailedshiphydrodynamicoptimizationallobjective
functionssuchasresistance,stability,seakeepingetc.
must be considered, because it is clear that
consideration of an objective function without the
otheronesgivesunrealisticandimpracticalresults.
Some researchers have considered two or three
objectivefunct
ionsforoptimizinghullformandsome
others only one objective functions. For example
Gammon (2011) uses three objective functions in his
study, Biliotti et al. (2011) and Grigoropoulos and
Chalkias(2010)utilizetwoobjectivefunctionsintheir
work and many researcher use only one objective
function(Hanetal.,2012,Zakerdoostetal.,2013,A.
Scam
ardellaandV.Piscopo,2014).
Zhang(2009and2012),Kimetal.(2009and2008)
andSahaetal.(2004)employeddifferenttypesofthe
Nonlinearlinearprogramming(NLP)asoptimization
techniques. Evolutionary Algorithm (EA) and
Artificial Neural Networks (ANN or NN) offer
effective method for conducting op
timization and
data analysis. EA techniques may be separated into
Genetic Algorithm (GAs), Evolutionary Strategies
(ESs)andEvolutionaryProgramming(EP).However
at present Genetic Algorithm (GA) and evolution
strategies (ESs) are most widely used in hull shape
modification. In this work, the term GA is used to
solving op
timization problem. Day and Doctors
(2001) studied hull form optimization using a GA
technique in which the objective was to minimize
Optimizing the Seakeeping Performance of Ship Hull
Forms Using Genetic Algorithm
H.Bagheri,H.Ghassemi&A.Dehghanian
DepartmentofOceanEngineering,AmirKabirUniversityofTechnology,Tehran,Iran
ABSTRACT:Hullformop
timizationfromahydrodynamicperformancepointofviewisanimportantaspectof
shipdesign.Thisstudypresentsacomputationalmethodtoestimatetheshipseakeepinginregularheadwave.
Intheoptimizationprocessthe Genetic Algorithm(GA)is linkedtothecomputationalmethodtoobtain an
optimumhullformbyta
kingintoaccountthedisplacementasdesignconstraint.Newhullformsareobtained
fromthewell‐knownS60hullandtheclassicalWigleyhulltakenasinitialhullsintheoptimizationprocessat
twoFroudenumbers(Fn=0.2andFn=0.3).Theoptimizationvariablesareacombinationofshiphulloffset
sand
maindimensions.Theobjectivefunctionoftheoptimizationprocedureisthepeakvaluesforverticalabsolute
motionatapoint0.15LBPbehindtheforwardperpendicular,inregularheadwaves.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 1
March 2014
DOI:10.12716/1001.08.01.06
50
resistance. Jun and Kuniharu (2004) presented a
single‐objective optimization algorithm based on
genetic algorithm to improve hull form of a
catamaran.
Duetotheimportanceofseakeepingperformance,
seakeeping optimization has become a popular
researchtopicforthelastthreedecades.
Bales(1980)optimizedadestroyer‐typehullform,
in head seas and at various speed, on the basis of
analyticalpredictions,subsequentlyderivingbysome
regression formulas correlating relevant
performancestoformparameters,theoptimumhull.
Griogoropoulos and Loukakis (1988) developed a
numericalmethod,basedonanonlineardirectsearch
algorithm to minimize RAO peak values in head
regularwaves.Similarstudieshavebeenalsocarried
outbyHearnetal.(1991),whodevelopedaninverse
design procedure, based on the optimum hull
nonlinear direct search process. Kukner and Sariöz 
(1995) optimized the seakeeping qualities of a high
speed vessel, generating by the Lackenby method
(Lackenby, 1950), several derived
hulls having
differentformparametersasregardstheparentones.
Peacock et al.(1997) defined a mathematical model
based on a multi‐objective research algorithm for
displacement mono‐hulls. Sariöz and Sariöz (2006)
proposedanewoptimization procedure,basedona
nonlinearproblemsolvedbydirectsearchtechniques.
Campana et al.
(2009) proposed a new optimization
techniquefortheheavemotionoftheS175container
ship,adoptedbytheITTCSeakeepingCommitteeasa
benchmark test, considering two different
optimization procedures, namely a filled function
based algorithm anda Particle SwarmOptimization
method. Diez and Peri (2010) presented a new
approachfor
therobustoptimizationofabulkcarrier
conceptual design, subjected to uncertain operating
and environmental conditions, so extending the
standard deterministic formulation for design
optimization to take into account the uncertainty
relatedtodesignvariables,operatingconditionsand
computational results of the simulations. Finally
Özüm et al. (2011) investigated the
seakeeping
qualities of fast ships, systematically varying both
maindimensionsandhullformparameters.Anyway,
in almost all cases, optimization procedures were
based on the assumption that the optimum hull is
foundwhenthe vertical plane motionsandabsolute
vertical acceleration in regular head waves due to
combinedpitch,heavemotions,
isminimized.
In this study, after problem formulation and
especially the explanation of strip theory and a
particularformoftheoptimizationalgorithm(genetic
algorithm),resultsofapplicationofthismethodology
usingtwo differentcasesof theWigleyhull andthe
S60 hull are presented, and in both ones allowing
principal parameters of length, beam and draft to
changesimultaneouslywiththeoffsetofhullsurface.
Itshouldbenotedthatthecurrentdesignprocedure
is restricted to the minimization of vertical plane
motions and roll is not included for the following
reasons:
The sensitivity of roll motion to weight
distributioncharacteristicswhicharegenerallynot
availableattheearlystagesofdesign.
Difficultiesinpredictingnonlinearrolldamping.
Thefactthatexcessiverollcanalwaysbereduced
bychangingheadingtoheadorbowseas.
2 OPTIMIZATIONPROBLEMANDGA
The general mathematical form of a numerical
constrained optimization problem has been
represented here. Design variables and constraint
conditionsareusedtocharacterizetheproblem.The
role of
design variables in hydrodynamic
optimizationproblemsiscontrollingthegeometryof
the hull during optimization procedure. Constraints
are the values by which the design variables are
restrictedandmaybeseparatedintwotypes,equality
and inequality constraints. A function being
maximized or minimized by users is known as the
objective
function andthevalueofthisfunctionisa
criterion to determine the efficiency of design
optimization methodology. If in an optimization
problem only one objective function is used, the
optimizationisknown assingle objectiveand iftwo
ormoreobjectivefunctionsareused,theoptimization
isknownas
multiobjective.Thestandardformulation
of an optimization problem mathematically is as
follows:
Optimize
12
n
( ) ( ), ( ),..., ( )
m
Fx f x f x f x x


(1)
Subjectto
( ) 0 i 1,...,q
g ( ) 0 i 1,...,
i
i
hx
x
p


(2)
where
i
f
x
is the objective function, m is the
number of objective function,
q is the number of
equality constraints,
p
is the number of inequality
constraints and
1
, . . .,
n
x
xx S
 is a
solutionor individual. The set
n
S defines the
search space and the set
S defines a feasible
searchspace.Thesearchspace
S
isdefinedasann‐
dimensional rectangle in
n
(domains of variables
definedbytheirlowerandupperbounds):
1
i
li x ui i n

The constraints define the feasible area. This
means that if the design variables vector
x be in
agreement with all constraints

i
hx (equality
constraint) and
i
gx (inequality constraint), it
belongstothefeasiblearea.
In this study design varia bles vector include the
main parameters (length, beam, draft) and the hull
offset which are limited by the lower and upper
bounds. The ship hull displacement also is an
inequalityconstraint.
Among the class of evolutionary algorithms,
genetic
algorithm(GA)isthemostpopularalgorithm
forsolvingcontinuousoptimizationproblems,i.e.for
optimizing real‐valued function
f
defined on a
subset of
n
for some dimension n . Genetic
algorithm can be applied to combinatorial problems
aswell.Geneticalgorithmisinspiredbytheevolution
51
theory(DarwinianTheoryofbiologicalevolution)by
meansofaprocessthatisknownasnaturalselection
andtheʺsurvivalofthefittestʺprinciple.Thecommon
idea behind this technique is similar to other
evolutionary algorithms: consider a population of
individuals; the environmental pressure causes
natural selection which leads to
an increase in the
fitness of the population. It is easy to see such a
process as optimization. Consider an evaluation
functiontobeminimized.Asetofcandidatesolutions
canberandomlygeneratedandtheobjectivefunction
can be used as a measure of how individuals have
performedin
theproblemdomain(anabstractfitness
measure) the lower the better. According to this
fitness, some of the better solutions are selected to
seed the next generation by applying recombination
and/or mutation operators to them. The
recombination(alsocalledcrossover)operatorisused
togeneratenewcandidatesolutions(offspring)from
existing
ones, they take two or more selected
candidates (parents) from the population pool and
exchange some parts of them to form one or more
offspring.Mutationoperatoris usedtogenerateone
offspringfromoneparentbychangingsomepartsof
the candidate solution.Applying recombination and
mutation operators causes
a set of new candidates
(theoffspring)competingbasedontheirfitnesswith
theoldcandidates(theparents)foraplaceinthenext
generation.
This procedure can be iterated until a solution
with sufficient quality (fitness) is found or a
previouslysetcomputationaltimelimitisreached.In
otherwords,
theendconditionsmustbesatisfied.The
composed application of selection and variation
operators (recombination and mutation) improves
fitness values in consecutive population. A general
flowchartofgeneticalgorithmisshowninFigure1.
Figure1.Generalflowchartofgeneticalgorithm
Genetic algorithm variables are divided into two
categories: object and genetic variables. Variables in
genetic algorithm commonly are as real‐valued
vectors because this algorithm is usually used for
continuous parameters. A form of an individual in
GAisasfollows:
1
,...,
n
x
x
where
i
x
is the object variable. In object variables
mutation, each gene (biologic name of a vector)
changed whit mutation rate (genetic variable) in
rangeoftheirlowerandupperbounds.Themutation
methodologyfor
i 1 , . . . , n isasfollows:
 
11
,..., ,...,
,,
nn
ii
x
xxx
where
xx li ui


(3)
Scatter recombination is one of main type of
recombination (crossover) used in GA. This type of
crossover creates a random binary vector. So, the
genes are selected from the first parent where the
vector is a 1, and from the second one where the
vectorisa0.The
μ , λ
survivorselectionscheme
has advantages over its competitor, the
μ λ
selection scheme but the

μ λ selection scheme
is an elitist mechanism that can maintain the best
solutiontoeachgeneration(EibenandSmith,2003).
3 SEAKEEPINGCALCULATION
Thedeterminationofhydrodynamicforcesactingon
ashipcanbeformulatedasalinearboundaryvalue
problem in potential theory. Under the assumption
that motion responses are
linear, or at least can be
linearizedandareharmonic,theequationsofmotion
fortheadvancingshipinwavesmaybewritteninthe
followinggeneralform:
kj j k
L H,ω, U η F , k,j 1,2, ,6
 (4)
where
H
represents the hull geometry, ω is the
wavefrequencyandUistheforwardspeed.Typically
theoperator
k
j
L
isoftheform
2
kj kj kj kj
MAωiBωC
kj
L
 (5)
where
M
is the generalized mass matrix, A and
B
represent the added mass and fluid damping
matricesassociatedwithforces/momentsinducedin
the
k th mode, as a consequence of motion in the
j
th mode and C is the hydrostatic restoration
matrix. The degrees of freedom,
j
, correspond to
surge, sway, heave, roll, pitch and yaw as
j
assumesthevalue1 ‐6,respectively. Thedependence
ofthehydrodynamiccoefficientsandthehydrostatic
restoration upon the hull form shape may be
expressedas:


,,
,,
kj kj
kj kj
kj kj
AAH U
B
BH U
CCH
(6)
Thewaveexcitation
k
F isalsoafunctionofwave
heading
,, ,
kk
FFH U
(7)
52
Figure2.ComparisonofheaveandpitchRAOcoefficientformodelsoftheWigleyhull
The added mass, damping, restoring force and
waveexcitingforcetermscanbecalculatedbyusing
well established numerical procedures. In order to
reduce the computing time a linear strip theory
approach is adopted as described by Salvesen et al.
(1970). The sectional added mass and damping
coefficients are calculated by
using the well‐known
Frank Close‐Fit method (1967). The seakeeping
responses in head sea are generally the most
important responses for mono‐hulls. Thus, all
calculationswerecarriedoutforverticalmotionsand
related kinematics certainly. The computed ship
responsesincludeverticalmotionandaccelerationat
bow region (at
a point 0.15LBP behind the forward
perpendicular). All the results are given for regular
headwaves.
ThecomparisonofDelftUniversityofTechnology
(DUT) Report experiment(1992) with a 3 m Wigley
hullswithlengthtobeamratioL/B=10andlengthto
draftratio L/T = 16inheadregular
wavewhit4 cm
wave height, heave and pitch RAO respectively are
shown in Figure 2. Using the numerical method
described above for computing Ship vertical motion
leads to good agreement and errors between
predictions and the experiments (white respect to
lineartheorywasemployed)liewithinabout%10for
the design Froude number (Fn=0.3). It should be
noted that according to the figure 2, the heave and
pitchRAOat
/L‐1.2thatthepeakvalueoccurs,have
a 180 degree phase difference. The vertical bow
motion(objectivefunction) isafunctionofthemain
dimension (length, beam and draft) and the hull
offsetsoftheshipintheoptimizationprocesswhich
mustbeminimized.
4 PROCEDUREOFTHEHULLFORM
OPTIMIZATION
Theprocedureofoptimizingashiphullforminorder
to find a hull shape with minimum bow vertical
motion is as follows. The optimization of hull form
can be performed by evaluating the hull forms that
are generated by variation operators and then
selecting the best forms of
lower vertical motion at
bowreignineachgeneration.
TheWigleyandS60hullformsareconsideredas
initialhullforms.Eachchromosome(biologicnameof
a solution) in the optimization algorithm consists of
ship offsets, length (waterline length), beam (in
waterline) and draft. Because of large number of
variables, the
genetic algorithm is a successful
technique for the hull form optimization problems
from a seakeeping point of view. The design
constraintsthatwereusedforthisstudyarethatthe
optimizer allowedno change in the total
displacement of the ship. In addition, sinkage and
trim effects are not considered
as a hydrodynamic
designconstraint.Somelimitshavebeenimposedon
theprincipaldimensionsandthehulloffsets.Inorder
to restrict the search space and to keep the optimal
hullneartheoriginaloneforcomparison,thelength,
beamanddraftarelimitedto±10percentvariationin
the principal
dimensions and the offsets points are
limitedto±3percentoftheinitialhulloffsets.Table1
representsvariationpercent of variablesusedintest
cases.
Table1.Variationpercentofvariablesusedintestcases
_______________________________________________
VariablesHulloffsetsL  B T
_______________________________________________
Variationpercent ±3±10 ±10 ±10
_______________________________________________
The Wigley model is a popular and well‐known
model in ship hydrodynamics experiments. Many
experimental and numerical results can be found in
theliteratureforthismodel.
We employed this model to compare numerical
results. The standard Wigley hull is a mathematical
displacement hull form, the geometric surface
of
whichcanbedefinedas:
53

22
2
, 1 1
2
Bx z
fxy
LT








(8)
where
B
is the ship beam,
L
is the ship length,
T
is
the ship draft,
L/2 x L/2 and Tz0 .
Vertical motions of hull section are predicted by coupled
strip theory and Frank method. The hull form optimization
is carried out at a single Froude number (
/ Fn U g L )
that constant for each model and that is
0.3 for Wigley
model and
0.2 for S60 model where U and L , speed
and waterline length of the model respectively. Table 2
shows the main dimensions of the Wigley and S60 hull
models.
Table2. Main dimensions of the Wigley and S60 hull
models
_______________________________________________
ModeltypeLength Beam Draft DesignFn
[m] [m] [m]
_______________________________________________
Wigleyhullform 30.30.1875 0.3
S60hullform 122 17  70.2
_______________________________________________
The process of optimization is performed by the
genetic algorithm. The offset points and principal
dimensionscanberepresentedbyreal‐valuedvectors
in the limits as already mentioned. The scatter
recombinationhasbeenusedintheobjectvariables.
The mutation operator has been applied to the
individualsasmentioned.Therecombinat
ionratehas
been0.80,whilethemutationratehasbeen1perone
individual.Theparentselectionhasbeenapproached
by a uniform random distribution. According to
results of tests carried out by authors the
μ , λ
scheme has been considered as an a
ppropriate
survivorselectionmechanismfortestcasesusedthe
Wigleyhullandwell‐knownS60asparentmodels.If
wedonʹtuseawaytosmooththehull,thegenerated
hulls are wavy and impractical. Therefore, we have
used a modification algorithm by meansof cubic B‐
Spline surface to obtain fair hull forms in the
op
timizationmethodology.
5 RESULTSANDDISCUSSION
5.1 CaseoftheWigleyhull
In order to perform the optimization of hull for
minimizing the vertical motion peak value at bow
regionoftheship,whichisaimportantfactorinthe
hydrodynamic design of hull, and to determine the
preliminary design parameters to satisfy the design
requirements given by the owner or client
, it is
necessary the candidate solutions generated are
permitted to vary by changing the offsetof the hull
form and the main dimensions. Thefirst example is
forthehydrodynamicop
timizationoftheWigleyhull
form with respect to the minimum peak value for
absoluteverticalmotionatapoint0.15LBPbehindthe
forward perpendicular. The Wigley model with
lengthtobeamratioL/B=10andlengthtodraftratio
L/T = 16 is optimized for a speed, corresponding to
Froude number of 0.3. The offset
s values and main
dimensionsofthehullarelimitedintherangeof97to
103and90to110percentofinitialonesrespectively
anddisplacementisfixed.Thenumber
130 hull forms
in each generation are
createdandamong them,thebest
10hullformsareselectedtoseedthenextgeneration
based on the fitnessi.e.thevertical bow motion the
better hull form. Figure 3 depicts body plan of the
optimalhullform(dashedlines)generatedbyuseof
the genetic algorithm optimization technique and
body plan of the init
ial Wigley hull(solid lines). The
optimizationprocedureimprovedtheinitialhulland
produced a reasonable hull form. The new hull is
smoothedbecauseofusingB‐Spline.
Figure3.BodyplanoforiginalWigleyhullandoptimalhull
(solidlineisinitialanddashedlineisoptimalhull)
As can be seen in Figure 3, the beam of the
optimized hull is wider than the beam of the initial
Wigleyhullinforeandaftsectionsandthinnerinthe
amidships. The draft of the optimized hull has
decreased
dramatically.The3Dviewoftheinitialand
optimizedWigleyhullformarepresentedinFigure4.
During the run of the optimization algorithm in
additiontothehulloffsetsthelength,beamanddraft
of the hull are changed. The variation of the ma in
dimensions of the hull versus iteration number are
shown in Figure 5. These two figures (5‐b and 5‐c)
confirm that thehullhasatendencytowardalessdraft
and approximately fixed beam during the
optimization algorithm.
The length of the hull is
rapidlyincreasedintheinitialiterationsandafterthat
is remained fixed. The changes in the variable
parametersofthehullaretoreachminimumvertical
motion peak value and match the constraint for the
displacement.
The changes of Fitness value versus iteration
numberoftheverticalmotionareshowninFigure5‐
d. The reduction of vertica
l bow motion peak value
leadstoreductionofverticalmotionandacceleration
intherangeofwavelengthasshowninFigure6.
54
Figure43Dhullform,(Redisoptimizedhullandblueisinitialhull)
a)Lengthb)Beam
c)Draftd)Fitness
Figure5.VariationofdimensionsparametersandthehistoryoftheFitnessvalueoftheWigleyhullbyiterationnumber
a)AbsoluteVerticalMotionb)AbsoluteVerticalAcceleration
Figure6.AbsoluteverticalmotionandaccelerationfortheinitialandoptimumWigleyhullform
55
5.2 CaseoftheS60hull
Inthisexample,a122minlengthoftheS60hullform
(
B
C = 0.7) with length to beam ratio L/B = 7 and
beamtodraftratioB/T=3ischoseninordertoderive
ahullwithminimumbowvertical motionatFn=0.2.
Aswassaidbeforetheoptimizationofthehullform
isbasedonminimizingthe
hydrodynamic factorsof
the ship i.e. bow vertical motion with given design
constraints.Thevariationrangeintheoffsetsva luesis
between 97 and 103 percent of the initial S60 hull
offsets and the main dimensions arechanged in the
limits between 90 and 110 percent of the main
dimensions
of initial hull anddisplacement is fixed.
Thebodypla noftheinitialhullform(
solid lines)and
theoptimizedhullform(dashedlines)are shownin
Figure 7.
In each generation 200 hulls are created and
then among them,thebest15hullformsareconsidered
to
go to the next generation based on lower vertical
motion
peakvalueinbowofship.Useofthegenetic
algorithmincombinationwiththeB‐splineproduced
optimized fair hull. To acquire a hull form with
minimum bow vertical motion and match the
constraint for the displacement. Thebeam and draft
of the optimized hull are approximately fixed and
deeper
thantheinitialS60hull.
The3DviewoftheinitialandoptimizedS60hull
formisshowninFigure8.During theimplementation
of the optimization algorithm in addition to hull
offsets the length, beam and draft of the hull are
variedandthechangesofthembyevaluation
number
are as in the previous case, butthedifference is the
hull has a tendency towards approximately smaller
length(seefigures9‐a,9‐band9‐c).Ascanbeseenin
this Figure the significant changes of four
characteristicsofthehullareattheearlyevaluationof
objectivefunctionandafterthatremainfixed.
Figure9‐ddemonstratesthechanges ofthefitness
valueofhullbyiterationnumber.Ascanbeseenin
this figure during the optimization process the
verticalmotionpeakvaluedecreased.This is dueto
variationofthelengthanddraftand
thehullformin
theoptimizationprocess.
Evaluatingthehydrodynamic performance ofthe
initial hull and the optimized hull in terms of the
vertical motion and acceleration is shown in
Figure10.
Figure7. Bodyplan of original S60 (
B
C = 0.7) hull and
optimalhull
(solidlineisinitialanddashedlineisoptimalhull)
Figure8.3Dhullform,(Redisinitialhullandblueisoptimizedhull)
a)Lengthb)Beam
56
c) Draft d) Fitness
Figure9VariationofdimensionsparametersandthehistoryoftheFitnessvalueoftheS60hullbyiterationnumber
a) AbsoluteVerticalMotion b) AbsoluteVerticalAcceleration
Figure10.AbsoluteverticalmotionandaccelerationfortheinitialandoptimumS60hullform
Itisinterestingtonotethatineachtestcase,trend
of variation main dimensions such as, length and
draft is different. In the Wigleytestcase length and
draftareincreasedanddecreasedrespectivelybutin
S60 test case length and daft are decreased and
increased. However, Lloyd (1992) expressed tha
t in
theoptimizationoffloatingbody,typeofhullformas
parameterchangesdependsontype ofhullform. In
eachtestcase;changeofthemaindimensionsleadto
thelowerverticalmotionandacceleration.
6 CONCLUSIONS
A numerical method has been proposed for
hydrodynamic hull form optimization in regular
wave with respect to vertica
l motion of bow of the
ship as the only objective function. The genetic
algorithmis combined with a numericalmethod for
minimizing peak value of vertical motion
characteristic(theshipmotioninwavebasedonstrip
theory and the sectional added mass and damping
coefficients calculat
ion by the well‐known Frank
Close‐Fitmethod).Thedesignvariablesareincluded
the hull offsets and the main dimensions (Length,
breadthanddraft)andthedisplacementisusedasthe
design constraint during the optimization with
Wigley and S60 hull forms as standard models at
constantspeedFn(is0.3forWigleymodeland0.2 for
S60 model) to develop optimized ship hull forms.
Compa
red with the initial hull the peak value of
vertical motion of the improved hull is reduced by
33%inthefirstexampleand27%inthesecondone.
Thehullfairingprocedurehasbeenappliedbyusing
B‐spline. As canbe showed in figures the reduction
percent achieved in vertica
l acceleration is
considerablecomparingwithotherpapers.Thegains
intermsoffitnessvaluereductionswereconsiderable
atbothcasesandthisresultedinimprovementsinthe
entire ship range. Therefore, we can get conclusion
tha
tgeneticalgorithmusinginthisstudyareeffective
androbusttechniquesforhullformoptimization.
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NavalHydrodynamics,Tokyo.
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D., Galliussi, M., Guadalupi, D. and Manfredini, A.
(2011):AutomaticParametricHullFormOptimizationof
Fast Naval Vessels, 11th International Conference on
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