optimization of fishing vessel

8/13/2019 Optimization of Fishing Vessel

1/11

Optimization of fishing vessels using a Multi-Objective Genetic Algorithm

Mark A. Gammon 1

Defence R&D CanadaAtlantic, Dartmouth, Nova Scotia, Canada

a r t i c l e i n f o

Article history:

Received 17 August 2010

Accepted 5 March 2011

Editor-in-Chief: A.I. Incecik

Available online 23 May 2011

Keywords:

Optimization

Multi-objective

Fishing vessel

Resistance

Seakeeping

Stability

a b s t r a c t

A fishing boat hull is used as an example of how hull form optimization can be accomplished using a

Multi-Objective Genetic Algorithm (MOGA). The particular MOGA developed during this study allows

automatic selection of a few Pareto Optimal results for examination by the designers while searching

the complete Pareto Front. The optimization uses three performance indices for resistance, seakeeping

and stability to modify the hull shape to obtain optimal hull offsets as well as optimal values for the

principal parameters of length, beam and draft. The modification of the 148/1-B fishing boat hull, the

parent hull form of the _Istanbul Technical University (_ITU) series of fishing boats, is presented by first

fixing the principal parameters and allowing the hull offsets to change, and secondly by simultaneously

allowing variation of both the principal parameters and the hull offsets. Improvements in all three

objectives were found. For further research the methodology can be modified to allow for the addition

of other performance objectives, such as cost or specific mission objectives, as well as the use of

enhanced performance prediction solvers. In addition, one or more hulls could be evaluated by

experiment to validate the results of using this particular optimization approach.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Hull form optimization is a process that involves changing aship or boat hull in order to improve performance such as

resistance, seakeeping, stability and so forth. The hull is a funda-

mental component of a vessel and has a significant influence on the

performance and consequently on overall success of the design.

A single design optimization problem optimizes a single objective

function while satisfying some design requirements, while multi-

ple objective design optimization examines trade-offs between

often conflicting aspects of the design problem. The individual

objective or cost functions, such as minimization of resistance by

Day and Doctors (1997) or minimization of the total catamaran

resistance byDanisman et al. (2001)or minimization of the wash

from high speed vessels by Zaraphonitis et al. (2003), represent

different aspects of design optimization.

The shape of the hull impacts every aspect of a design. Threeperformance objectives are considered as examples from among

the numerous issues facing a design team, namely stability,

resistance and seakeeping. Stability must satisfy or exceed certain

constraints and is often modeled as a constraint rather than an

objective function. Seakeeping obviously impacts human safety

and comfort. Resistance is one of the chief costs in the operation

of the vessel, such that minimizing resistance by even a few

percent can lead to substantial savings, especially in large ships.

For example, using a bunker fuel charge of approximately $450/

metric ton,2

given a ship that burns 150 ton/day over a 14 day tripacross the Pacific,3 the overall cost for fuel alone would be

$945,000. An improvement of even 2% would represent a savings

of $18,900 per trip. Minimizing resistance by creating a slender

hull, for example, conflicts with stability performance, which is

increased by the greater beam. Greater beam in turn increases

viscous resistance. An optimized design requires that these

conflicting performance criteria can reach compromise.

Evolutionary Algorithms (EA) and Artificial Neural Networks

(ANN or NN) offer effective methods for conducting optimization

and data analysis. EA techniques may be separated into Genetic

Algorithms (GAs), Evolution Strategies (ESs) and Evolutionary

programming (EP). In this study, the term GA is predominantly

used to reflect the encoding and characteristics of the algorithm,

unless reference is made to a specific technique. For example, Dayand Doctors (1997) studied hull form optimization using a GA

technique in which the objective was to minimize resistance.

Their study varied a wide range of hull displacements and

examined the optimization trends that occurred on the basis of

variation of the principal parameters. Yasukawa (2000) and

Dejhalla et al. (2002)have both conducted a resistance optimiza-

tion analysis of a hull form using GA methods where the objective

was also to minimize wave resistance. Those studies focused on

Contents lists available atScienceDirect

journal homepage: www.elsevier.com/locate/oceaneng

Ocean Engineering

0029-8018/$- see front matter & 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.oceaneng.2011.03.001

E-mail addresses: [email protected], [email protected] Research conducted while on leave at Yildiz Technical University, Istanbul,

Turkey.

2 http://www.bunkerworld.com/markets/surcharges/tsa3 http://www.tsacarriers.org/fs_bunker.html

Ocean Engineering 38 (2011) 10541064
http://-/?-http://www.elsevier.com/locate/oceanenghttp://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.oceaneng.2011.03.001mailto:[email protected]:[email protected]://www.bunkerworld.com/markets/surcharges/tsahttp://www.tsacarriers.org/fs_bunker.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.oceaneng.2011.03.001http://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.oceaneng.2011.03.001http://www.tsacarriers.org/fs_bunker.htmlhttp://www.bunkerworld.com/markets/surcharges/tsamailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_5/dx.doi.org/10.1016/j.oceaneng.2011.03.001http://www.elsevier.com/locate/oceanenghttp://-/?-


2/11

existing hulls that were modified by varying the hull offsets

slightly while maintaining the same principal characteristics of

the length, beam, draft and displacement. While other optimiza-

tion methods such as simulated annealing, Lipshitz Global Opti-

mization and other methods are routinely used, as stated by Gen

and Cheng (2000), the inherent characteristics of genetic algo-

rithms, i.e. multiple directional and global search, lack of math-

ematical requirements, ability to handle all types of objective

functions and ability to be combined with conventional methods,make MOGA techniques well suited to multiple objective optimi-

zation problems.

The MOGA approach presented in this study can be extended

to any hull form optimization problem in which the design

requirements are known and can be formulated as a multiple

objective problem. As an example, the MOGA methodology was

applied to fishing boats in order to determine whether a more

optimal boat hull could be derived. The current study represents

one example of how this specific MOGA can be applied during the

initial and concept stages of vessel design. The significant pro-

blem faced by the designer, whether the vessel is small or large, is

the choice of the optimal principal parameters that will lead to a

successful design. Most, if not all, MOGA methodologies conduct

design optimization by searching out the entire Pareto Front,

which will be described later. While effective in determining the

optimal candidates, the plethora of possible solutions leads to a

solution space nearly equal to the population sample size, which

can number in the hundreds. It is usually left to the designer to

choose the more favoured design, which can be a daunting task.

The current methodology allows an automatic selection of the

number of optimal compromise solutions to give to the designer.

In addition, the calculation of the performance objectives in this

study is deliberately not computer intensive, enabling cost-

effective initial boat design studies to be conducted as in

Gammon (2004). Future research would focus on the use of more

advanced functional representations of the performance objec-

tives as inMaisonneuve et al. (2003)using this MOGA approach,

as additional resources become available.

This paper is structured as follows. Section 2 is concerned with

the problem formulation and in particular the definition of the

multi-objective problem along with the development of the

relevant indices that represent the individual cost or performance

functions for each of the objectives. Then, a particular form of

MOGA is presented in Section 3 with some methods for encoding

the problem. Section 4 presents results of application of this

methodology using two different examples of the Istanbul Tech-

nical University (ITU) fishing hull, the first with fixed principal

parameters of length, beam and draft, and the second allowing

these parameters to change simultaneously with the hull offsets.

The fishing boat series as described by Kafal et al. (1979) was

developed by ITU for Turkish fishermen in order to have a

standard series with known and measured characteristics in

terms of seakeeping and resistance, for which experimental datais well known. Finally, Section 5 gives some conclusions regarding

this particular approach along with the scope for future work.

2. Optimization problem formulation

Determining the optimal principal parameters for length (L), beam

(B) and draft (T), as well as volumetric displacement (r), is most oftenaccomplished by parametric variation of a parent hull. Usually hull

form optimization consists of only changing offsets of an already

suitable hull in order to optimize a particular performance objective.

However, at the preliminary design stage, the principal parameters of

the vessel must be determined. These are often determined through

regression based analyses predicting performance attributes from a

database of known designs. The focus of this study is to compute the

performance factors directly for each candidate hull. In addition to the

principal parameters, the optimal hull offsets for the hull shape or

hull form should be determined simultaneously. That is to say, the

near-optimal hull form should also include the near-optimal length,

beam and draft, as well as satisfy a displacement requirement, in

order to create a near-optimal design.

2.1. General multi-objective problem definition

In generic terms, the functional form of the problem is given as

follows. We need to determine the vector of decision variables as

described inCoello Coello (1996):

x!

x1,x2,x

3,. . .,x

n

T

where xj,j 1,2,. . .,n are the decision variables. As an example,

for this study, the decision variables include the principal para-

meters of the vessel and the hull offsets, i.e.

x1 L; x2 B; x3 T; x4W

where L, B and Tare the length, beam and draft, respectively. The final

decision variableWis the hull offsets represented as a matrix.

The solution must satisfy the m number of inequality con-

straints:

giZ0,i 1,. . .,m

andp the number of equality constraints:

hi 0,i 1,. . .,p

wherep as the number of equality constraints should be less than

the number of decision variables n in order to avoid being over-

constrained. Most design factors can be captured as constraints,

as well as limits of the solution domain. The constraints are

discussed further under the design requirements.

The solutions must optimize the vector function:

f!

f1x!

,f2x!

,. . .,fkx!

T

The objective functions f1x!, f2x! and f3x! representresistance, seakeeping and stability indices, respectively. In shor-

tened form:

f!

optx O

f!

x!

f!

:O-Rk

O fx!AR

n9g!x!Z0,hx! 0g

wherek is the number of objectives.

The multi-objective definition of optimality, known as Pareto

Optimality, is defined as a point in n-dimensional space repre-

sented by

x!AO

such that for every, x!AO and I{1,2,y,k}, I either

8iA Ifix!

fix!

or there is at least one iAI such that

fix!

4fix!

(for maximization problems) or fix!

ofix!

(for

minimization problems).

In this study, the term near-optimal is used to describe a

design choice that achieves some compromise in the performance

objectives while satisfying constraints for the design features.

2.2. Formulation of performance indices

2.2.1. Objective 1resistance performance index

The non-dimensional total resistance coefficient CT)shipis

CTship Cv CWship ca 1 kCFCW ca

M.A. Gammon / Ocean Engineering 38 (2011) 10541064 1055


3/11

whereCv is the viscous resistance coefficient, CW)shipis the wave

making resistance coefficient and cais a correlation allowance. Cvcan be represented in terms of the frictional resistance coefficient

CF and form factor k, i.e. Cv(1 k)CF. The form factor k is

determined from the model test and is assumed independent of

speed and scale. For example, in the ITU fishing hull forms the

tow tank test for the parent form of the ITU series, ITU 148/1-B,

showed a form factor of 0.25 whose tests were done with

5 models with different scales as described by Kafal et al.(1979). The same form factor is assumed for the full-scale ship.

The non-dimensional form of the total resistance RT)ship is a

function of the ship speedVand wetted surface areaSof the ship:

CTshipRTship

0:5rV2S

wherer is the density of water.The International Towing Tank Conference (ITTC) proposed a

frictional resistance formula based on the Reynolds number. The

ITTC 1957 frictional line is calculated as follows:

CF 0:075

logRn22

whereRn is the Reynolds number given by

Rn rVL

m

wherem is the viscosity,Vis the ship speed and the length of thevessel isL .

In order to determine CT)ship, we need to determine CW)ship, the

wave making resistance coefficient. CW)model for a model is

assumed to be equal to the full scale shipCw)ship, i.e.

CWship CWmodel

Hence

CTship CWmodel 1 kCFca

For the example in this study, wave resistance CW is calculated

using a transom modified Michell integral using potential flowtheory, as described in Gammon (1990). A comparison of wave

resistance with experimental, Michell integral and the modified

transom integration is shown in Fig. 1. It would appear that the

transom effect is considerable for vessels with a low L/B ratio as in

Gammon and Alkan (2001). At the higher Froude number (Fn) of

0.5 the effect is over pronounced using the transom theory, but as

the normal vessel speed is approximately 10 knots, the prediction

up to Fn 0.4 is in good agreement, and considerably closer to the

experimental curve as compared to the unmodified Michell integral.

A Resistance Coefficient Index (RCI) is formulated from each CTvalue at each speed or Froude number as a representation of the

area under the resistance curve to measure the overall resistance

performance. In the current approach, the speeds are treated

equally. The RCI is calculated as follows:

RCIXN1i 1

1

2CTi CTi 1 Fni 1Fni

where N is the number of Froude numbers, CTi the resistance

coefficient at speed i and Fni the Froude number at speed i.

The resulting objective for f1x!

is then represented as

follows:

opt f1x! minRCIL,B,T,W

2.2.2. Objective 2seakeeping performance index

Seakeeping performance is a complex area of analysis and needed

resolution into a single seakeeping performance index similar to the

resistance coefficient index in order to be useful in the current multi-

optimization problem. In ship motion, numerous seakeeping factors

are relevant including acceleration at various points on the vessel,

slamming effects, crew response and motion sickness index. Since

there are numerous seakeeping factors, and these represent aspects of

this particular performance attribute of the hull form, it was prudent

to resolve these into a single performance index.

The hull form optimization hypothesis is that the best hull

form is the one that minimizes all of the motions. While there

may be conflicting influences in the motions between heave, pitchand rolling, the latter was considered to be characterized by the

beam and may also be regarded as part of the stability criteria.

The focus for the seakeeping performance is the heave and pitch

motions as shown inFig. 2.

For the purpose of comparing candidate hull forms, the problem is

then simplified by considering only the vertical motion from the pitch

and heave. The total vertical motion, measured at the bow, is

combined from the maximum heave and pitch motions. This is

multiplied by the heave acceleration to give a pseudo-equivalent

momentum. The result is averaged over each ship speed to determine

pseudo energy density. The mass of the vessel is deliberately left out

as the combined pitch and heave are figurative and the maximum

values of each motion do not frequently occur simultaneously.

Vertical motion could be combined into one vertical seakeepingmotion index by integrating the values obtained at each heading

but just head seas were utilized over each ship speed. The equation

for the seakeeping index is given as

SKIXN1i 1

1

2Verti Verti 1Vi 1Vi

whereVertrepresents the vertical calculation at each ship speed (V)

using the heave (Hrms), pitch (frms) and heave acceleration ( Hrms):

Vert Hrms Hrms L

2sinfrms

As for the first objective, the optimization for the second

objectivef2x!

is represented as follows:

opt f2x!

minSKIL,B,T,W

2.2.3. Objective 3stability performance index

Stability is an area of ship research that is by itself too large to

treat in detail. It is a fundamental performance criterion that is

regulated by various ship classification societies such as the American

Bureau of Shipping (ABS) and Lloyds and must be part of the

evaluation of any concept design. A stability performance index is

used in the hull form optimization program that was developed by

Gammon and Yilmaz (2003) using design model parameters for

stability that had previously been modeled using regression-based

formulas fromGrubisic (2001)andYilmaz (1999). These parameters

take the form of stability constraints defined for the particular ship

design problem, given requirements from the International Maritime

0.000

0.010

0.020

0.030

0 0.30.1 0.2 0.5 0.60.4

Fn

Cw,Cr

MichellGammon

Experimental

Fig. 1. Comparison of Michell and Transom-modified wave resistance with

experimental result for ITU Fishing Boat ITU 148/1-B at a particular load case

(L.C.1).

M.A. Gammon / Ocean Engineering 38 (2011) 105410641056


4/11

Organization (IMO) codes on intact stability or other regulation

sources.

A single measure for the stability index in order to minimize

the number of design objectives was required in order to develop

a similar metric as used in other hull design problems such as for

sailing yachts given in Larrson and Eliasson (2000), but which

could still provide a general indication of stability performance.

The use of the stability index based on a single stability char-

acteristic such as either the area under the GZ curve or the

vanishing angle can be erroneous as these single measurements

may be the same for different hulls. As the objective is to compare

different hulls then the stability index should have the ability to

differentiate between different hulls. A stability index that uses

multiple stability characteristics provides a better assessment for

the purpose of evaluating which hulls should be considered as

more optimal, when considering multiple objectives.

As a result the use of both the GM as a constraint according to

regulations and also a GZ curve is utilized as depicted in Fig. 3.

The positive area under the GZ curve up to the vanishing angle fngives a good measure of the kinetic energy that can be absorbed

by the hull. The angle at which maximum GZ occurs, fm, is an

indication of the angle after which the hull may have a tendency

to capsize as a result of a diminishing GZ.The hydrostatics are calculated for each hull form and the GZ

curve is used to generate a stability index as follows:

STIX fmRfv

0 GZfdf

This is taken as the area under the GZ curve up to the

vanishing angle multiplied by the angle at which maximum GZ

occurs. The resulting stability index is indicative of the overall

stability of the hull form, but does not preclude other stability

requirements. For example, additional constraints to limit stabi-

lity in order to avoid unwanted stiffness in the optimal results

could be used, though the current study only used a constraint

based on minimum GM requirements. For the third objective

f3x!

, the optimization is then represented as

opt f3x

!

maxSTIXL,

B,

T,

W

3. Genetic algorithm approach

Multi-objective problems exist in a wide range of practical

applications. Though other methods such as weighted averaging

techniques can be used, multiple objective problems can be

treated by the determination of the Pareto Front, in which no

solution is dominated by another in one or more performance

criteria as described by Gen and Cheng, (2000). Genetic Algo-

rithms are stochastic search and optimization techniques that

have the following five basic components:

A genetic representation of solutions to the problem; A way to create an initial population of solutions; An evaluation function rating solutions in terms of their

fitness;

Genetic operators that alter genetic composition of offspringduring reproduction; and

Values for parameters of Genetic Algorithms.

For the ship designer, finding solutions all along the Pareto

Front using these techniques raises the problem of choosing the

near-optimal compromise solutions, from which some will have

to be considered as more favorable as a compromise than others.

Most often, the choice of a compromise solution is left to the

designer. The need to automate this approach or at least provide

some assistance in achieving a compromise or near-optimal

solution has been a significant driver in the development of the

current optimization methodology.

For this study investigation into a particular MOGA was used

to address the multiple objective issues by automatically deter-

mining a compromise solution. The purpose of generating this

MOGA solver was alluded to earlier, that is, the problem facing

the designer is not, conversely, the search for all solutions from

the entire Pareto Front, which is usually the only optimal strategy

available in multi-objective problems. While aggregation or other

preferential and interactive techniques are used, the goal of this

study was to achieve some level of automation, i.e. to be able to

come up with a few compromise solutions, which could then be

examined by the design team.

3.1. Multi-Objective Genetic Algorithm (MOGA)

The following was developed in order to address some of these

specific issues. The canonical Genetic Algorithm by Goldberg

(1989)is modified as shown inFig. 4 by treating each objective

sequentially. For each objective the population is evaluated

separately, and the genetic operations applied after each evalua-

tion to generate the next population. The current optimum, if

there is one, is returned at each evaluation. In some ways this

approach is similar to the VEGA approach presented by Schaffer

(1985) where different subpopulations are kept separate for a

number of generations, and then allowed to mix. That method

allowed the population to approach a compromise solution that

DWL

HEAVE

Wave

Total Vertical MotionHEAVE

PITCH

PITCH

Fig. 2. Pitch and heave motion combined into total vertical motion.

GZ [m]

GM [m]

m 1 rad

GZmax

v

Fig. 3. GZ curve with stability index elements.



5/11

would perform well in more than one objectives. Unlike VEGA,

the proposed methodology selects parents that are based only oneobjective. The next objective in the sequence is evaluated with

the population generated from parents that performed well from

the previous objective. The treatment of the multi-objective

problem is reduced to single objectives in sequence, similar to a

gradient method in which each functions evaluation leads to a

determination of the direction of search. The relative importance

of which objective is used was found to be immaterial, as long as

the requisite number of iterations, of a minimum of approxi-

mately 10 generations, was used. However, this could vary with

the design problem and only the specific design problem here is

discussed. Further research in the generic application of this

method would be required. It should be noted that the require-

ment to have a sufficient population size, as well as a minimum

number of generations, means that the efficiency of the genetic

algorithm is quite subject to the degree of processing required to

evaluate each objective. Furthermore, the accuracy of the resultsis also subject to the individual solutions provided by the

functional evaluations of each objective.

3.2. Hull modeling using chromosomes

In order to be able to use evolutionary algorithms for hull form

optimization, it is necessary to develop a scheme to map the

problem into a format that can be utilized by the algorithm. The

parameters of the problem need to be defined. In every applica-

tion of an GA, the problem of mapping the parameters for

candidate solutions follows from the development of the Genetic

Algorithm. As stated by Gen and Cheng (2000), encoding the

solutions may require further development of heuristics to

manage the solution properties. For the first part of the hull form

Fig. 4. Multi-Objective Genetic Algorithm approach.



6/11

model the principal parameters are considered. Given the length,

beam and draft the basic dimensions of the hull are defined. Gen

and Cheng (2000)show how the accuracy and the upper and the

lower limits are defined for a single chromosome. Using the

following representation for the domain [aj,bj] for each variablexj:

2mj 1objaj 103r2mj 11

where the accuracy of 0.001 represented by the range fromajtobj

is multiplied by 103

to move the decimal point by the requirednumber of digits. The power mj then represents the number of

bits required in the chromosome. The mapping of each variable is

obtained by

xj aj dchrbjaj

2mj 11

wheredchris the decimal value between 0.0 and 1.0 determined

by the chromosome.

The parameters for the principal parameters of the hull are put

into a format for the GA. The length, beam and draft can be

described by a binary representation where the limits above are

used to determine binary values. Using the equation above to

determine the number of bits required for the ranges assumed for

the length, beam and draft and a decimal accuracy of 0.001 gives

the following, for an example of length limitation between 10 and

30 m, a breadth limitation between 3 and 5 m, and a draft

limitation between 1 and 3 m:

Length: 2mj1o3010 103r2mj 1,m1 15

Beam: 2mj 1o53 103r2mj 1,m2 11

Draft: 2mj 1o31 103r2mj 1,m3 11

To represent the hull offsets, the matrix Wis formed from m

stations and n waterlines such that

W

station 1,waterline 1 . . . stationm,waterline 1

^ . . . ^

station 1,waterlinen . . . stationm,waterlinen

0B@

1CA

Recombination is approached by choosing a random point inthe matrix and in the string representing only the hull offset at

that position. The recombination can be done in several ways,

however in keeping with the GA methodology; the matrices are

recombined following the point in the offset, swapping the

remaining row after the offset point and the remaining column

below the offset point.

While it is simple to use the offsets directly in the chromo-

some, in order to create hulls that are at least somewhat fair in

shape, without compromising on the use of offsets versus math-

ematical hull shapes, a method was adopted to use both iterative

B-Spline surfaces as described in Gerald and Wheatley (1999),

and a representation of the offsets using offset intervals. The

method transforms the offsets into an array of offset intervals,

with the premise being that a station can be drafted using eachneighbor. The matrix Wis then transformed from the offsets at m

stations and n waterlines into differences between offsets. Using

yij as an individual element in the array of offsets

yij 1yij Dy w ij

where Dy is the difference between adjacent offsets; wij is the

chromosome representation of next change in offset and

wij wl wuwldchr

wherewl is the lower limit for difference; wuthe upper limit for

difference;dchrthe decimal value between 0.0 and 1.0 determined

by chromosome.

It should be noted that while for convenience the hull was

modeled in terms of offsets, so that a table of offsets could be

automatically generated, given the fact that a B-spline surface

was in fact used for modeling of the hull, a more direct and

accurate interpretation of the hull surface could have been

achieved using the control points of the B-spline surface directly

in the optimization, rather than the use of varying hull offsets, as

one of the input parameters sets that were varied during the

optimization.

4. Fishing vessel optimization

Fishing vessels have typically developed from what were

historically small inshore fishing vessels that gradually evolved

into larger vessels, as depicted inFig. 5. Possibly as a result of this

historical evolution, Turkish fishing vessels often have a wide

high beam and low depth, as well as low draft as described by

Alkan (2004), and for the fishing vessels that were the focus of the

study, this could result in the possibility of reduced large angle

stability and higher block coefficients, that as one detrimental

factor can lead to higher resistance. It is the authors observation

that their evolution from small craft that was built and hauled up

on shore has resulted in shallow draft and broad beam. Hull forms

for small boats originally built up to 10 m in length have been

scaled up to vessels as large as 60 m in length for commercial

fishing. Scaling the hull form has provided large working areas for

the decks and shallow draft, but this has not always proven

advantageous in terms of the resistance, stability and seakeeping

characteristics.

The problem formulation begins with the requirement to

satisfy some particular design characteristics, in this case the

owners requirements for a fishing boat hull. The fishing boat can

be considered a difficult design problem for optimization because

it is a small craft relative to ordinary cargo vessels, and require-

ments such as the working conditions on the deck are critical for

safety concerns. The fishing boat example uses a number of

factors representing the design criteria and the owners require-

ments that are given next.

4.1. Fishing boat design characteristics

The resistance, seakeeping and stability evaluations all have a

large impact on the design. For fishing boats, stability is a primary

concern and regulations concerning stability are dictated by

Fig. 5. Typical Turkish fishing trawler 49 m in length (http://www.maritimesales.

com/EU10.htm).

http://www.maritimesales.com/EU10.htmhttp://www.maritimesales.com/EU10.htmhttp://www.maritimesales.com/EU10.htmhttp://www.maritimesales.com/EU10.htm


7/11

regulation societies. As an example in this study, a typical GM

requirement is assumed of 0.40 m. For prediction of the GM

pertaining to stability an empirically derived formula for fishing

boat models can be used (Grubisic, 2001).

The GM formula is given as follows using breadth (B) and

depth (D):

GMmax 0:163e0:742B=D

The minimum depth (Dmin) that can be used is a function of thelength (L):

Dmin 0:266L0:77

In addition to the stability requirement, an owners require-

ment is assumed by specifying a fish-hold volume as used by

Grubisic (2001). Fish hold volume (VFH) is largely governed by the

size of the vessel, and is directly related to the economic value of

the bull. For comparison, a design value is assumed as an example

for a fish hold volume of 95.2 m3 as in the study by Grubisic

(2001). In that model the fish hold is obtained by the following

relation by first obtaining a fish hold length (LFH). This is

calculated using a correlation formula with respect to the length

of the waterline (Lwl):

LFH 0:157L1:26wl

Fish hold volume is then obtained by

VFH 0:38 LFHB D1:08

One parameter that is not included specifically is the depth of

the model. For our purpose, as we are mostly concerned with the

underwater portion of the hull, the depth is simply modeled as a

function of draft (T) according to the following relation:

D 1:27 T

In addition to the minimum fish hold requirement and the GM

requirement, a desired volumetric displacement can be used,

which can also be considered as an owners requirement. An

additional design requirement, in the form of a constraint, was

imposed for a waterplane coefficient of 0.80. This represents a

secondary hull form coefficient, rather than a principal parameter,

which is used as a means of maintaining a workable deck area,

but not directly to influence the hull form. If other methods for

ensuring deck area are used as a constraint then this waterplane

coefficient restriction does not have to be used.

The fishing boat example introduced some restrictions on the

hull for the length, beam and draft.Grubisic (2001)used a length

restriction between 10 and 30 m. In all of the runs in this study, it

was shown that the length tends towards the maximum limit.

Unless the optimization penalizes length, possibly due to cost or

another restriction, which could be based on restrictions accord-

ing to the type of fishing as imposed by quotas, or port restric-

tions, as well as by the cost of the vessel, the tendency is for the

length to move towards the maximum allowable length. Hence,should a shorter vessel be required then a limit must be imposed

by the maximum allowable length.

It should be noted that cost has not been included in this

study, though this will an overriding consideration in any real

optimization problem. For our study, reliable costing data was

unobtainable for fishing boat construction, as most of the data is

commercial and propriety information. Also in the current meth-

odology, imposing arbitrary limits on the hull form using known

coefficients is replaced by a search of the design space driven by

performance indices. Since these secondary coefficients are not

used it is prudent to limit the main dimensions so as to

investigate a reasonable design space. In addition to restricting

the beam, limits are also imposed on the draft. Besides the design

requirements, for the example fishing vessel used in this study

the following conditions and limits are imposed, and are sum-

marized inTable 1along with the other criteria.

In order to include these constraints in the optimization

process, the penalty method is utilized. The penalty is found per

candidate using a method byGen and Cheng (2000)according to

the two main design requirements for fish hold volume and GM:

penalty 11

2

DVFHDVFHmax

DGMDGMmax

whereDVFHis the deviation of the fish hold from the required and

DGMis the deviation of GM from the required. For example, for the

fish hold volume:

if rVFH RequiredVFHVFH

DVFHrVFH, ifrVFH40

0, ifrVFHo0

( )

The maximum and minimum are from among the population

in each generation. The penalty times the performance objective

gives the fitness function for the hull for the particular objective.

For example, for RCI, the fitness function is then given by

Fitness 1 RCIRCIminRCImaxRCImin

penalty

As the previous outline shows, each objective can be tested

accordingly with each of the design requirements included as a

constraint. Alternatively if there is the possibility of maximizing

or minimizing a particular design requirement, then these can be

included as objectives. However additional objectives take addi-

tional computation time whereas using constraints take almost

no additional time at all, therefore, where possible, the use of

constraints should be considered rather than objectives. This doesnot preclude the fact that design requirements could be modeled

as objectives.

In some cases the displacement was considered as a require-

ment. It is modeled in a similar way as the previous constraints,

but because of the importance of displacement as a design

requirement, it was given a larger priority. Taking it as a separate

term rather than averaging it together with other constraints

resulted in the following formulation:

penalty DrDrmax

11

2

DVFHDVFHmax

DGMDGMmax

The deviation is calculated in a similar manner for the fish hold

volume or GM requirement and the penalty is again used as

multiplication factor of the fitness for each objective.

Table 1

Fishing boat design characteristics.

Characteristic Requirement Formulati on

GM Minimum

GM0.40GMmax 0:163e0

:742B=D

Depth As relates to VFH Dmin 0:266L0:77

Fish hold volume (VFH) VFH95.2 m3

VFH 0:38LFHB D1:08

Fish hol d length As rel ated to VFH LFH 0:157L1:26wl

Depth Related to draft (T) D1.27T

Waterplane coefficient

(Cwpl)

Cwpl0.80 Cwplwaterplane area/(L B)

Length (L) 10.0rLr30.0 m Change in parameter

example 2

Beam (B) 3.0rBr5.0 m Change in parameter

example 2

Draft (T) 1.0rTr3.0 m Change in parameter

example 2



8/11

4.2. Exploration of genetic algorithm functionality

Because using a Genetic Algorithm is a stochastic and heuristic

approach, it is useful to conduct some initial investigations that

determine to what extent the algorithm can be used to change

parameters and produce useful results. ITU fishing hull series

have been used mainly to compare the optimal hulls derived with

the well-known resistance characteristics of the original series. As

a series, the different hull forms are similar enough in applicationto test the methodology for the development of an optimal fishing

boat. Since none of the hulls are exactly alike, they represent a

good series of offsets to use for the optimization.

Using the ITU 1B hull for comparison, the optimization was

first conducted at a single of Froude number (Fn0.28176) to

examine the feasibility of the optimization. As shown in Fig. 6,

length, beam and draft, as well as fish hold volume and displaced

volume, vary for the best or increasingly optimal hull forms. The

optimal stability characteristic is shown in the GM value given in

Fig. 7is near the required value.

In addition to the optimization of a single hull some investiga-

tion into the GA aspect was conducted. A comparison of the

number of hulls per generation indicates that while according to

GA practice 100 hulls would yield superior results, even 20 hulls

can provide good results as shown in Fig. 8.

4.3. ITU fishing boat with fixed principal parameters

The ITU fishing boat (ITU 148/1B) is optimized with the given

constraints on the length, beam, and draft. It is convenient for

comparison to look at the resulting hull form if the principal

parameters remain constant and the displacement is set as a target

objective in the form of a constraint, as previously described. In this

case the only change is the hull form and in the offsets. As the

displacement is set as a constraint, the fish hold constraint can

actually be removed. Two iterations of the B-spline surface are used

to obtain a fair hull, and the maximum variation in the offsets

is 790% of each offset interval.Fig. 9shows the change in the hull

form in which the principal dimensions are fixed for ITU 148/1B usingan initial population of 20 hull variants that are optimized over 100

generations. The last optimal hull (in solid lines) is overlaid with theoriginal hull (in dashed lines) inFig. 9. The changes in the hull form

are not very great, as expected, though some difference in the sections

can be seen. The extreme ends of the hull appear to have widened

whereas the mid-ship sections, though nearly the same, have

narrowed.

The waterline except at the mid-section shows a tendency to

narrow. This is probably in response to the objective to minimize

the resistance, which is subsequently made up in the rest of the

body by having fuller sections elsewhere. However, since the

optimization is not solely a function of resistance, this observa-

tion is made on the basis of only one performance index, and may

in fact be subject to other performance factors.

The performance indices for resistance, seakeeping and stabi-

lity are plotted inFig. 10to show how the results evolve over the

0

30

60

90

120

150

L(m)V,F

HV(m3)

Generations

Fish Hold VolumeVolumeLength

1 3 5 6 9 10 12 15 16 21 37 38 40 48 49

Fig. 6. Volume, length and fish hold volume for increasing optimal hulls.

0

1

2

3

4

5

6

1 21 23

GM,B,T

(m)

Generations

Beam

Draft

GM

3 5 7 9 11 13 15 17 19 25 27 29

Fig. 7. Maximum GM with beam and draft for increasingly optimal hull forms.

0.00140.00145

0.0015

0.00155

0.0016

0.00165

0.0017

0.00175

0.0018

0

ResistanceIndex

Generations

20 Hulls

50 Hulls

100 Hulls

20 40 60 80 100

Fig. 8. Comparison of number of hulls for each generation using ITU 1B.

Fig. 9. ITU 148/1-B original and modified hull with fixed principal parameters.

0 10 20 30 40 50 60

Generation

0.0070

0.0072

4.3000

4.6000

0.0500

0.0520

Performance for ITU 1B with Fixed Dimensions

RCI

SKI

STIX

Fig. 10. Stability, Seakeeping and resistance index performance by generation.



9/11

different generations. The stability index at the top graph starts

low and increases rapidly, over 60 generations. The seakeeping

index also starts off high and is lowered over subsequent genera-

tions as seakeeping motion is minimized. Finally, the resistance

index also starts off high and lowers, quite quickly, becoming

more or less the same after 10 generations and is maintained over

the course of the next 60 generations. After 60 generations, no

further Pareto Optimal hulls were found.

Comparing the actual performance from the evolved hull withthe original ITU 148/1-B hull, for resistance, the total and wave

resistance coefficients are shown in Fig. 11. The wave resistance

at higher Froude numbers is lower, from 3.85 102 to

3.28 102 at a Froude number of 0.5, which corresponds to a

reduction of 14.8% of the wave resistance.

The pitch is somewhat larger at lower Froude numbers but is

reduced at higher Froude numbers, as seen in Fig. 12. The heave

as shown in Fig. 13 is lower at smaller Froude numbers and is

coincidental at larger Froude numbers. The overall result is to

lower the seakeeping index.

Though the stability index increased, these improvements in

resistance and seakeeping come with a nominal cost in the GZ

stability from the original hull form, as dynamic stability as given

by the area under the GZ curve, shown in Fig. 14, is reduced. The

stability can vary and a different optimal form having good

resistance and seakeeping, as well as stability characteristics,

can also be chosen. For the ITU 1B example the GM of 1.111 m

was used for the original hull form while a GM of 1.057 m was

obtained for the modified hull. The KM, which is independent of

KG, is 2.749 m and 2.65 m for the original and modified hulls,

respectively.

4.4. ITU fishing boat with change in principal parameters

If the principal parameters are allowed to vary according to the

limits described previously, some quite different and unusual

results occur. Using a fish hold volume requirement of 95.2 m3, as

in the example by Grubisic (2001), and re-running the ITU 148/1-B

example yields the optimal hull as shown in Fig. 15. No constraint is

set for the actual displaced volume in this particular run. The beam in

this case is quite wide and the draft quite shallow. The limits in the

main dimensions explored a space with a minimum draft of 1.5 m, a

maximum beam of 8 m and a maximum length of 30 m. In trying to

Resistance Coefficients for ITU 1B given Fixed Dimensions

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0

Froude Number

ResistanceCoefficients

Original Wave resistanceModified Wave resistanceOriginal TotalModified total

0.1 0.2 0.3 0.4 0.5 0.6

Fig. 11. ITU 148/1-B original and modified total and wave resistance.

ITU 1B Original and Modified Pitch

0

1

2

3

4

5

6

7

8

0.60.50.40.30

Froude Number

Pitch

Original Pitch

Modified Pitch

0.1 0.2

Fig. 12. ITU 148/1-B original and modified pitch motion.

ITU 1B Heave Motion for Original and Modified

given Fixed Dimensions

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6

Froude Number

Heave

Original Heave

Modified Heave

Fig. 13. ITU 148/1-B original and modified heave motion.

GZ Curve fro ITU 1b Original and Modified

with Fixed Dimensions

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 20 30 40 50 60 70

Heel (deg)

GZ(m)

OriginalModified

10

Fig. 14. GZ curve for original and modified ITU 148/1-B given fixed dimensions.

Fig. 15. ITU 148/1-B original and evolved hull form with change in principal

parameters.



10/11

achieve minimum resistance the hull is evolving towards maximum

length, while for stability the hull tends towards the maximum beam.

The shallow draft is driven by the minimization of resistance given

that there is no restriction on displacement. The displacement

achieved in this case was only 110 m3. However much that this wide

flat hull is notable in Turkish fishing fleets, the results may be

impractical.

As in the previous case, only 100 generations with a popula-

tion of 20 variants was run. Two iterations of the B-spline surface

are used to obtain a smooth hull and 790% variation in theoffsets interval is allowed. The body plan shown inFig. 15for the

optimal hull shows a larger beam to achieve a larger vessel to

match the requirement for the fish hold volume. This results in a

vessel with more displacement but, interestingly, a somewhat

shallower hull.

Resistance index trends for optimal RCI versus generation is

shown in Fig. 16. Large improvements in the RCI is seen in the

first 10 generations, with nominal changes after 10 generations

and no change after 70 generations. Similarly, the SKI perfor-

mance by generation is shown inFig. 17and indicates improve-

ments in the SKI up to 65 generations. The stability index is

shown inFig. 18and also shows an increase in stability index.

Fig. 19shows one view into the performance for resistance and

seakeeping as they tend towards their respective minimums, with

the last Pareto Optimal 67th generation data point plotted

indicating how the optimization is working.

5. Conclusions

A method for conducting optimization of hull forms was

applied to Turkish fishing vessels with the intent of improving

the resistance, seakeeping and stability performance for a given

set of constraints. A fishing boat hull is used as an example of how

hull form optimization can be accomplished using a Multi-

Objective Genetic Algorithm (MOGA). The particular MOGA

developed during this study allows automatic selection of a fewPareto Optimal results for examination by the designers while

searching the complete Pareto Front. The optimization uses the

three performance indices for resistance, seakeeping and stability

to modify the hull shape and obtain optimal hull offsets, as well as

optimal values for the principal parameters of length, beam and

draft. The modification of the Istanbul Technical University (ITU)

148/1-B fishing boat series hull was presented by first fixing the

principal parameters and allowing the hull offsets to change, and

secondly by simultaneously allowing variation of both the princi-

pal parameters and the hull offsets. Improvements in all three

objectives were found. For further research the methodology can

be modified to allow for the addition of other performance

objectives, such as cost or specific mission objectives, as well as

the use of enhanced performance prediction solvers. In addition,

Fig. 16. RCI optimal performance by generation for ITU 148/1-B with change in

principal parameters.

Fig. 17. SKI optimal performance by generation for ITU 148/1-B with change inprincipal parameters.

Fig. 18. STIX optimal performance by generation for ITU 148/1-B with change in

principal parameters.

Fig. 19. SKI versus RCI optimal for ITU148/1-B with change in principal parameters.



11/11

one or more hulls could be evaluated by experiment to validate

the results of using this particular optimization approach.

References

Alkan, A.D., 2004. The Turkish fishing fleet: technical features and designevaluations. Brodogradnja 52 (1), 2129.

Coello Coello, C.A., 1996. An Empirical Study of Evolutionary Techniques forMultiobjective Optimization in Engineering Design. Ph.D. Thesis. Tulane

University, New Orleans, Louisiana.Danisman, D.B., Goren, O., Insel, M., Atlar, M., 2001. An optimization study for the

bow form of high speed displacement catamarans. Marine Technology 38 (2).Day, A.H., Doctors, L.J., 1997. Resistance optimization of displacement vessels on

the basis of principal parameters. Journal of Ship Research 48 (4), 249259.Dejhalla, R., Mrsa, Z., Vukovic, S., 2002. A genetic algorithm approach to minimum

ship wave resistance problem. Marine Technology 39 (3), 187195.Gammon, M.A., 1990. Modifying Thin-Ship Wave Resistance Computation for

Transom Stern Ships. Master of Applied Science Thesis. Dalhousie University,Halifax, Canada.

Gammon, M.A., Alkan, A.D., 2001. A resistance study of low L/B vessels withTransoms. In: Proceedings of the Techniques and Technology of FishingVessels Conference, Ancona, Italy.

Gammon, M.A., 2004. Ship Hull Form Optimization by Evolutionary Algorithm.Ph.D. Thesis. Yildiz Technical University, Istanbul, Turkey.

Gammon, M.A., Yilmaz, H., 2003. Stability evaluation for fishing boat hulloptimization. In: Proceedings of the Techniques and Technology of FishingVessels Conference, Ancona, Italy.

Gen, M., Cheng, R., 2000. Genetic Algorithms and Engineering Optimization.Wiley-Interscience, New York.

Gerald, G.F., Wheatley, P.O., 1999. Applied Numerical Analysis, 6th editionAddison-Wesley Longman, Reading, Massachusetts.

Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization and MachineLearning. Addison-Wesley Longman, Reading, Massachusetts.

Grubisic, I., 2001. Improvement of the fishing vessel concept design model. In:Proceedings of the 7th Symposium on Techniques and Technology of FishingVessels, Ancona, Italy.

Kafal, K., S-aylan, O., S-alc, A., 1979. Development of hull forms of fishing boatssuitable for Turkish Waters (in Turkish). TUB_ITAK (The Scientific and Techno-

logical Research Council of Turkey), Project Number G-416, Istanbul, Turkey.Larrson, L., Eliasson, R., 2000. Principles of Yacht Design, London. Adlard Nautical.Maisonneuve, J.J., Harries, S., Marzi, J., Raven, H.C., Viviani, U., Piippo, H., 2003.

Towards optimal design of ship hull shapes. In: Proceedings of the 8thInternational Marine Design Conference, National Technical University ofAthens, Athens, vol. 2, pp. 3142.

Schaffer, J.D., 1985. Multiple objective optimization with vector evaluated geneticalgorithms. In: Genetic Algorithms and their Applications: Proceedings of the FirstInternational Conference on Genetic algorithms, Pittsburgh, PA, pp. 93100.

Yasukawa, H., 2000. Ship form improvement using genetic algorithm. ShipTechnology Research 47, 3544.

Yilmaz, H., 1999. Effect of form parameters on stability of fishing vessels. In:Proceedings of the 7th Symposium on Techniques and Technology in FishingVessels, Ancona, Italy.

Zaraphonitis, G., Papanikolaou, A., Mourkoyannis, D., 2003. Hull form optimizationof high speed vessels with respect to wash and powering. In: Proceedings ofthe 8th International Marine Design Conference, vol. 2. National TechnicalUniversity of Athens, Athens.


optimization of fishing vessel

Documents