Multi-objective optimization of oil tanker design

ORIGINAL ARTICLE

Multi-objective optimization of oil tanker design

Apostolos Papanikolaou • George Zaraphonitis •

Evangelos Boulougouris • Uwe Langbecker •

Sven Matho • Pierre Sames

Received: 12 November 2009 / Accepted: 26 June 2010 / Published online: 22 July 2010

� JASNAOE 2010

Abstract Parametric optimization was applied to a

double-hull AFRAMAX tanker design in order to reduce

oil-outflow probability and increase cargo carrying capac-

ity, and the results are presented here. A multi-criteria

optimization procedure was set up in modeFrontier� using

the cargo volume, the mean oil-outflow parameter and the

steel weight of the cargo block as the objective functions.

Calculations are based on a parametric geometric model of

the ship created in NAPA�, and on a structural model

created in POSEIDON�. Integration of the above software

packages leads to an automated optimization procedure

that provides improved feedback to the designer regarding

the trade-off between the various design parameters and

optimization criteria involved. The results obtained suggest

notable improvements in transport capacity and oil-outflow

performance for known, well-established yard designs. The

presented work derives from a joint industrial project

between Germanischer Lloyd (GL) and the Ship Design

Laboratory of the National Technical University of Athens

(NTUA-SDL), which continues the work done and coor-

dinated by NTUA-SDL within the SAFEDOR project on

the same subject.

Keywords Design optimization � Risk-based design �Genetic algorithms � Multi-criteria decision making �Accidental oil outflow

1 Background

1.1 Project outline

Following a series of catastrophic single-hull tanker acci-

dents, current IMO regulations (and long before that, US

OPA90) state that double-hull tanker designs are the only

acceptable solution for the safe carriage of oil in tanker

ships. According to current MARPOL regulations, the tank

arrangement of the cargo block of an oil tanker should be

properly designed to provide adequate protection against

accidental oil outflow, as expressed by the so-called mean

outflow parameter. The present paper outlines the risk-

based parametric optimization of a double-hull AFRA-

MAX tanker in order to achieve innovative designs with

increased cargo carrying capacities, reduced steel weights

and improved environmental protection.

The research presented here is based on the results of a

joint industrial project between Germanischer Lloyd (GL)

and the Ship Design Laboratory of the National Technical

University of Athens (NTUA-SDL). This work is a further

elaboration of an innovative risk-based oil tanker design

procedure that was initiated in the framework of the EU

project SAFEDOR. Building on the work presented earlier,

the integration of the structural design software POSEIDON

[1] into the multi-criteria optimization procedure allows the

realistic estimation of the steel weight of the alternative

designs, and the latest MARPOL regulations for accidental oil

outflow (applicable to all newbuildings after 1 January 2010)

have been implemented [2]. The fully automated optimiza-

tion procedure developed here provides improved feedback to

the designer regarding the trade-off between the various

design parameters and the optimization criteria involved.

The present study focuses on the optimization of the

arrangement of the cargo area of an AFRAMAX class

A. Papanikolaou (&) � G. Zaraphonitis � E. Boulougouris

Ship Design Laboratory, School of Naval Architecture

and Marine Engineering, National Technical University

of Athens, Athens, Greece

e-mail: [email protected]

U. Langbecker � S. Matho � P. Sames

Germanischer Lloyd AG, Hamburg, Germany

123

J Mar Sci Technol (2010) 15:359–373

DOI 10.1007/s00773-010-0097-7

tanker, with the aim being to identify the best-performing

designs in terms of both reduced accidental oil outflow and

improved economic competitiveness. However, the pro-

posed methodology can be extended to include additional

objectives or design aspects, such as the ship’s hull form

and internal arrangements, and can be easily extended to

other oil tanker classes.

1.2 Reference design

An existing AFRAMAX tanker was selected as the basic

reference design. Its main particulars and general arrange-

ment are presented in Table 1 and Fig. 1, respectively. It is

a typical modern AFRAMAX tanker with six tanks along

the cargo space and two cargo tanks across, already

adequately optimized by the shipbuilder.

1.3 Regulatory framework

Chapter 4 of MARPOL 73/78 [2], which specifies the

requirements for the arrangement of the cargo areas of oil

tankers constructed after 2010-01-01, was used as the

regulatory basis in the present work. In particular, the

following regulations were implemented:

• Regulation 18—requirements for the minimum capac-

ity of segregated ballast tanks (SBT)

• Regulation 19—requirements for the double-hull

arrangement

• Regulation 23—requirements for ‘‘accidental oil out-

flow,’’ along with the procedure for its calculation

• Regulation 27—criteria for intact stability

• Regulation 28—criteria for damage stability.

For crude oil tankers of C20,000 tonnes DWT and

product carriers of C30,000 tonnes DWT delivered after

1982-06-01, Regulation 18 requires a sufficient capacity of

segregated ballast tanks. Under ballast conditions, includ-

ing conditions consisting of lightweight plus segregated

ballast only, the ship’s draughts and trim should meet the

following requirements:

• Molded draught amidships, dm C 2.0 ? 0.02 L

• Trim by stern B0.015 L

• Draught aft (Taft) should always lead to full immersion

of the propeller(s).

For oil tankers of C5,000 tonnes deadweight delivered

on or after 1996-07-06, Regulation 19 requires ballast tanks

or spaces other than tanks carrying oil along their entire

cargo tank length to effectively protect the cargo space, and

these tanks or spaces must have the following minimum

dimensions:

• Wing tanks or spaces, w = min {0.5 ? DWT/20,000;

2.0 m} [1.0 m

• Double-bottom tanks or spaces, h = min {B/15;

2.0 m} [1.0 m.

It should be noted that the requirements of Reg. 19

regarding the minimum spacing of wing and double bottom

from the outer shell (2.0 m for AFRAMAX) are challenged

herein; namely, they are kept flexible during the optimi-

zation runs and set equal to a minimum of 1.7 m for

AFRAMAX-sized tankers.

Regulation 23 applies to oil tankers delivered on or

after 1 January 2010. For oil tankers of 5,000 tonnes DWT

and above, it sets the limits for the mean oil outflow

parameter (OM), along with the procedure for its calcula-

tion. For the vessel used in this particular study, with a

total volume of cargo oil \200,000 m3, an OM value not

exceeding 0.015 is required. The mean oil outflow

parameter is calculated independently for side damage and

bottom damage and then combined in nondimensionalized

form as follows:

OM ¼ 0:4OMS þ 0:6OMBð Þ=C; ð1Þ

where OMS and OMB are the mean outflows for the side

damage and bottom damage, respectively, and C is the total

volume of cargo oil in m3 for a 98% full tank. The mean

outflow due to bottom damage is calculated independently

for tide conditions of zero and minus 2.5 m, and averaged

as follows:

OMB ¼ 0:7OMBð0Þ þ 0:3OMBð2:5Þ: ð2Þ

The calculation of the mean outflows for side damage

and bottom damage is based on a probabilistic approach.

The side damage outflow is calculated by the following

formula:

Table 1 Main particulars of the reference design

Length, oa (m) 250.10

Length, bp (m) 239.00

Breadth, molded (m) 44.00

Depth, molded (main deck) (m) 21.00

Width of double skin sides (m) 2.50

Width of double skin bottom (m) 2.50

Draught scantling (m) 14.60

Deadweight, scantling draught (tonnes) 112,700

Cargo capacity (cbm) 127,271

Slops (cbm) 2,890

HFO (cbm) 3,380

DO (cbm) 260

Water ballast (cbm) 41,065

Peaks (cbm) 3,500

Classification Lloyds register

Propeller diameter (mm) 7,200

Number of cargo tanks (6 9 2) 12 plus 2 slop tanks

Cargo block length (m) 181.44

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OMS ¼ C3

Xn

1

PSðiÞOSðiÞ ðm3Þ; ð3Þ

where PS(i) is the probability of penetrating cargo tank

i through side damage, OS(i) is the corresponding outflow in

m3, while C3 is an appropriate coefficient. Accordingly, the

bottom damage outflow for either zero or minus 2.5 m tide

conditions is calculated by the following formula:

OMB ¼Xn

1

PBðiÞOBðiÞCDBðiÞ m3� �

: ð4Þ

In the above equation, CDB(i) accounts for the capture of

oil flowing out of a tank in the double bottom.

2 Design optimization

The main objective of this study was to improve the

accidental oil-outflow performance of the reference cargo

tank arrangement, while at the same time minimizing the

steel weight and maximizing the cargo capacity. Improving

the performance of a ship in terms of oil outflow, maxi-

mization of cargo capacity, and minimization of steel

weight are contradictory objectives; for example, the for-

mer requires an increased distance of the cargo space from

the outer shell, resulting in a reduction in cargo tank vol-

ume; also, a reduction in the mean outflow parameter can

be achieved with more subdivision, by decreasing the

average size of each cargo tank, and at the same time

increasing the steel weight (with a corresponding increase

in construction cost and reduction in payload). Therefore,

to optimally achieve these contradictory objectives, a for-

mal multi-objective optimization procedure was developed

and applied.

2.1 Optimization framework

A generic optimization framework for a system S incorpo-

rates the following main elements (see Fig. 2):

• Input EI

• Design variables D

• Design parameters P

• Merit functions L

• Constraints G

• Output EO.

Fig. 1 General arrangement of the reference design

Fig. 2 Generic optimization framework

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In the context of the present work, the difference

between the design parameters and the design variables is

that the former are kept constant during an optimization

study, while the latter are systematically varied to facilitate

the efficient exploration of the design space and to obtain

the optimum solution(s).

At the core of the developed optimization framework

there is a ‘‘parametric design tool,’’ developed within the

well-known ship design software NAPA� [3]. It consists of

a set of macros, developed in NAPA Basic, that facilitate

the fully automatic generation of the detailed layout of the

cargo block of a vessel, based on the values of a series of

design parameters and design variables. The design pool is

then created by systematically varying the design variables

while using predefined (user-selected) values for the design

parameters. This procedure evaluates the fulfillment of a

set of constraints, while a set of objectives are optimized at

the same time. This approach is holistic in nature and

allows the integration of as many objective functions and

constraints as needed for the design problem at hand [4].

The generic optimization framework developed by

NTUA-SDL was applied previously to a variety of prob-

lems, including the optimization of the watertight subdi-

vision of RoRo passenger ships [5], and the external

hullform optimization of high-speed ships [6]. This generic

procedure was adapted to the present optimization problem

by adding methods and the corresponding software tools

for the structural design of the steel structure of the ship

and for the probabilistic assessment of oil-outflow

performance.

2.2 Multi-objective optimization

Ship design is a typical optimization problem involving

multiple and frequently contradictory objective functions

and constraints. The easiest way to address such a multi-

objective problem would be to combine the objective

functions into one, assuming that the relative weights and

relationships between the objectives are known. In most

cases, however, these weights and relationships are

unknown, and there is little knowledge regarding the space

of feasible solutions. Hence, a truly multi-objective meth-

odology is required, leading to a set of ‘‘best designs;’’ in

other words, designs in which no one objective can be

improved without sacrificing the performance of another

objective. This set of ‘‘best designs’’ is known as the Pareto

set. It is represented graphically as the Pareto frontier.

For the present problem, multi-objective genetic algo-

rithms (GA) were selected as the most suitable optimiza-

tion method [7]. Genetic algorithms are stochastic,

nonlinear optimization methods that apply the principles of

biological evolution [8]. In particular, they utilize popula-

tions of solutions and apply selection, reproduction and

mutation methods, in contrast to more traditional optimi-

zation methods which use gradient information to move

between (successively better) points in solution space. This

makes them uniquely adaptive to multi-objective problems

such as finding Pareto frontiers.

With the Pareto set of nondominated designs in hand,

the designer can select an optimal solution according to

his preferences. This can be done in a number of ways,

such as:

• Using a utility function to rank the different designs

• Using scatter 2D and 3D diagrams to visually identify

the more attractive designs, comparing them on the

basis of the designer’s preferred criteria and experi-

ence-based selection

• Using other visual tools (parallel plots, histograms,

frequency plots, Student plots, etc.), and deciding

according to the designer’s experience.

2.3 Implemented optimization procedure

The optimization procedure applied herein is show sche-

matically in Fig. 3. It integrates the following software

packages:

• NAPA� [3], a naval architectural software package

• POSEIDON� [1], a structural design and analysis

software package developed by GL

• modeFrontier� [9], a general optimization software

package.

Within NAPA�, a set of macros were developed in

order to:

• Create the parametric 3D model of the hullform and

internal compartmentation

• Calculate loading conditions

• Perform intact and damage stability calculations

Fig. 3 Implemented optimization procedure

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• Calculate the accidental oil outflow

• Prepare the necessary geometric data for the software

tools (POSEIDON) that perform the structural design.

POSEIDON� implements GL’s latest rules for classi-

fying a ship’s structure (Edition 2008, [10]). It allows the

automatic calculation of the scantlings for all structural

components based on rule requirements for the particular

vessel parameters, class notation, global bending, cargo

loads, and external sea pressure. Note that an additional

module was developed/implemented to create POSEI-

DON� models from a set of parameters. The same set of

parameters was used to define compartments in NAPA�

and to create the structural model in POSEIDON�, hence

ensuring consistency between the two models.

modeFRONTIER� is a general-purpose optimization

scheduler. It provides several optimization algorithms:

genetic algorithms, conjugate gradient method, quasi-

Newton method, sequential quadratic programming, sim-

plex, etc. The various optional algorithms can be com-

bined, such as genetic algorithms for global search and

another algorithm for local search (refinement). Software

modules running on different platforms can be integrated

via a network.

2.4 Design variables

The parametric definition of the layout and structural

arrangement of the cargo area of a ship requires a large

number of parameters, controlling the details of the

arrangement and of the various structural components. In

the present study, some of these parameters were kept

constant during each optimization run, while others were

treated as free variables and their values were selected (in a

predefined range) by the optimization scheduler. More

details on the design parameters employed and variables

are given in the following section describing the geometric

model.

2.5 Objectives

The following objectives were used:

• Maximization of the cargo capacity

• Minimization of the accidental oil-outflow parameter

according to MARPOL Annex I Regulation 23

• Minimization of the structural steel weight in the cargo

area while fulfilling the requirements of GL rules for

the construction of double-hull oil tankers (non-CSR).1

2.6 Constraints

The following constraints were employed:

• MARPOL Regulation 18 for mean draft, trim, propeller

immersion, etc.

• MARPOL Regulation 23, except for the minimum

spacing of the wings and double bottom, which was set

here for AFRAMAX tankers equal to 1.7 m2

• MARPOL Regulation 27—requirements for intact

stability

• MARPOL Regulation 28—requirements for damage

stability.

3 Geometric model

The geometry of the reference hullform was modeled in

NAPA using available offsets (see Fig. 4). A series of

NAPA macros were developed to parametrically define the

internal compartmentation of the design alternatives. In the

geometric modeling, the external hullform and the length

and position of the cargo block area were kept fixed.

Typical examples of the variety of configurations that

can be parametrically defined are illustrated in Figs. 5, 6, 7

and 8. The details of the internal layout and the structural

arrangement of the ship along the cargo area are controlled

by a series of 41 design parameters. The most important of

these can be summarized as follows:

• Compartmentations with one (central) or two longitu-

dinal bulkheads over the entire cargo block can be

Fig. 4 Hullform modeled in NAPA

1 An optimization with respect to CSR is planned for presentation in

the future.

2 The minimum spacing according to MARPOL is 2.0 m; however in

the research presented here, this semi-empirical MARPOL limit was

not considered a hard constraint, but challenged in the framework of a

risk-based design/regulation and approval procedure, as promoted by

the project SAFEDOR [11, 12].

J Mar Sci Technol (2010) 15:359–373 363

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developed. The number of longitudinal bulkheads is

controlled by the corresponding parameter.

• The number of transverse bulkheads in the cargo area

can be controlled by the user by assigning the value of

the corresponding parameter.

• A set of parameters is used to define the position of the

transverse bulkheads in the cargo area.

• A set of parameters is used to define the double bottom

height within each main transverse zone.

• An additional set of parameters is used to define the

inner hull clearance within each main transverse zone.

• A set of parameters is introduced to control the type of

inner hull and double bottom. Depending on the values

of the corresponding parameters, the side of the inner

hull and the double bottom may be:

• Parallel to the center plane and bottom

• Inclined (see Fig. 6)

• Stepped (see Fig. 7).

• The transverse and longitudinal bulkheads can be either

flat or corrugated. The type of bulkhead is controlled by

the corresponding design parameter.

• A set of parameters is used to control the details of the

geometry of the hopper plates of the inner hull.

• In the case of two longitudinal bulkheads, the width of

the central tank as a percentage of the ship’s breadth is

specified by the corresponding design parameter.

• A set of parameters is introduced to control the details

of the geometries of the upper and lower stools in the

case of corrugated bulkheads.

• A set of parameters is used to define the various

structural details, such as the number and positions of

the stringer decks, the stiffener spacing on the shell,

inner bottom, strength deck, transverse members, and

longitudinal bulkheads, etc.

For practical purposes, and considering the importance

of the various design parameters, it was decided to select a

subset of them and treat them as free variables, while the

others were assigned constant values. The values of the free

variables (herein called the ‘‘design variables’’) were sys-

tematically varied by the optimization scheduler while

searching for the optimal solutions; the most important

design variables are those that define:

• The position of the transverse bulkheads in the cargo

area

• The double bottom height within each main transverse

zone

• The inner hull clearance within each main transverse

zone

• The number of longitudinal bulkheads (either one or

two)

Fig. 5 Arrangement with 6 9 2 tanks, corrugated bulkheads, con-

stant double-bottom height, and inner side clearance

Fig. 6 Arrangement with inclined double bottom and constant inner-

side clearance

Fig. 7 Arrangement with stepped double bottom and inner hull

Fig. 8 Arrangements of the reference design

364 J Mar Sci Technol (2010) 15:359–373

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• The width of the central tank as a percentage of the

ship’s breadth in the case of two longitudinal bulkheads

• The distance between transverse frames

• The distance between longitudinal stiffeners

• The inclination of the hopper plate that connects the

double bottom with the inner hull.

For example, for the typical case of a vessel with 6 9 2

or 6 9 3 tanks (i.e., with five transverse bulkheads inside

the cargo block and one or two longitudinal bulkheads),

this results in a total of 26–27 design variables.

4 Structural model

4.1 Typical AFRAMAX structure

AFRAMAX-sized oil tankers (80,000 tonnes DWT to

119,999 tonnes DWT) are commonly longitudinally

framed ships over the full length of the cargo block. They

usually include a large number of continuous, longitudinal,

closely spaced stiffeners and a small number of web frames

that are spaced more sparsely. A centerline bulkhead sep-

arates across the two cargo tanks. A hopper sloping plate at

the lower part connects the longitudinal girder with the first

stringer and provides strength and rigidity at the double-

bottom wing space interface. There are typically three

stringers in the wing space that connect the inner hull with

the side shell. Floors, vertical webs in the wing tanks and at

the longitudinal bulkheads, and deck transverses are

arranged at every web frame.

A structural model was created within POSEIDON� for

the reference design based on available structural infor-

mation [1]. The model was more detailed in the cargo area

and limited in the bow and stern region; see Fig. 9. The

structural model was created in such a way that all layouts

and topologies addressed in the previous section on

geometry modeling could easily be built up in an automatic

way. As well as the 15 (16) design variables necessary for

geometry modeling, an additional 21 structural design

parameters were introduced for the parametric structural

model; see for example Fig. 10.

4.2 Classification rules

Germanischer Lloyd rules [10] were applied to calculate

the minimum scantlings for the structural arrangements of

the design according to the class notation ‘‘GL ?100A5 Oil

Tanker.’’ Common structural rules (CSR) were not imple-

mented here, as the reference ship was not designed under

CSR rules and the optimized designs should remain com-

parable to the reference design. Two modules were

developed/implemented on top of POSEIDON. The first

one creates a POSEIDON model from a set of parameters,

while the latter invokes POSEIDON to determine mini-

mum scantlings for plates and stiffeners according to GL

rules. This allows the calculation of the structural weight of

longitudinal and transverse members. The following sim-

plifications were made for the POSEIDON model:

• Local structural details required for structural continu-

ity (i.e., brackets, etc.) were not included in the model

• Holes and cut-outs were not considered

• The material for the whole structure was Grade A

(mild) steel

• Scantlings were calculated from a longitudinal strength

assessment without taking into account global FE

calculations, local buckling, or a fatigue assessment.

Fig. 9 Sample POSEIDON model with outer shell

Fig. 10 Sample POSEIDON model without outer shell

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5 Case studies

5.1 Alternative configurations

Five different configurations were considered, with six or

seven tanks in the longitudinal direction, two or three tanks

in the transverse direction, and flat or corrugated bulk-

heads. The five different combinations are summarized in

Table 2. A total of 21,500 designs were examined in the

present study. In the following figures, only the feasible

designs are shown. The open circles correspond to domi-

nated designs, while the full circles correspond to designs

on the Pareto front. For comparison, the reference design3

is also included, and is marked by a full triangle. It should

be noted that the steel weight of the reference vessel is not

its actual weight as built, but the weight calculated by the

POSEIDON software. This ensures full comparability with

the generated optimal designs.

5.1.1 Configuration 1

This configuration corresponds to the tank arrangement of

the reference design. This is the standard configuration for

most AFRAMAX vessels. By comparing the obtained

designs with the reference design, we can identify whether

the reference design is already on the Pareto front and

whether improvements are still needed. The results for the

three selected objective functions (cargo volume, structural

weight and oil-outflow index) are shown in Figs. 11, 12

and 13.

5.1.2 Configuration 2

The second configuration considers a change in the struc-

tural design from flat to corrugated bulkheads. The results

are given in Figs. 14, 15 and 16.

5.1.3 Configuration 3

The third configuration was created by introducing an

additional longitudinal bulkhead (flat) in the cargo area.

The results are shown in Figs. 17, 18 and 19.

5.1.4 Configuration 4

Configuration 4 was derived from configuration 3 by

replacing the flat bulkheads with corrugated ones. The

results are given in Figs. 20, 21 and 22.

5.1.5 Configuration 5

Finally, for configuration 5, an additional transverse bulk-

head (flat) was introduced, leading to the results shown in

Figs. 23, 24 and 25.

5.2 Discussion of results

The five alternative configurations were selected to allow

the characteristics of the reference design to be validated,

as well as to identify possible improvements through an

analysis of the respective Pareto frontiers. Putting all of the

Pareto frontiers into a single diagram provides better

insight into the relationships between design objectives,

design parameters and alternative configurations.

Figure 26 clearly shows that the ‘‘6 9 3 flat’’ Pareto

designs dominate over all other designs. Furthermore, there

are several Pareto designs that have significantly better oil

outflow and cargo volume performances than the reference

design. This is very interesting result, considering that the

steel weights associated with the following graphs are com-

parable to or even lower than that of the reference design.4

As expected, Fig. 27 shows that, for the same cargo

volume, most of the generated ‘‘6 9 2 flat’’ Pareto designs

have lower steel weights than the other configurations; note

that the structural weights of the generated Pareto designs

and the reference ship were calculated using the same

model, namely POSEIDON. The reference design is again

dominated by several ‘‘6 9 2 flat’’ and ‘‘6 9 3 flat’’ designs.

In Fig. 28, the ‘‘6 9 3 flat’’ designs as well as the

‘‘6 9 2 flat’’ designs dominate over all other designs. The

reference design is again clearly dominated by several

‘‘6 9 3 flat’’ designs. At the same time, practically all of

the ‘‘6 9 2 flat’’ Pareto designs have lower steel weights

than the reference design with acceptable oil-outflow

performances.

In addition to the above, the following observations can

be made:

Table 2 Alternative configurations

Arrangement

of cargo tanks

Bulkhead

type

Number

of designs

Configuration 1 6 9 2 Flat 7,287

Configuration 2 6 9 2 Corrugated 1,738

Configuration 3 6 9 3 Flat 6,147

Configuration 4 6 9 3 Corrugated 3,270

Configuration 5 7 9 2 Flat 3,043

3 With a 2.5 m side clearance/double-bottom height and an oil-

outflow index of about 0.010 (compared to the corresponding

MARPOL limits of 2.0 m and 0.015, respectively), the reference

design is very environmentally friendly; however, the design shows

room for improvement with respect to both cargo carrying capacity

and steel weight.

4 Which is a successful practical design, implemented by a major

shipbuilder.

366 J Mar Sci Technol (2010) 15:359–373

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Fig. 11 Oil outflow versus

cargo volume for

configuration 1

Fig. 12 Oil outflow versus steel

weight in cargo area for

configuration 1

Fig. 13 Cargo volume versus

steel weight in cargo area for

configuration 1

Fig. 14 Outflow versus cargo

volume for configuration 2

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123

• None of the corrugated arrangements proved to be better

than the flat bulkhead designs. This does not mean that

the corrugated geometries should be disregarded as

alternative configurations in general. They have impor-

tant advantages in terms of ease of production and

maintenance that have not been considered in this study.

Fig. 15 Outflow versus steel

weight in cargo area for

configuration 2

Fig. 16 Cargo volume versus

steel weight in cargo area for

configuration 2

Fig. 17 Outflow versus cargo

volume for configuration 3

Fig. 18 Outflow versus steel

weight in cargo area for

configuration 3

368 J Mar Sci Technol (2010) 15:359–373

123

• The ‘‘7 9 2 flat’’ arrangement performed poorly, as the

steel weight increased without any significant gains in

the outflow or the capacity.

• The reference design appeared to be on the Pareto front

of the ‘‘6 9 2 flat’’ designs. It has already been noted

that the reference design is a proven design in practice,

Fig. 19 Cargo volume versus

steel weight in cargo area for

configuration 3

Fig. 20 Outflow versus cargo

volume for configuration 4

Fig. 21 Outflow versus steel

weight in cargo area for

configuration 4

Fig. 22 Cargo volume versus

steel weight in cargo area for

configuration 4

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Fig. 23 Outflow versus cargo

volume for configuration 5

Fig. 24 Outflow versus steel

weight in cargo area for

configuration 5

Fig. 25 Cargo volume versus

steel weight in cargo area for

configuration 5

Fig. 26 Outflow versus cargo

volume—Pareto designs from

different configurations

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which was optimized with respect to steel weight (by

the yard designer, most likely using FEM).

• The proof of the dominance of the ‘‘6 9 3 flat’’ designs

holds for this particular AFRAMAX vessel size, which

is on the border with that of SUEZMAX.

5.3 Multi-criteria decision-making (MCDM) problem

and optimal design selection

Two different MCDM scenarios were examined using the

utility functions technique [9]:

Fig. 27 Cargo volume versus

steel weight in cargo area—

Pareto designs from different

configurations

Fig. 28 Outflow versus steel

weight in cargo area—Pareto

designs from different

configurations

Fig. 29 Design ranking

according to scenario #1

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1. Scenario #1: the same preference for all objectives is

assumed; see Fig. 29, Eq. 5, Table 3.

2. Scenario #2: the cargo volume (corresponding to the

revenue) is considered more important than the initial

cost (steel weight) and the environmental impact

(outflow); see Fig. 30, Eq. 6, Table 4.

wcv ¼ wsw ¼ wout ¼1

3ð5Þ

wcv ¼3

4and wsw ¼ wout ¼

1

8; ð6Þ

where wcv, wsw, and wout are the utility functions at satu-

ration for the cargo volume, steel weight and oil outflow,

respectively.

When all three objectives are considered to be equally

important (scenario #1), design #1710 (with the charac-

teristics shown in Table 3) is found to be the optimal one.

This is due to the significant reduction in the oil outflow

during collisions or grounding accidents (-23%). At the

same time, the cargo volume is also increased (?2%) and

the steel weight is reduced by 2%. This design is in every

respect better than the reference design. It is interesting to

note that design #2122, which is ranked second, achieves

less of a reduction in oil outflow (-6%), but a greater

increase in cargo volume (?7%) and a small reduction in

steel weight of 1%.

Based on the results of the first assessment scenario

assumed, the preferences were modified in the second

scenario; namely, the increase in cargo volume was con-

sidered to be much more important than the other objec-

tives (relative weights of 0.75: 0.125: 0.125). In that

scenario, design #2069, with the characteristics shown in

Table 4, becomes the optimal one. This is due to a sig-

nificant increase in the cargo capacity (?8%). For this

design, the accidental oil outflow is increased by 10% (but

it still remains well below the regulatory requirements),

while the steel weight is reduced by 2%. This design is also

better than the reference design. Design #2122 is again

ranked second here due to a smaller increase in cargo

volume (?7%) and reduction in steel weight (1%). Its

arrangement is shown in Fig. 31.

6 Conclusions

A multi-objective optimization procedure for the devel-

opment of efficient and environmentally friendly tanker

designs has been developed. The implemented procedure is

largely automated and combines the use of the naval

architectural software package NAPA�, the optimization

software FRONTIER�, and the structural design software

POSEIDON�. The application of the optimization proce-

dure to an AFRAMAX design—already optimized by the

yard—showed that:

Table 3 Comparison of optimum and reference designs according to

scenario #1

Ref. design 6 9 3 Flat 6 9 3 Flat

ID 1710 2122

Rank 1 2

Cargo vol 126765 129804 (?2%) 135950 (?7%)

Oil outflow 0.01006 0.00777 (-23%) 0.00942 (-6%)

Wst cargo area 11077 10908 (-2%) 11013 (-1%)

Fig. 30 Design ranking

according to scenario #2

Table 4 Comparison of optimum and reference designs according to

scenario #2

Ref.

design

6 9 3 Flat 6 9 3 Flat

ID 2069 2122

Rank 1 2

Cargo

volume

126765 137494 (?8%) 135950 (?7%)

Oil outflow 0.01006 0.0111 (?10%) 0.00942 (-6%)

Wst cargo

area

11077 10894 (-2%) 11013 (-1%)

372 J Mar Sci Technol (2010) 15:359–373

123

• The reference design was close to the Pareto designs

(optimal solutions) generated, which confirms the

validity of the modeling set-up

• Several Pareto designs exhibited improved oil-outflow

performances and comparable steel weights and capac-

ities to the reference design, whereas other designs

showed improved capacities but slightly worse oil-

outflow performances

• Particular design features of optimal designs observed

in [13] with respect to an increase in double bottom

height and a decrease in tank size towards the bow were

confirmed

• Fine-tuning the hullform around the cargo block is

expected to further improve the oil-outflow and cargo

carrying capacity performances of the generated

designs.

The way ahead may include:

• Enhancing the optimization procedure by including:

• Optimization of the local structural design for the

least structural weight

• The implementation of common structural rules

(CSR) for the structural design

• Other design criteria (e.g., ease of production and

maintenance, etc.)

• Economic criteria (building, maintenance and oper-

ating costs, RFR, NPV)

• Optimization of the fit of the hullform to the cargo

block, along with the minimization of fuel con-

sumption and emissions

• Extending to other ship sizes such as ULCC, VLCC,

SUEZMAX, PANMAX, etc.

• Refining the probabilistic assessment of oil outflow by

introducing probabilities derived from more recent

damage statistics (beyond MARPOL) in the framework

of a risk-based design procedure, and challenging

existing regulations [12].

References

1. Germanischer Lloyd (2008) POSEIDON ND v.8.119. Germani-

scher Lloyd, Hamburg (see http://www.gl-group.com/)

2. Marine Environment Protection Committee (2004) Resolution

MEPC.117(52): Amendments to the annex of the protocol of

1978 relating to the international convention for the prevention of

pollution from ships, 1973 (MEPC 52nd Session, Agenda Item

24, Annex 2, adopted on October 15). International Maritime

Organization, London

3. NAPA Ltd. (2010) NAPA software. NAPA Ltd., Helsinki (see

http://www.napa.fi/)

4. Papanikolaou A (2009) Holistic ship design optimization. Com-

put Aided Des. doi:10.1016/j.cad.2009.07.002

5. Boulougouris EK, Papanikolaou A, Zaraphonitis G (2004) Opti-

misation of arrangements of Ro-Ro passenger ships with genetic

algorithms. Ship Technol Res 51(3):99–105

6. Zaraphonitis G, Papanikolaou A, Mourkoyiannis D (2003) Hull-

form optimization of high speed vessels with respect to wash and

powering. In: Proceedings of IMDC 03, Athens, Greece, 5–8 May

2003, pp 43–54

7. Sen P, Yang J-B (1998) Multiple criteria decision support in

engineering design. Springer, London

8. Goldberg D (1998) Genetic algorithms in search, optimization,

and machine learning. Addison-Wesley, Upper Saddle River

9. ESTECO (2010) modeFRONTIER software. ESTECO, Trieste

(see http://www.esteco.it/)

10. Germanischer Lloyd (2008) Rules for classification and

construction, ship technology, seagoing ships, hull structures.

Germanischer Lloyd, Hamburg

11. SAFEDOR (2005) Integrated project on design, operation and

regulation for safety (EU-funded project, contract TIP4-CT-

2005-516278). Germanischer Lloyd, Hamburg (see http://www.

safedor.org)

12. Papanikolaou A (ed) (2009) Risk-based ship design—methods,

tools and applications. Springer, New York (ISBN 978-3-540-

89041-6)

13. Papanikolaou A, Tuzcu C, Tsichlis P, Eliopoulou E (2007) Risk-

based optimization of tanker design. In: Proceedings of 3rd

international maritime conference on design for safety, Berkeley,

CA, USA, 26–29 Sept 2007

Fig. 31 Tank arrangement for design #2122. This design, for which

the tank length was varied lengthwise, demonstrates that finding the

best cargo tank sizes to optimize oil outflow, cargo capacity and steel

weight is not a trivial task, though equally sized tanks are preferable

from a production point of view. In fact, the likely additional

production cost for this flexibility in tank sizes should also be

considered in an update of the optimization procedure presented here,

in which additional costs and benefits should be rationally assessed.

Note that the procedure presented here allows also the easy

identification of generated Pareto designs where the tanks are equal

in size (as an additional design constraint)

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