Optimization of Arrangements of Ro-Ro Passenger Ships with Genetic Algorithms

Evangelos K. Boulougouris, Apostolos D. Papanikolaou, George Zaraphonitis NTUA-SDL 1

1 Introduction

Ships are complex and multifunctional systems, thus their design involves innumerable design variables and an overwhelming number of constraints. Under these circumstances finding a mathematically optimal solution to the entire ship design problem appears prohibitive. Yet there have been numerous attempts and a variety of optimization methodologies introduced over the years addressing at least parts of the entire ship design problem (Nowacki, 2003). A commonly adopted strategy for practical results is the suitable breakdown of the overall design process into manageable, well-defined modular steps, similar to the traditional decomposition of the manual design into different design stages, even if this does not ensure an optimal solution to the entire design problem. One of these modular and major steps in the initial ship design is the definition of the watertight compartmentation. Although there are many considerations to be made for the arrangement of the internal watertight boundaries (space requirements by the equipment installed or space users, structural and ergonomic considerations etc), there are three main aspects that could be considered as the most critical ones already in the initial ship design stage. Those are the ship’s response in case of damage (‘survivability’) and the requirements imposed by the relevant stability regulations, the building cost and the transport capacity of the ship. The above considerations pertain especially to passenger carrying ships, to be considered in this paper.

Given the fact that the ship’s damage stability is strongly related to the safety level provided by

the ship to its passengers, crew and cargo, the maximization of her survivability is a primary merit function for the designer, especially in view of recent changes of the damage stability regulations towards more stringent requirements (Stockholm Agreement and proposed new harmonized damage stability rules). The probabilistic damaged stability assessment concept, originally introduced by K. Wendel (1960) more than 40 years ago, was adopted by the International Maritime Organization in IMO SOLAS A.265 (VIII) (1974) as an alternative to the deterministic concept for the assessment of passenger ships and was much later reaffirmed by IMO Resolution MSC.19 (58) (1990) as to its mandatory application to all dry cargo ships built after February 1992, as laid down in SOLAS B-1 Reg. 25. The probabilistic damage stability concept is expected to become the future damaged stability regulatory standard for all types of ships through the currently under completion harmonized damage stability rules (see IMO-SLF46, 2003).

The present paper is based on research work of NTUA-Ship Design Laboratory within the

ROROPROB EU project (see Zaraphonitis et.al., 2002 and Boulougouris et.al., 2003a) and presents results of the employed formalized multi-objective optimization procedure for the internal compartmentation of Ro-Ro Passenger ships (see Zaraphonitis et.al., 2003 and Boulougouris, 2003b). The used procedure utilizes latest advances in the field of the multi-criteria design optimization with Genetic Algorithms (GA) and achieves a maximization of ship’s resistance against capsize, expressed by the Attained Subdivision Index, as well as of her transport capacity, herein expressed in terms of both increased deadweight and garage deck space. Building cost reduction is herein considered mainly as the result of steel weight minimization. Additionally, it

1 Ship Design Laboratory, School of Naval Architecture and Marine Engineering, National Technical University of

Athens

1

could be argued, that the minimization of the number of watertight boundaries may result to equipment costs savings. 2 Outline of the Optimization Procedure

Recent advances in the optimal design techniques and increased computing power allowed the introduction of a wide range of tools for the exploration of the design space once it is described in a parametric way. Given the fact that there was very little information about the mathematical behavior of the objective space of the present problem –especially with respect to the attained subdivision index for which there appears that it is of multi-modal type– and there were multiple conflicting objectives and constraints, the adoption of multi-objective GAs appeared like the only solution to the set optimization problem (see Sen and Yang, 1998).

The GAs were herein implemented by use of the general-purpose optimization software

package modeFRONTIER (see E.STE.CO, 2003). A parametric ship model was created in the environment of the well-known ship design software package NAPA (see Napa Oy, 2001) by use of NAPA Basic programming language. Assuming that the hull form and the main layout concept were developed independently at the previous design stages, the vessel’s watertight subdivision is parametrically generated, as explained in 2.1.

For each design variant the attained subdivision index, along with the total vehicles lane length

in the lower hold and main garage deck, and the steel weight up to the top of the main garage deck are calculated. The limitation of the number of the objectives to three permitted the 3D representation and exploration of the Pareto-frontier. Additional objectives related to the layout (i.e. minimization of the propellers’ shaft lengths or the number of bearings) can be easily incorporated to the optimization model. The main features of the employed procedure are outlined in the following. 2.1 Parametric Model

Using the NAPA Basic commands the appropriate macros were created for the generation of the ship’s internal watertight arrangement, based on a set of carefully selected design variables according to the features of the initial design. For the particular example Ro-Ro passenger ship, selected for the exploration of the optimization procedure (see Figure 1), a total number of 31 design variables was used. The optimization scheduler -that is modeFRONTIER- systematically updates their values performing the design space exploration.

Additionally the user is supplying a set of design parameters that includes all those quantities

that are not under the designer’s control. They were 27 design parameters finally used. Their user-supplied values determine the vessel’s intact loading conditions in partial and full draught, and provide necessary data for a variety of calculations (specific weights for the structural weight calculation, vehicle dimensions for the lanes length calculation etc.). The design parameters are kept constant during the optimization. Additionally some of the design variables may also be treated as parameters if the user decides to keep them constant for subsets of designs. For instance, if the user wants to explore the impact of the watertight subdivision of the part of the ship forward of the main engine room only, then the variables affecting the aft ship compartmentation may be treated as parameters. Thus specific subspaces of the total design space can be investigated more thoroughly. The parametric model and the optimization procedure has been developed under the following assumptions (see also Zaraphonitis et.al., 2003):

2

• The vessel’s hull form and draughts are kept constant during the optimization. Therefore the vessel’s displacement is fixed and the lightship weight variations are compensated by corresponding variations of DWT. The hullform used in this investigation is shown in Figure 1 and its main particulars are given in Table 1.

Figure 1: Hullform of selected example Ro-Ro Passenger Ferry

• The vertical position of the bulkhead deck is one of the design variables. The resulting change of the vertical center of gravity VCG in the various loading conditions is taken into account by use of proper relations supplied by the user.

• The calculation of the structural weight and of the corresponding center of gravity position is based on user-supplied specific weight relations.

• Given the hull dimensions and the initial layout of the ship, two lower holds may be generated forward and aft of the Main Engine Room (MER), but only the former can carry vehicles. The existence and extent of both lower holds is controlled by appropriate design variables and parameters.

• Both central and side casing main deck configurations are available to the user. The parametric design in both cases generates the appropriate aft casings on each side of the main deck that accommodates the passengers staircases, storerooms, auxiliary rooms, etc. usually located in this area (see Figure 2 and Figure 3).

• The measure for the vessel’s transport capacity is the total vehicles lanes length. It is calculated separately for the main deck and the lower holds. The user defines the typical size of the vehicles carried. A user-supplied equivalence coefficient is used to account for carrying different kinds of vehicles on the main deck and in the lower hold.

• Downflooding openings at constant height provided by the user may be defined to limit the range of positive stability after damage.

Table 1: Main Particulars

Length o.a. 193.6mLength b.p. 176.0mBreadth 25.0mDepth (reference) 9.100mDesign draught 6.550mFull load draught 6.520m

Full load displacement 17520tFull load reference GM 2.440mPartial load draught 5.884mPartial load displacement 14880tPartial load reference GM 1.830m

3

Figure 2: Design variant with aft lower hold and central casing

Figure 3: Design variant without aft lower hold and side casings

2.2 Objective functions

Following the generation of the internal arrangement, the procedure evaluates each design variant, using the built-in calculation functions of NAPA. Appropriate NAPA macros were developed to control the damage stability analysis, to calculate the structural weight and transport capacity (both in terms of DWT and lanes length) and to verify the consistency of each design. The flowchart of the procedure that integrates modeFRONTIER with NAPA is shown in Figure 4. Both the structural weight and the total lane meters are made non-dimensional using the relevant values of the initial design.

The initial calculations for the attained subdivision index within the ROROPROB project were

performed according to the probabilistic damage stability concept of Regulation 25 of SOLAS Part B-1, actually applicable to cargo ships, instead of using Resolution A.265 that applies to Ro-Ro Passenger vessels. This was done for simplicity and for computing time savings. Additional runs were later performed using the harmonized damage stability formulation of SLF 43 (2000) on the

4

way to examine the possible impact of the different damage stability regulations on the Pareto-optimum designs. The calculation of the heeling angles was limited to 30°. No down-flooding openings were considered in the case studies presented herein. The permeability of the garage spaces is set equal to 0.90, for the engine rooms is 0.85 and for the rest of the spaces is set equal to 0.95.

The objectives of this optimization problem were herein the maximization of the attained

subdivision index, the maximization of the total lanes lengths and the minimization of the structural weight. It was obvious from the beginning that the first two objectives are contradicting because the maximization of the A requires thorough compartmentation while this will limit the lower hold length and thus the total lane meters. The minimization of the structural weight is also a contradicting objective against the maximization of A.

Figure 4: Flowchart of optimization procedure

2.3 Genetic Algorithms

The presence of multiple and conflicting objectives, the large and complex solution space and the complex characteristics of the objective functions (especially those of the attained subdivision index), favor the use of a stochastic optimization process such as the Genetic Algorithms (GA) (see Goldberg, 1989). Their basic structure is shown in Figure 5.

The modeFRONTIER implements a Multiple Objectives Genetic Algorithm (MOGA)

optimization scheduler (see E.STE.CO, 2003) that searches for the Pareto-optimum solutions. The drawback of the procedure is the large number of direct calculations required to converge to optimum solutions. The advantages of the algorithm are that:

• It avoids converging into local optimum solutions in the design space • Starting from the initial population, it allows it to evolve in such a way that some individuals

can meet different objectives. This results to a “set of best designs” (Pareto set) • It poses no limitation to the characteristics of the objective function

5

A multi-objective problem may be treated with three different strategies using a GA according to Sen and Yang (1998):

• Make the multiple criteria decisions first and arrive to a composite measure of fitness by combining the different criteria, and then use the composite measure to search for the best solution

• Conduct the search to assemble a range of possible solutions and then select one or more of these on the basis of multiple criteria decision making

• Combine the search with the Multiple Criteria Decision Making (MCDM) The third solution is implemented within the modeFRONTIER. The basic pattern is as follows: • A multiple objective search is performed to obtain an approximate idea of the Pareto

surface. • Multiple criteria choice or ranking is applied to capture the preferences of the decision

maker. Then a new search is launched but using the priorities assigned by the decision maker.

Figure 5: The Basic Genetic Algorithm (Sen and Yang, 1998)

The MOGA optimization scheduler has the following parameters: • The initial population • The number of generation • The probability of directional cross-over that is a proprietary operator that gives efficiency

to the algorithm but decreases its robustness. The default value that is 0.5 was used. • The probability of selection, which gives the probability that design configurations are not

changed during the evolution. The default value that is 0.05 was used. • The probability of mutation that gives the probability that a design configuration is

randomly perturbed. The default value that is 0.1 was used. • The DNA String Mutation Ratio that gives the percentage of the individual DNA that is

perturbed by the mutation operator. The default value that is 0.05 was used. • The usage (or not) of Elitism, which ensures that the best solutions (for each objective) are

preserved during the evolution • The MOGA type. There are three types:

o MOGA - Generational Evolution that works on a set of design configurations that are periodically updated when one generation is completed

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o MOGA - Steady Evolution that uses all the computed configurations as soon as they are available in a first in - first out mode

o MOGA - Adaptive Evolution, where the choice of the genetic algorithm operators is done dynamically during the search

2.4 Results analysis

For the analysis of the results produced by the present optimization procedure, the various options provided by the modeFRONTIER were used (see Boulougouris et.al., 2003a), namely:

- Parallel graphs - Scattered diagrams - Student plots

The later are capable of showing the importance of each input variable on the output value. They use the Student’s t-Tests, which for a variable x is defined according to the formula (see E.STE.CO, 2003):

2 2

M MtS Sn n

− +

− +

− +

−=

+

(1)

where: M+ , M− are the mean values of the output variable y corresponding to these x1 values given by the formulas:

,

1

x

x

n

i ni

x

yM

n

+

+

+

=+ =

∑, (2)

,

1

x

x

n

i ni

x

yM

n

−

−

−

=− =

∑, (3)

nx+ is the number of values in the upper part of domain of x and nx- is the number of values in the lower part of domain of x, and is the variance of the population for the input variable x in the upper part of the domain of the output variable,

S+S− the variance of the population for the input

variable x in the lower part of domain of the output variable. The corresponding formulas for their calculation are:

2

2 ( )1x

x MS

n+

+ ++

−=

−∑ , (4)

2

2 ( )1x

x MS

n−

− −−

−=

−∑ (5)

The Student plots use bar graphs of the Significance and Delta parameters. The Significance is calculated based on the value of t-score and the comparison of this value with a built-in table that determines the confidence level on the hypothesis that the mean values of the two samples are the same. Great values of Significance parameter indicate that there is a relationship with that input variable.

The Delta parameter on the other hand is the difference between M− and M+ . The Delta parameter shows how strong the relationship is. A Delta parameter greater than zero shows a direct

7

relationship with the input variable, a value less than zero indicate that there is an inverse relationship (see E.STE.CO, 2003). 3 Case Studies

Several case studies were conducted by applying the above procedure to the sample Ro-Ro passenger ship. In the first three cases the search capabilities for the formation of the Pareto-frontier were investigated while a fourth case studied the full potential of the modeFrontier combining the MOGA with additive utility functions (UTA). The first case study investigated the impact of alternative garage deck casing type (central or side). The second one investigated the effect of an alternative probabilistic damage stability concept, namely the SLF 43 harmonized rules proposal, on the Pareto-optimum designs produced using the SOLAS B-1. The third case study examined the impact of the initial population on the optimization procedure. Finally, a combined search and multiple criteria decision-making (MCDM) procedure was conducted that included both multi-objective optimization and the implementation of a SIMPLEX algorithm (Nelder and Mead, 1965). In the following paragraphs the results of these case studies are presented.

3.1 Comparison of the Central and Side Casing layouts

A subset of 12 design variables (see Table 2) was used to investigate and compare the characteristics of the central and side casing configurations. The optimization case included the maximization of both the attained subdivision index A (according to SOLAS B-1 Reg. 25) and the lane meters, while the structural weight should be minimized (see also Table 2) and the relevant logical diagram is shown in Figure 6.

The results of this investigation are shown in Figure 7 up to Figure 9. The study of these figures

shows that the side casings configuration results in considerably increased transport capacity, combined with an appreciable increase of the attained subdivision index. The increase of transport capacity is partly attributed to the more efficient utilization of the main deck area. In addition, the existence of side casings has a positive impact on the vessel’s stability characteristics following damage, enabling the increase of the lower hold area while fulfilling the requirements for an increased attained subdivision index. No significant differences between the two design concepts regarding structural weight may be observed from the comparison. However it should be noted that the structural weight calculations are based on predefined specific weights per square meter, provided by the user for various areas of the ship, regardless of the selected design concept. In this respect the comparison may be somehow misleading, since the central casing configuration is considered to result to increased structural stiffness. Due to the lack of the support provided by the central casing, heavier transverse beams, deep longitudinal girders and a number of pillars are necessary to support the deck weight in the case of vessels constructed with the side casings concept. It is interesting to note that successful Ro-Ro passenger ship designs follow in practice the side casing concept, though they were developed without use of formal optimization schemes like the presented one (see Kanerva, 1999).

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Figure 6: Logical diagram of the optimization process used for the comparison of the central and side casing

Table 2: Design variables and objective functions used in case studies

Input Variables The depth of the ship DEPTH The minimum double bottom margin, in the transverse direction, outwards of the longitudinal bulkhead fwd of the engine room DBMARG

The minimum breadth of the fwd lower hold at its fwd end (used to select the transverse bulkhead forming the fwd limit of the lower hold) LHBMIN

The maximum half breadth of the fwd lower hold MXLBKDWDTH The number of bulkheads forward of the main engine room excluding the collision and the fore engine room bulkhead NBKHDFWD

BKHDAFT1 BKHDAFT2 Heights for the definition of control points of the aft bulkhead

distribution curve BKHDAFT3 BKFWD1 BKFWD2 BKFWD3

Heights for the definition of control points of the forward bulkhead distribution curve

BKFWD4 Output Variables

Calculated attained subdivision index outA Calculated total Lane Meters OutLaneMeters Calculated Steel Weight OutWeight

Objective Functions Maximization of the attained subdivision index acc. to SOLAS B-1 maxA Maximization of the total Lane Meters maxLaneMeters Minimization of the Steel Weight minWeight

Constraint Attained subdivision index greater than 0.79 Constr_MinA

9

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89

Attained Index

Wei

ght (

nond

imen

sion

al)

Central CasingSide Casing

Figure 7: Scatter diagram of the attained subdivision index vs. the non-dimensional weight

0.93

0.95

0.97

0.99

1.01

1.03

1.05

1.07

1.09

1.11

1.13

0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89

Attained Index

Lane

met

ers

(non

dim

ensi

onal

)

Central CasingSide Casing

Figure 8: Scatter diagram of the attained subdivision index vs. the non-dimensional lane meters

10

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.93 0.95 0.97 0.99 1.01 1.03 1.05 1.07 1.09 1.11 1.13

Lane meters (nondimensional)

Wei

ght (

nond

imen

sion

al)

Central CasingSide Casing

Figure 9: Scatter diagram of the non-dimensional lane meters vs. the non-dimensional weight

3.2 Comparison of different Probabilistic Damage Stability Models In order to investigate the impact of calculating the attained subdivision index using different

probabilistic models, a set of 30 non-dominated (Pareto-optimum) designs was used. The designs were of side casings layout type and the damage stability calculations were by use of SOLAS B-1 and alternatively by the SLF 43. The original ranking of the designs is shown in Figure 10, while the results using the SLF 43 proposal are shown in Figure 11.

228 4

234

183

235 61

123

116

224

181 14 18 5

75 19 17

129

134

97 42 20

149

198 3

74

203 78 91

120

156

162

B-1

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

Design ID

A-Index acc. to SOLAS B-1

Figure 10: Design ranking according to the SOLAS B-1 attained subdivision index

11

228 4

234

235

183

91 85 97

162

116

101

191

198

36 94 40 3

74

218

192

199

202

103

123

14

154

61 24

133

28 99

SLF-A

0.81

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

Design ID

A-Index acc. to SLF proposal

Figure 11: Design ranking according to the SLF 43 attained subdivision index

From these figures it is obvious that the ranking is different. Therefore the non-dominated design set will not (and cannot) be identical. Even though, it is worth noticing that the best five designs are the same in both cases.

3.3 Investigation of the impact of the initial population size When using GAs, the computing cost is proportional to the number of designs in the initial

population and the number of generations required for obtaining the Pareto-frontier. Therefore three different initial populations were selected with a number of 12 (as many as the design variables), 24 and 96 initial designs respectively. Using these three populations, two different optimizations were performed. In the first case the total number of direct calculations was the same for all three populations. This is analogous to almost equal total computing time. A total number of 384 designs were selected. This resulted in 32 generations for the first population, 16 generations for the second and 4 generations for the third population respectively.

The scatter diagrams of the results of this study in the three 2D representation of the design

space are shown in Figure 12, Figure 13 and Figure 14 respectively. From the results the scattering of the designs of the third population (96) is obvious. This is due to the larger diversity of the phenotypes of the initial designs. Even though, there are several designs of the other two populations that contribute to the formation of the Pareto-frontier.

A second set of calculations was performed using the above three populations but assuming

that the number of generations was the same. This resulted to 192 designs for the first population (12 initial designs), 384 designs for the second population (24 initial designs) and 1536 designs for the third population (96 initial designs). Figure 15, Figure 16 and Figure 17 present the results in scatter diagrams of the design space. It is interesting to note that even though most of the non-dominated designs belong to the third population, there are still Pareto-optimal designs that belong to the second population.

12

0.97

1.00

1.02

1.05

1.07

1.10

1.12

1.15

0.77 0.79 0.81 0.83 0.85 0.87 0.89outA

Out

Lane

Met

ers

Init Population 12Init Population 24Init Population 96

Figure 12: Scatter diagram of the attained subdivision index vs. the non-dimensional lane meters for the three

different initial populations, for the same total number of designs

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.77 0.79 0.81 0.83 0.85 0.87 0.89outA

Out

Wei

ght

Init Population 12Init Population 24Init Population 96

Figure 13: Scatter diagram of the attained subdivision index vs. the non-dimensional weight for the three

different initial populations, for the same total number of designs

13

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14

OutLaneMeters

Out

Wei

ght

Init Population 12Init Population 24Init Population 96

Figure 14: Scatter diagram of the non-dimensional lane meters vs. the non-dimensional weight for the three

different initial populations, for the same total number of designs

0.97

1.00

1.02

1.05

1.07

1.10

1.12

1.15

0.77 0.79 0.81 0.83 0.85 0.87 0.89outA

Out

Lane

Met

ers

Init Population 12Init Population 24Init Population 96

Figure 15: Scatter diagram of the attained subdivision index vs. the non-dimensional lane meters for the three

different initial populations, for the same number of generations

14

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.77 0.79 0.81 0.83 0.85 0.87 0.89outA

Out

Wei

ght

Init Population 12Init Population 24Init Population 96

Figure 16: Scatter diagram of the attained subdivision index vs. the non-dimensional weight for the three

different initial populations, for the same number of generations

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14

OutLaneMeters

Out

Wei

ght

Init Population 12Init Population 24Init Population 96

Figure 17: Scatter diagram of the non-dimensional lane meters vs. the non-dimensional weight for the three

different initial populations, for the same number of generations

Summarising the above it is obvious that the larger initial population assures the better approximation of the Pareto-frontier but it involves larger computing cost. Therefore the sizing of the initial population is significant for the balance between cost and effectiveness of the algorithms.

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On the other hand the stochastic processes involved in the MOGA in the cross-over and mutation genetic operations increases the probability of gaining optimal solutions even with smaller populations.

3.4 Combining MOGA, MCDM and SIMPLEX

In this case the MOGA is combined with additive utility functions to form an interactive solution procedure. The decision maker compares pairwise a collection of non-dominated solutions obtained from the MOGA’s search or direct specification of relative importance between design’s attributes. The information on these pairwise comparisons result to one of two kinds of ordering:

• Solution i is preferred to Solution j • Solution i is considered to be just as attractive as Solution j Using these relations a set of utility functions for each criterion can be derived analytically for

all the attributes of a design. The utility functions are then combined, forming a composite fitness function that captures the preference structure of the decision maker. The new search will tend to concentrate on those areas of the Pareto surface that are in harmony with its sense of priorities. This new search may also be made either by the MOGA or the SIMPLEX scheduler. The later was the case for the study presented herein.

In the following figures the results of this case study are shown. In Figure 18 the utility

functions and the relevant weights of the three (3) objectives are shown. The corresponding logical diagram is shown in Figure 19, while the history diagram of the SIMPLEX optimization is depicted in Figure 20. Table 3 contains the values of the design variables and the attributes of the optimum design that resulted from the application of the combined procedure. It is obvious for this design that the compromise of the conflicting objectives resulted to larger weight savings (almost 5%) but reduced the total length of lane meters (a little more than 2%). If a real design maker dislikes this outcome, then a new search using different weights and utility functions can be launched.

The relevant area on the Pareto frontier on the scatter diagram of the attained subdivision index

vs. the non-dimensional lane meters, where the SIMPLEX searches for the optimum, is shown in Figure 21. The relevant areas on the scatter diagrams of the attained subdivision index vs. the non-dimensional weight and the non-dimensional lane meters vs. non-dimensional weight are shown in Figure 22 and Figure 23 respectively. The initial (gray colored) and the optimal (black colored) arrangements are compared in Figure 24.

Figure 18: Utility Functions and Weights assigned

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Figure 19: Logical diagram of the optimization procedure using the MCDM

MaxMCDM

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 200 400 600 800 1000 1200 1400 1600 1800 2000Design ID

Max

MCD

M

Figure 20: History diagram of SIMPLEX search for the optimum using the combined fitness function

Table 3. Design variables and attributes of the optimum design

DEP

TH

DB

MA

RG

LHB

MIN

MX

LBK

DW

DTH

NB

KH

DFW

D

BK

HD

AFT

1

BK

HD

AFT

2

BK

HD

AFT

3

BK

FWD

1

BK

FWD

2

BK

FWD

3

BK

FWD

4

8.6 2.5 1.75 6.5 8 -2.4 6.4 1.6 0.8 2.4 -2.4 0.9

Output Variables outA OutLaneMeters OutWeight 0.854 0.979 0.952

17

0.97

1.00

1.02

1.05

1.07

1.10

1.12

1.15

0.7700 0.7900 0.8100 0.8300 0.8500 0.8700 0.8900outA

Out

Lane

Met

ers

Figure 21: Scatter diagram of the attained subdivision index vs. the non-dimensional lane meters where the

area were the SIMPLEX searches for a better design is shown

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.77 0.79 0.81 0.83 0.85 0.87 0.89outA

Out

Wei

ght

Figure 22: Scatter diagram of the attained subdivision index vs. the non-dimensional weight where is shown

the area were the SIMPLEX searches for a better design

18

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14OutLaneMeters

Out

Wei

ght

Figure 23: Scatter diagram of the non-dimensional lane meters vs. the non-dimensional weight where is

shown the area were the SIMPLEX searches for a better design

Figure 24: Comparison of optimum (black colored) and initial (gray colored) arrangement

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4 Conclusions

The above case studies led to the following conclusions regarding the developed and implemented optimisation procedure:

• The developed optimisation procedure can be used both at the conceptual design stage to generate from scratch the internal subdivision of a new design, and at later design stages to improve significantly the survivability of an existing design. It allows the designer to gain an overview of the design space and identify the Pareto frontier.

• The changes of ship’s weight, in the course of this optimisation procedure, after performing the evaluation of almost 2000 designs, are small showing that improvements in the economic efficiency of the ship, expressed by larger length of the lanes are achievable with minor changes to the weight of the ship.

• The comparison of the obtained results for the alternative central and side casings concepts proved the latter to clearly result to considerably increased transport capacity (increased lanes length), combined with an appreciable increase of the attained subdivision index. It should be however noted, that the change of the main car deck structural design for the two alternative concepts might be the reason for some changes in the associated steel weight and this is not considered in the present optimisation code.

• The selection of the probabilistic damage stability model affects the ranking of the designs. Thus a Pareto optimum design that resulted from the application of a specific attained subdivision index formulation may become a dominated one if another probabilistic model is used.

• The size of the initial population is a significant parameter in the optimization procedure, closely linked to the computational cost. Small initial populations permit the production of more generations for the same total computing time. On the other hand they have limiting diversity that may prevent them from exploring the whole Pareto frontier.

• The combination of MOGA, MCDM and SIMPLEX is a very powerful tool for reaching and optimum design. Combining the exploration capabilities of the MOGA for sketching the Pareto frontier with the capture of the decision maker’s preference and the robustness of the SIMPLEX yields a very efficient tool in the search for the optimum.

• Due to the large number of calculations, required within the NAPA shell in order to define the watertight subdivision and especially for the calculation of the attained index, the required time for each run takes approximately more than 3.5 min using a PC with P4@2.4GHz. This should be not a real constraint for the developed procedure, considering continuous improvements of computer technology. Even though, measures to limit the number of actual computations should be further investigated. In this direction the use of neural networks that will be properly trained to substitute the actual calculations might lead more effectively to best results.

References

BOULOUGOURIS, E.; ZARAPHONITIS, G.; PAPANIKOLAOU, A. (2003a), Optimization Procedure for Fast Ferry Watertight Subdivision (WP 5), ROROPROB Project Report, Project funded by the European Commission, contract G3RD-CT-2000-0030, NTUA-SDL

BOULOUGOURIS, E.K. (2003b), Ship design optimization for enhanced survivability after damage for Ro-Ro passenger and naval ships, Dr.-Eng. Thesis (in Greek), National Technical University of Athens

E.STE.CO (2003), modeFRONTIER software v.2.5.x, http://www.esteco.it/

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GOLDBERG, D. (1989), Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publishing Company, Inc., USA

IMO (1974), Regulation on Subdivision and Stability of Passenger Ships (as an Equivalent to Part B of Chapter II of the 1974 SOLAS Convention), London. This publication contains IMO Resolutions A.265 (VIII), A.266 (VIII), and explanatory notes

IMO-Resolution MSC.19 (58) (1990), New regulations for subdivision and damage stability for dry cargo ships built on or after 920201, 25 May

IMO, Sub-Committee On Stability And Load Lines And On Fishing Vessels Safety (SLF) (2000), SLF 43-Revision of SOLAS Chapter II-1 –Subdivision and Stability, 11-15 September

IMO, Sub-Committee On Stability And Load Lines And On Fishing Vessels Safety (SLF) (2003), SLF 46/INF.5-Development of Revised SOLAS Chapter II-1 Parts A, B and B-1, 6 June

KANERVA, M. (1999), Ferries for the Future, CRUISE+FERRY 99, London UK

NAPA Oy (2001), NAPA software, http://www.napa.fi/

NELDER, J.A.; MEAD, R. (1965), A Simplex Method for Function Minimization, Computer Journal 7 (1965) 308

NOWACKI, H. (2003), Design Synthesis and Optimization-An Historical Perspective, OPTIMISTIC-Optimization in Marine Design, 39th WEGEMT Summer School, Berlin, Germany, March 19-23, pp. 1-27

Probabilistic Rules-Based Optimal Design of Ro-Ro Passenger Ships –ROROPROB, Contract Number G3RD-CT-2000-00030

WENDEL, K. (1960), Die Wahrscheinlichkeit des Überstehens von Verletzungen, Journal of Ship Technology Research, 7:36, pp. 47-61

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ZARAPHONITIS, G.; BOULOUGOURIS, E.; PAPANIKOLAOU, A. (2002), Development of an Optimisation Procedure for Passenger Ro-Ro Ship Subdivision, ROROPROB Project Report, Project funded by the European Commission, contract G3RD-CT-2000-0030, NTUA-SDL

ZARAPHONITIS, G.; BOULOUGOURIS, E.; PAPANIKOLAOU, A. (2003), An Integrated Optimisation Procedure for the Design of RO-RO Passenger Ships of Enhanced Safety and Efficiency, Proc. IMDC 03, Athens, Vol. I, pp.313-324

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