DSpace at VNU: Automatic interior space arrangement of mid-sized superyachts using a constraint-based genetic algorithm

Space arrangement is performed by considering various design constraints that are expressed in terms of numerical values such as space occupation, shapes of spaces, and distance of stair

O R I G I N A L A R T I C L E

Automatic interior space arrangement of mid-sized superyachts

using a constraint-based genetic algorithm

Jong-Ho Nam•Tat-Hien Le

Received: 2 January 2012 / Accepted: 3 May 2012 / Published online: 25 May 2012

Ó JASNAOE 2012

Abstract The interior of superyachts is either designed

by an expert or modeled on previous layouts that have been

successfully designed Changing one arrangement to the

other is challenging and has not been tried without the

buyer’s request, mostly dissuaded by the current manual

design procedure In this work, an approach to determine

the interior space arrangement is introduced Space

arrangement is performed by considering various design

constraints that are expressed in terms of numerical values

such as space occupation, shapes of spaces, and distance of

stairs connecting relevant spaces, and a combination of

those The genetic algorithm is adopted to yield the space

arrangement formulated as an optimization problem

con-taining multiple objectives The solution to the space

arrangement problem has proven that the designer is able to

generate a specific result due to the degree of freedom

allowed by the formulation The proposed design approach

has led to efficient layouts for general arrangement of

mid-sized superyachts These possible candidates help the

designer to choose a right arrangement based on his or her

design concept or intention, which will make the interior

arrangement task much easier and faster

Keywords Superyachts  Interior space arrangement 

Constraint-based genetic algorithm Weighted sum of

multi-objective optimization problem

1 Introduction The superyacht industry is an increasingly valuable market and an attractive business As of July 2011, the superyacht market has grown by 43 %, and the wide range of mid-sized superyachts shares 70 % of the market [1] Up to now, most superyachts have been built in Europe, where the advanced shipbuilding countries like Italy, Netherlands, United Kingdom, and Germany dominate the passenger ship market Korea and China, on the other hand, have not actively participated in this business, choosing to focus on the production of commercial vessels in which they dom-inate As a result, they fall behind in design and technology stressed in the luxurious interior design of superyachts The conceptual design of superyachts pursues a different direction unlike the commercial vessels that are well equipped with modern technology and advanced engi-neering analyses Systematic research has not been carried out and therefore such publications are very rare

An approach to determine a preliminary hull form of superyachts was published by Nam et al [2] They focused

on the construction of a hull form by the analysis of pre-viously built ships Lee and Byun [3] suggested that the analysis of deck layout could lead the designer towards a systematic way of modern design They also mentioned that, with no universal concept or guidelines, most interior design works were executed by experts in advanced ship-building countries

In regards to the determination of space, a trial attempt for performing an interior space arrangement using the genetic algorithm was introduced, where they tried to convert the design concept into an engineering analysis problem [4] Lee et al [5] suggested that the problem of compartment layout could be improved by using the

J.-H Nam ( &)

Division of Naval Architecture and Ocean Systems Engineering,

Korea Maritime University, Busan, Korea

e-mail: jhnam@hhu.ac.kr

T.-H Le

Department of Naval Architecture and Marine Engineering,

Ho Chi Minh City University of Technology,

DOI 10.1007/s00773-012-0182-1

but did not take the stairs into consideration in spite of their

important role in space arrangement Other efforts for the

optimization of general arrangement of ships were made by

Parsons et al [6] and updated by Daniels et al [7] They

had a number of compartments to be arranged but treated

each deck separately without considering the connectivity

between decks

Evolutionary algorithms, including the genetic

algo-rithm (GA, hereafter), have been recognized as being

efficient in solving complicated optimization problems

The concept of GA was invented by John Holland at the

University of Michigan in the 1960s and popularized by

Goldberg [8] The GA is a method for moving one

popu-lation (strings or genes) to a new one by using a kind of

‘‘natural selection’’ together with crossover and mutation

processes Design variables required in determining the

interior arrangement are treated as constraints that are

combined with the GA In this paper, the GA is adopted as

a primary solver since our problem can be regarded as a

variant of a multi-objective problem

The main contribution of this research is to propose a

method of determining space arrangement based on a

constraint-based genetic algorithm (CBGA) This approach

allows constraints to be added according to specified

requirements and a client’s preferences [9,10] Section2

explains the fundamental concept and the mathematical

formulation required for the optimization of interior space

arrangement Various mechanisms of genetic algorithm

such as encoding, evaluation, production, crossover, and

mutation are applied to the proposed CBGA in Sect 3

Section4 discusses the results of space arrangement

examples performed for different designer’s requirements

2 Formulation of space arrangement problem

In the stage of conceptual design, the designer establishes

major characteristics of a ship without violating technical

requirements, which is normally challenging and

compli-cated In addition, he or she has to satisfy all technical and

aesthetical expectations of the client, who usually has

many requests that may be conflicting with the designer’s

guideline This situation becomes critical and sometimes

even controversial in designing the interior space

arrangement in which no specific engineering formulas

exist The feasible solution is normally obtained by

com-promising the client’s expectations and the designer’s

restrictions The expectations of the client and the

engi-neering restrictions faced by the designer result in a

com-plicated and nonlinear formulation in which a number of

objective functions with design variables and constraints

are involved This kind of problem can be regarded as a

complex example of multi-objective functions

Our space arrangement problem involves multiple, contradictory, and mostly subjective requirements, such as confliction due to the irregular shapes of neighboring spaces and their locations To reflect all the multiple yet conflicting requirements, it is suggested that the problem should be formulated as a variant of a multi-objective function, which can be achieved by converting the effect of multi-objectives to a single value constructed using weight factors normalized

2.1 Problem formulation of multi-deck space arrangement

The space arrangement problem, in the form of a general multi-objective problem, can be defined as Eq (1): Optimize FðxÞ ¼ ½FSpaceðxÞ; FSubðxÞ; FStairðxÞ;

subject to gjðxÞ; j¼ 1; 2; m; ð1Þ where x is the design variables, gj(x) is a set of inequality constraints, and m is the number of constraints Each objective function has its role in the optimization process The first two functions, FSpaceand FSub, relating to the area requirement are defined by:

FSpace¼jAC Alowerj þ jAC Aupperj

ADeck

and

FSub ¼jASub ASub lowerj þ jASub ASub upperj

ADeck

where ADeck, AC, and ASubare the area of a deck, a main space, and a subordinate space, respectively The sub-scripts, lower and upper, represent the lower and upper limits of the corresponding area and they are defined by the user’s preference Detailed descriptions of those spaces will be made later The objective functions, FSpaceand FSub are the sub-fitness values in the percentage of space occupancy of a certain compartment compared to the maximum area of a deck

On the other hand, FStairis the sub-fitness value in the ratio of stair distance obtained to the longest distance in each deck, as illustrated in Fig.1

Our goal is to minimize the sum of stair distance while optimizing the area of space within the client’s preferences

or expert’s requirements The objective function possesses conflicting goals and constraints like the ordinary multi-objective optimization problems

To solve the problem, we assume that each deck is represented by 40 9 11 equally sized grids, following our previous work [4] This assumption comes from the anal-ysis of the current design of general mid-sized superyachts that approximately have the length of 40 m and the width

of 11 m The number of grids is flexible and can be defined differently in the beginning stage The design variables,

shown in Eq (1), are supposed to define spaces and are

assumed to represent the two dimensional coordinates of

spaces on the deck To accelerate the calculation of the

objective function, all values are encoded in integers rather

than in binary Thus, the design variables are real coded

values in our CBGA, which means the chromosome in GA

will be an integer rather than binary or floating

2.2 Formulation as sum of weighted factors

It is important to choose a good objective function in

applying the CBGA to a problem It can have a set of

multiple components but should be represented as a

com-bined numeral value Important design factors such as space

occupancy, shape of spaces, and stair connectivity are taken

into consideration in determining an optimal layout of

spaces in this work Each factor emphasizes the importance

of its own role It would be more plausible, however, to

combine and reasonably balance out the three factors

The fitness value, F, in Eq (3), chosen as an objective

function, is assumed to be the weighted average of the

defined design factors In our research, the combination of

these factors is formulated as a function of a set of

domi-nant factors determining the space allocation such as space

area, stair distance, and shape constraint of space:

F¼wSpaceFSpaceþ wStairFStairþ wSubFSubgShape

wSpaceþ wStairþ wSub

j

The weighting factors balancing the three sub-values

wSpace, wStair, and wSub, should be defined by the designer

in the beginning stage and are set between 0 and 1 It

should be noted that other factors could be added upon the

request of the owner or the designer The constraint

func-tion gj(x) is considered as a penalty function, as discussed

in the coming section

3 Constraint-based GA application for space arrangement

The aim of this work is to suggest a ‘‘good’’initial space arrangement for the designer and the client so that they are able to not only reduce the time that might have been devoted to manual design, but also consider various arrangements previously unconsidered A typical design procedure includes the compromise between different layouts With a set of good layouts in hand, it becomes much easier to reach a final decision It should be noted that the proposed algorithm for the space arrangement, as described in Fig.2, is meant to suggest a probable and reasonable solution rapidly and is subject to a so-called tuning process for a final arrangement

A previous approach to find an optimal space arrange-ment of a superyacht established an objective value of space arrangement that considered rectangular space, connecting information between the two spaces via stairs [4] Even though they applied a GA technique, the results were not fully satisfactory because of its limitations in shape and inefficient convergence, partly caused by the inappropriate application of the GA This limitation has to

be resolved for the practical application of the algorithm

A modified and improved technique is introduced here

A set of design constraints is simultaneously considered in the problem formulation These constraints are incorpo-rated to establish a new constraint-based genetic algorithm (CBGA) that automatically determines the arrangement of various irregular-shaped spaces and stairs Other con-straints are free to be added if necessary

3.1 Major constrained elements Every space is basically assumed to be rectangular, defined

as MAIN space in this work The idea of using equally sized grids in each deck is efficient for the definition of

Fig 1 Definition of fitness

value for stairs

each space Then, a space can be represented by the (x,

y) coordinates of a corner point and by its width and height

The concept of SUB space is significant to consider for

the irregular shape of spaces in real superyachts The SUB

is defined as a sub-compartment connected to a MAIN, as

depicted in Fig.3 The necessity of the SUB space can be

suggested by the clients in the beginning either by their

preference or by technical or performing issues By adding

a SUB to a MAIN, a general, non-rectangular shape can be

generated This irregular shape will add more complexity

in determining the layout of two neighboring spaces

Considering a general shape generated by MAIN and

SUB spaces is not straightforward Instead of allowing

impractical SUB shapes that are either too slender or too

fat, SUBs with a reasonable shape factor defined, gShapeas

a ratio width to length of SUB is introduced in Eq (4) This

assumption is very plausible and can be adopted without

loss of generality

gShape¼ widthðSUBÞ

Another simplification is assumed in positioning SUBs

Even though a SUB can be floating along an edge of a

connected MAIN, the resulting shape of combined MAIN and

SUB can be impractical in most cases in that the SUB could

create unusable spaces for the neighboring space This

dilemma is solved by assuming the position of the SUB fixated at either the top or bottom of a MAIN In other words, the top edge of SUB is aligned with that of MAIN or the bottom edge of SUB with that of MAIN Using a penalty method in the fitness function, an impractical shape can be easily discarded after each generation during the CBGA process

Another constraint considered in the space arrangement

on decks is the stair connectivity Stairs connect spaces or compartments across decks Some stairs should be located within specified spaces for technical and operational purpose Private stairs are preferred for guests as well as the owner, reducing the likelihood of encountering the crew more than necessary With all these constraint factors in mind, our goal

is to find an optimal arrangement of stairs that enables the shortest connection from space to space across decks

In summary, the constraints considered in the problem are gShapeand g(x) functions The role of g(x)s is to avoid the violation of technical requirements or user’s preference

by imposing penalties When the space is encoded into a chromosome, those constraints are evaluated by the corner positions of each space that are expressed in terms of (x, y) coordinates (Table 1)

The information of initial space connection is given in the first step Even though the number of guest and crew stairs can be generally arbitrary, the CBGA will generate the number of stairs based on the connection from space to

Fig 2 A design procedure for

interior space arrangement

Fig 3 Definition of MAIN and

SUB elements

space following the initial recommendation Our assump-tion for the initial layout is described in Fig.4

3.2 Encoding and selection process The proposed CBGA uses the string of x–y coordinates as variables A set of x–y coordinates in this chromosome is exchanged during the CBGA mechanism to generate a new chromosome in next generation Three major elements such as MAINs, SUBs, and stairs encoded to form chro-mosomes are illustrated in Fig.5

Table 1 List of constraints g(x)

Constraints g(x) Technical requirements or user’s

preferences Neighboring spaces (NS) Prevent the overlap of neighboring

spaces (MAIN and SUB) SUB connection (SC) Locate a SUB aligned with the top

or bottom of MAIN where the SUB is supposed to attach Stair location (SL) Prevent stairs from locating

outside specified spaces

Fig 4 Initial layout of stairs

Fig 5 Encoding process for

MAINs, SUBs, and stairs

The steady-state selection is known to be the generic

method of selection of chromosomes [10] Each

chromo-some in the population has a fitness value and the whole

chromosomes are sorted in terms of the fitness value from lowest to highest Some of the lower chromosomes need replacement with better ones The purpose of the replace-ment, called reproduction, is to improve the quality of current chromosomes that will become the components of the next population, expecting the forthcoming individuals achieve the higher fitness values This replacement and deletion strategy is more practical than others because some characters of good individuals are preserved for reproduction while they are destroyed in crossover or mutation processes

The question here is how many of the current chromo-somes are to be replaced From our experiment graphed in Fig.6, the reproduction rate of 90 %, which means 10 % dropout, shows the best performance This trend was also observed in our previous application of the ship hull fairing process [11] Therefore, at a stage,10 % of the population are dropped out to discard the worst individuals and the vacancy is replaced by the new offspring that are regen-erated from the 90 % that survived at that stage

Fig 6 Convergence results for different reproduction percentages

Fig 7 Crossover process for

three major components

Fig 8 Overlap constraint in

crossover process

3.3 Probabilities of crossover and mutation

The efficiency of the CBGA in general depends on the

population size, crossover rate, and mutation rate The

probabilities of crossover and mutation should be changed

at each generation to guarantee diversity and to speed up

the convergence rate in an efficient manner

In our practice, the crossover probability pc and the

mutation probability pmare adaptively applied in response

to the fitness value for every individual in the population If

the values of pc and pm are greater than the default rate,

crossover and mutation processes occur, respectively The

values of pcand pmare documented in Srinivas and Patnaik [12], shown in Eq (5):

pc¼ ðf

0 fminÞ

ðfavg fminÞ and pm¼

ðf  fminÞ

ðfavg fminÞ; ð5Þ where f0is the smaller fitness value of the individuals to be crossed in crossover process, f the fitness value in mutation process, and fminand favgthe minimum and average fitness values of the population, respectively According to the formulations, pc and pm automatically increase when the solution gets stuck at a local optimum or decrease when the solution scatters in the population

3.4 Crossover process The idea of crossover is to exchange the ‘‘parent’’ chro-mosomes in the population to generate the two new‘‘child’’ chromosomes in the next population The examples of crossover for the three major components used in the space arrangement are depicted in Fig.7

Our crossover with probability approaches to real value

of crossover based on the lower and upper bounds of (x, y) components These bounds can be practically described

as the borders (walls) between spaces in the space arrangement problem

It is possible that crossover operation is not feasible owing to the space restriction in our problem For example, after a crossover operation, compartments may be over-lapped to each other As shown in Fig.8, the MAIN space

of i-th individual is successfully transferred to j-th, but the

Fig 9 The mechanism of crossover

Fig 10 Mutation processes

other way is not feasible If that happens, the fitness

function gets a penalty As a result, only the individuals

without penalty will be allowed for mutation Otherwise,

other ‘‘parent’’ individuals will be selected to regenerate

the acceptable ‘‘child’’individuals This mechanism is

described in Fig.9

3.5 Mutation process

Mutation is an exploitation creating a deviation from a

regular population The role of mutation in the CBGA has

been considered to prevent the premature convergence of a solution

In the mutation process with probability, the position of

a stair and the shape of a space are subject to change by moving, adding, or subtracting some rows and/or columns

of grids, as shown in Fig.10 Considering that the large change in the mutation step has seriously affected the convergence [11], we recommend that the numbers of changed grids, dx and dy, be less than 5 % of the total grids

in the longitudinal and vertical directions, respectively, to reduce the chance of possible divergence Then, the new design variables are expressed in term of dx and dy, as given by Eq (6)

Fig 11 Flowchart of proposed CBGA

Fig 12 Space arrangement for requirement of occupancy only (initial and final)

Fig 13 Convergence of fitness value of space occupancy only over generations

½xnew ¼ ½x  dx and ½ynew ¼ ½y  dy ð6Þ

3.6 Proposed CBGA summarized

Figure11illustrates the flowchart of the CBGA technique

for the space arrangement process Each step is

self-explanatory

4 Application examples

In order to demonstrate the proposed algorithm, an interior design of a mid-size superyacht is examined Four exam-ples from a simple case where only rectangular shaped spaces are considered to a complicated combination of all objective functions are extensively investigated The GA

Table 2 Fitness values for

space occupancy User’s preference

(range of area in %)

1st generation (area in %)

1st generation (fitness value)

100th generation (area in %)

100th generation (fitness value) Flybridge 100–100 100 0 100 0

Pilot house 30–35 25 0.075 32 0.025

VIP room 30–35 50 0.175 32 0.025 Master room 24–26 10 0.15 25 0.01

Dining room 24–26 40 0.15 25 0.01

Crew space 25–30 8 0.195 28 0.025 Guest room 30–35 10 0.225 33 0.025 Engine room 30–35 8 0.245 33 0.025 Tender boat 5–10 74 0.665 7 0.025

process implemented in this work was written in C?? and

has shown to converge rapidly in most cases

4.1 Space occupancy for simple rectangular

compartments

As a starting example, a simple case where the space

occupancy is solely considered is examined The shapes of

all spaces or compartments are assumed to be rectangular

to make the problem simpler This problem has a single

objective function that is supposed to satisfy the area

requirement defined by the designer

The result depicted in Fig.12shows a good arrangement following the area requirement Figure13, where the x-axis

is the number of generation and y-axis the fitness value, demonstrates that the given problem rapidly converges Technically, the solution of this simple problem depends

on the range of each area requirement The solution would become unique if the upper and lower bounds of areas were sufficiently close The fitness values obtained over gener-ations are listed in Table2

4.2 Space occupancy with SUB elements Quite a number of existing superyachts possess non-rect-angular compartments commonly used to represent crew space, galley, and lobby A non-rectangular shape consid-ered as an additional space attached to a compartment was defined as a SUB Taking care of SUBs in the algorithm requires the higher value of the corresponding weighting factor and naturally increases the computing time Fig-ure14 displays the initial and final arrangement of given spaces and the convergence rate is graphed in Fig 15 4.3 Shortest stair passage

The stair connectivity between spaces is also an important design factor In this example, the shortest connection between stairs among crew space, galley, lobby, and fly bridge is selected as an objective function This specific stair connectivity is intentionally made up for the test of the

Fig 15 Convergence of fitness value of SUB implementation over

generations

Fig 16 Space arrangement for requirement of shortest stair connection (initial and final)