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CON THE OPTIMIZATION OF HULL FORMS WiTH
RESPECT TO SEAKEEPING
GJ.Grigoropoulos T.A.Loukakls
Naval Atchitect, PhD Prof. N.T.U.A.
ABSTRACT
A method for
analytical seakeeping optimization is described. The method Is based on a computer code with predicts seakeepingperformance when the ship profile, the design waterline,, the sectional area curve and the distribution along the ship of the centroid, KB(x),
of the
cross sections are prescribed.The code can
automatically generate variant hull forms differing from a parent In.the main
dimensions and in one or more parameters such as Cp, LCF, LCB,
KB distribution, Cp etc.
When appropriate ranges for the principal characteristics and
parameters of the hull form under Investigation are prescribed, a
formal optimization procedure is used to obtain the variant with the
best seakeeping behaviour. The optimization procedure uses as
objective function the weighted average of a number of peak ship
responses In regular waves for a number of ship speeds and headings
and determines the optimum hull form using the HoOke and Jeeves
Algorithm.
The applicabfflty of the method is demonstrated using as examples a
reefer ship, a containership, a destroyer-type ship and a fishing vessel.
1. INTRODUCI'ION
Seakeeping Is the branch o Naval Architecture, which deals with the prediction of the dynamic behaviour of the ship in waves. Indeed, this
has been the main goal of Seakeeping from the development of the
first practical strip theory In 1955 by Korvin-Kroukovsky1 until 1980,
when Bales2 published a paper formally treating the optimization of
seakeeping performance of Destroyer-type hull forms. By that time
the analytical tools available to the profession have been shown to be
reliable enough to be used for optimization purposes, whereas
seakeeping experiments cannot be used for the same purpose due to
the excessive time and cost involved.
The description of the efforts of several researchers
In the area of
Seakeeping optimization during the last decade can be found In Ref. 3
by Grigoropoulos and Loukakis and a similar description of earlier
efforts can be found in Ref. 4.
In the aforementioned Ref. 3
a new method for
developing hullforms with superior seakeeping qualities was presented. The new
method was used for the analytical development of an optimized hull
form for a reefer ship. Models of both the parent and the
optiinimum hull forms were tested at the Towing Tank of N.T.U.A. and the analytical predictions have been experimentally vetlfled.
The purpose of the present paper is to present additional results for
the reefer ship and to
further demonstrate the applicability of the new optimization procedure using three other hull forms:a containership, a destroyer-type hull form and a fishing vessel.
2. SEAKEEPING CONSIDERATIONS IN SHIP DESIGN
AND THE NEW METHOD
The Incorporation of superior seakeeping qualities In
a new ship
design is obviously desirable, although seakeeping is not usually a
dominant parameter In the design process, especially for merchant ships.
However, recent studies have shown that seakeeping considerations
can and should be incorporated from the beginning in the design
procedure but that there is also room for considerable seakeeping
Improvements even when the displacement and the principal
characteristics
of a new design have been determined without any
seakeeping considerations.
The new method has been developed with the above two application areas In mind, that is It can either be incorporated directly in the
preliminary design spiral or It can be used to modify a parent hull
form.
In both cases the objective of the new procedure is not to ensure,
for example, that a hull. form will have less than a predeterminedamount of deck wetness in a specified sea state. Nobody designs
ships In this manner. The objective Is to ascertain that a ship designed with a very complex objective function and many practical
constraints In mind, will have as good seakeeping qualities as possible. The last reservation is In order because there are Indications
that Increased seaworthiness is usually accompanied by somewhat
increased resistance. However, as it will be discussed in the sequel, the interplay Is not really between seakeeping qualities and ship
resistance. Rather, the real problem Is how to ensure good
propulsion characteristics both In calm water and in waves, coupled
with good seakeeping performance. That Is the propulsion system of the ship should be Included in the optimization scheme.
3.. A BRIEF DESCRIPTION OF THE NEW METHOD
The new method for optimizing hull forms for seakeeping has been
described In detail In Refs. 3 and 5. However,
for the sake
ofcompleteness, the main tools and assumptions of the method and a
brief description of the formal optimization scheme will be presented
3.1 Hull Form Desrlption
The hull form is described lfl adequate detail for seakeeping
calculations, but In a simple form to allow for the generation of the
man variants required by the op;Irrj12tiOn scheme. Thus, the
hull form Is considered to be known If the following characteristics
are specified: the main dimensions LBP, B, T the sectional area curve S(x), the waterline curve B(x), the longftudinai profile curve Z(x) and
the curve of the loflgitudinal distribution of the centroids of the ship
sections KB(X).
From these curVes all traditional ship design variables can be derived
I.e. A, CB, Cp, CM, Cvp, Cp, LCB, LCF, KB e.t.c.
3.2 Hull Form Variants.
To obtain variant hull
forms from a parent,
described as above,Lackenby' S6 method was extended so that waterlines and sectional
area curves of any shape can be accomodated and, more Important,
that any of the
six form parameters {Crp, LCF, CB, LCB CM,
KB(x)) can be. independently varied. Thus, vaiiant hull forms differing In one parameter otily can be generated and by successiveapplications of the method, hull forms with prescribed values of these parameters are obtained.
3.3 AnalytIcal Tools for Seakeeping Calculation
As is common practice in all seakeeping optimization work a strip theory7 Is used for the calculations, coupled in the ptesent method
with a threepararneter LewLs-forrn representation of the ship
sections. In the Usual two-parameter Lewis-form representatiOn of
ship sections, the beam, the draft and the ectiona1 area. describe the
section. The aforementioned description of the hull form provides the
required third parameter KB(x), the centroid of the section. In this
manner, a more detailed description
of the hull
forth Is available,which has been shown8 that it can have an important effect on the
calculations.
3.4 The figure Of metit
To obtain an optimum solution a figure of merit should be specified.
lii contrast to other methods, which In general use the seakeeping
performance at sea to define a flgure of merit, the present method
postulates that
"ship responses at sea are rninirrium when the corresponding
peak value of their Response Amplitude Operator (R.A.0) is minimum" and that, therefore. seakeeping optimization
can be athleed on the basis of regular wave results only.
Numerical compUtations have shown that this assertion is true for ships with displacement and dimensions close to those of the parent hull form.
However, the magnitude of the peak value Of the relatIve vertical
motion R.A.O. is not adequate to describe seakeeping events related
to the underwater part of the hull, as bottom slarnrriing and propeller ernergenée. Thus, these events can not be expUcitly lnàluded In the
optimization process and the correspondUg peforrnance of the
optimum hull form can be established only a posteriorl. This is a
slight shortcoming when, draft Is kept constant or Is changed only a
little
ftom the
parent, because the mjnimlzatlon of the relativemotion provides a strong indication that the corresponding seakeeping
events wifi also be reduced. 3.5 The optimization problem
With the previous discussion in mind, the opthnivtion problem. can
be stated as follows:
Find the variant with the optimum seakeeping performance of a parent hull form, described by the set of four curves S(x), B(x),
6
Z(x) and KB(x) and Identified by the set of design variables (LBP,
B, T, CB, C, LCB, LCF, KB) under given constraints.
Seakeeping performance Is expressed as
the wlghted sum of the
peak values of a prescribed set of ship responses In regular waves, for various ship speeds and headings. Optimum performance
corresponds to the minimum value of this sum, which Is the object
function of the problem.
The constraints to be Included In the optIrnI2atIon problem are
classified In the following two categories:
Equality conditions established by hydrostatic and stability considerations or economical reasoning.
Inequality constraints imposed by common design practice
limitations.
- In the first class of constraints the following relations are included:
The relation between the displacement, the main dimensions
and the block coefficient:
S = CB * LBP
* B * T
= constantGeometrical relations that hold between the various form
parameters, Le.
I
CB=CV,rp*C\rp
I
CB= CM *CHP
In the second class of constraints the following Inequalities should be taken into account for reasons shown In parentheses:
I
LCB1<LCB<LCB2 ()
GM>GMM (transverse stability)
CWp1<CW<Crp2 (deck space, calm Water resistance)
CM1<CM<C,1j (calm water resistance)
The following characteristics of the opt ion problem can help In selecting the appropriate optimization method:
the non-linearity of the constraints
the existence of both equality and inequality constraints the unlmodality of the object function, experimentally
verified by setting up the optimization procedure from different starting points and arriving at the same result
O the continuous character of all decision variables.
On the basis of the above the direct optimization method proposed
by Hooke and
Jeeves9 In conjuction with the External PenaltyFunction Method1° has been selected. The External Penalty Function Method is used to convert the constrained optimization problem to
an unconstrained one and Is more efficient than the Internal Penalty
Function Method. The method of Hooke and Jeeves is simple to
program and has found to be very effective for the particular
optimization problem in comparison to other direct search methods.
4. APPLICATIONS OF THE NEW METHOD
The optimization procedure has been applied In four cases, which will
be presented In this section. But before proceeding with the
presentation, it should be clarified here that the hull forms, which are
developed by the computer code, do not possess fair ship lines. The representation of their cross sections is
the one provided by the
three- parameter Lewis-form, see for example fig. 4. Thus, when the
optimization procedure has yielded an "optimum hull form", a set of ship lines which
incorporate as many of the
characteristicsof the
analytical calculations as possible, should be developed manually. Obviously, the seakeeping characteristics of this final hull form will be
8
corresponding to the afOre mentioned procedure will be 1abeled "parent", "optimum" and "faked opthnum".
For all cases treated, the object function necessary fOr the
optimization procedure was chosen as
the sum of the peak R.A.O.
values for vertical acceleration and relative motion axa point
0.1LBp behind the forward perpendlicular. 4.1 The reefer ship case
For an Initial experimental verification of the optlinitatlOn procedut
the hull
form of
a93.4 m long
reefer ship was selected andoptimized with respect only to secondary hull form parameter, i.e.
LCB, LCF and KB(x). In this way the contention, that even
with cOnstant principal characteristics the seakeeping performance of a
ship can be significantly improved, could be Validated..
The principal and secondary hull fotm characteristics of the "parent", "optimum" and 'Taired. optimum" for the reefer Vessel are shown in
Table 1. In the same Table the r.m.s. values for the vertical
acce1eraton and vertici telative motion ax a point 0.1 *LBp behind
the Forward Perpendicular are shown. The seakeeping resUlts pertain to a sea State With a significant wave height H'/3=4 m and a modal
period Tp=10 sec The ship speed for the calculations was 14 knots.
The constrained secondary hull form parameters were allowed to
change during the optimization as follows:
8(LCB, LCF)=±0.O4LBp, 8Cp=±0.04Cjp, 6KB=±O02T
From the contens of Table 1
it can be seen that In order to obtain
an optimum hull form
the procedure Increased C, shifted LCF
forward and shifted the VCB downwards, all as much as allowed. It
The optimized hull form had a considerable reduction In both
acceleration and relative motion in comparison to the. parent by 19%
and 21% respectIvely. However, when a set of ship lines had to be
produced, not all characteristics of the "optimum" hull form could be retained and the "faired optimum" hull form was developed for which
the reduction of the aforementioned responses was 13% and 16%
respectively. The body plan of the parent and the falred optimum hill forms are shown In Fig. 1.
PARENT HULL
- OPTIMUM HULL
'C
Fig. 1:. Body Plan of Parent and Faired Optimum Reefer Ship
- - - - I.
--
-WauJFihj
-
/ I.../ 4111ArF &UF'.
-
I I / I,,! \\ - I /A.
ii -r ' /
- - --------
p. 2 2 ITahkl: Gcomctrfcil CharacterIstfc. and Seakeeping Responses of Optimization Examples
CASE L8p B' T Ap C8 Cp CM Cp LCB LCF KB V.ACC.. R.MOT.
[mj, [rn] [rn] [t] [m2] [%L.BP] [%LBp:J [rn] [m/s2] Em] REEFER PARENT 93.4 17.0 6.5 6108 1222 0.577 0.749 0.974 0.770 -3.23 -5.04 3.62 2.056 2.116 REEFER OPTIMUM CONSTANT LBPB,T 93.4 11.0 6.5 6108 1284 0.577 0.713 0:.1985' 0.809 -2.33 -0.98 3.49, 1:666 _19% 1.722 -21%
REEFER FAIRED OPT
CONSTANT L8.8.T 93.4 17.0 6:5 6108 1256 O577 0.730 0.979 0.790 -1.67 -1.24 3.64 1.793 -13% 1.821 -16% REEFER OPTIMUM 1 'VARIABLE L8.8 89.9 16.2 6.5 6108 1306 0.634 0.705 0.985 0.899 -2.21 -1.23 3.49 1.493 -27% 1.619 -26% REEFER OPTIMuM 2 VAP.IIABLE 98.1 16.2 6.5 .6108 1220 0.577 0.149 0.97.4 0.770 -3.23 -1.46 3.62 1.719 1.784 LBP,B -14% -18%
DESTROYER PARENT 128.0 15.1 4.2 3135 1359 0.450 0:639 O.759 0.704 -3.11 -6.41 2.58 2.112 2.016 DESTROYER. OPTIM. CONSTANT 128.0 15.1 4.2 3735 1438 0.450 0.604 0.747 '0.745 -2.98 2.60 2.49 1.721 1.689 LBP.BT -21% -16% CONTAINER' PARENT 11,75.0 25.4 9.5 244.94 3153 '0.566 '0.1,98 01.957 0.709 -2.01 -3.91 5.20 1.115 '2.036 CONTAFNER OPT'I'M. '175.0 CONSTANT L8B.T 25:4 9..,5 24494 3293 0:566 0.764 ogs8 0.741 -1.00 0.32 . 5.01 0.1910 -18% 1.722 -15% IRLIIANTIIU I'Ak[NI 12 96 3 826 1 0 20 2 30 60 0 396 0 641 0 720 0 618 -3 31 -0 05 0 60 3 010 0 432 TREHANTI'RII OPTIM, CONSTANT L8,B..T. 12.96 3.826 1.0 20.2 31.65 '0.396 0.62.1 0.71.9 0.638 0.46 3.52 0.58 2.680 -'11% 0.367 -15% iR[IIA.FAIQID OPT. CONSTAW[ 12.96 3.626 1.0 20.4 31.20 O.'iO4 0..63 0.113 0.634 -1.91 0.98 0.61 2.802 0.402 L8pB..T -7% -1%
N S N T0 0 A.V.A. = Absolute Vertical Acceleration R.V.M. = Relative Vertical Motion
Fig. 2: Analytical and Experimental Responses. Reefer Ship.
V5=14 knots. ANALYTICAL RESULTS PARENT HULL
- OPTiMUM HULL
EXPERIMENTAL. RESULTS * PARENT HULL S QPTIMTJM HULL-N N N C' C 12 ANALYTICAL RESULTS PARENT HULL
- OPTIMUM HULL
EXPERiMENTAL RESULTS * PARENT HULL o OPTIMUM HULLFig. 3 : Analytical and Experimental Responses. Reefer Ship.
Two meter models with these lines have been bull and tested In the Towing Tank of NTUA for both resistance and seakeepitig. As it has
been reported in Ref. 3, the resistance Characteristics
of the two
models were quite sitnilar with the parent being somewhat better at the higher speeds, whereas the optimized hull fOrm was superior to
the parent In waves, as predicted. The analytically determined r.m.s.
vertical acceleration and vertical
relative motion for the two hull
forms Is shown In FIgs. 2 and 3 for ship speeds V5=l4 knotS and 17knots. As it can be seen frrr these figures the superior seakeeping
performance of the optimized hull form Is preserved for all sea
states and headings and for the higher speed, whereas the
optimization was done for head seas and V5=l4 knots only. On the
same figures the experimental results are plotted
and one
canobserve that the predicted differences in seakeeping performance are
to a large extent verified experimentally, even though the absolute values of the responses might not be predicted accurately by strip theory calculations, as Is hi particular true for the relative motion
response.
To further demonstrate the Use of the method, the optimization was
performed on the reefer hull form under the following constraints:
z,T=constant, 8LBp=±O.O5LBp, 8B=±O.05B
ÔCB=±O.1CB, ÔKB±O.02T, 6(LCB,LCF)=±O.O4Ls
In this case no restriction was imposed on Cp but the waterplane
area was allowed to increase by up to 7%.The results of this optimization are aLso shown In Table 1, where the case is denoted as "Reefer Optimum 1". In this case the optimization
has yielded a shorter, less bearny and fatter ship, with a very large
waterplane coefficient. The vertical acceleration and relative motion in
this case are further reduced by 27% and 26% respectively, but the resulting hull form Is not practical from the resistance point of view due to the excessive waterplane coefficient.
14
The final optimization example for the reefer ship Is also shown in
Table I and Is denoted as "Reefer OptImum 2". The constraints
imposed In this case are the same as for the previous except for the
value of Cp, which is kept constant. As It can be seen from the
Table, the optimum hull form Is longer, narrower and with LCF
shifted considerably fOrwards. The rrns values for vertical acceleration and relative motion are reduced by 14% and 18% respectively. If this
hull form has also reduced resistance characteristics, It might
represent a better alternative for the final product than the parent.
An indication of the relative resistance characteristics between the two hull forms can be obtained using the FORMDATA method which
gives a 10% advantage in resistance to the optimized hull form for a ship speed of 17 knots.
4.2 The contalflership case
As a second example, the hull form of a successful large containership was selected for optimization. This hull form, denoted as S-175, Is being used by the International Towing Tank Conference as a vehicle for comparative seakeeping studies and in this case the
accuracy !
analytical results has been verified experimentally. The
optimization was performed on the secondary hull form parameters only and the results are shown also in Table 1. The body plans of
the two hull: forms, In three -parameter Lewis-form representation are
shown in FIg. 4. The ship speed of the optimization corresponds to
Fr.No.=0.2 and the sea state is
the same as
for the reefer ship.From the contents of the Table It can be concluded that by increasing Crp, moving LCB and LCF forwards and lowering VCB, the vertical
acceleration and relative motion are reduced by 18% and 15%
respectively. The analytically determined, i-ms vertical acceleration for
Fig. 4 Body Plan of Parent and Optimum Containership. Lewis-form
representation
4.3 The Destroyer-type case
The characteristics
of the parent and the optimum hull
form are
shown in Table 1. On the basis of the optimization results, which was performed on the secondary hull form parameters only, at Fr.No=O.3
and for the same as previously sea state,. it can again be concluded that by increasing C, moving LCB and LCF forwards and lowering
VCB, the vertical acceleration and relative motion can be reduced by 21% and 16% respectively. The anaiytically predicted ship responses for the two hull forms are shown in Fig. 6.
\\\i\
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v,
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Ii ,./
/
/ / /
/
/1 1 1f
I,/
/ /
/1 ,/,/
/
#/./
/ (;Ii';'
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PARENT HULL OPTIMUM HULL-16
ANALYTICAL RESULTS PARENT HULL
- OPTIMUM HULL
ANALYTICAL RESULTS PARENT HULL
- OPTIMUM HULL
Fig. 6 Analytical Responses of Destroyer-type Hull Form.
4.4 The fishing vessel case
The final example of seakeeping optimization pertains to a hull form
particular to fishing vessels of the Trehantiri type, which abound In
Greek waters. By performing the optimization for the secondary hull form parameters only, at a ship speed corresponding to Fr.No.=O.3 and for a sea state with a significant wave height H1/3=1.2 m and a
modal period Tp=5.48 sec, the results of Table 1 were obtained. The
optimum result was again achieved by increasing Cp, moving LCF
and LCF forwards considerably and somewhat lowering VCB. After these modifications the values of the vertical acceleration and relative motion were reduced by 11% and 15% respectively. Nevertheless, no
hull form reminiscent of a trehantiri could be designed on the basis
of these characteristics. When, finally,
a set of ilnes was produced,
the computed seakeeping performance did not show considerable
Improvement. The characteristics of the parent, optimum and faired
optimum trehantiri hull forms are shown In Table 1. The body plans
of the parent and the faired optimum are shown In
Fig. 7 and the
analytically computed seakeeping performance of these two hull forms Is shown In Fig. 8.
18
PARENT :HULL - OFTIMUM: HULL
Fig. 7 : Body Plan of Parent and Faired Optimum Fishing Vessel.
--
-:
2 ( -I,J
4/
\....
II
S/
L
:N
ANALYTICAL RESULTS PARENT HULL
- OPTIMUM HULL
20
5. DISCUSSION AND CONCLUSIONS
The main advantages of the present seakeeping optimization method
can. be summarized as follows:
The use of the three-parameter Lewis-form representation of
the ship sections allows the desirabifity of U forms or V form to be Investigated.
The method Is suitable for immediate incorporation in the
preliminary design spiral and It can readily accommodate all necessary design constraints.
The method Is very efficient so that It can nm on a personal computer as It circumvents the need of computing both the full
R.A..O. and the performance at sea for all hull form variants. The method does not. depend on empirically imposed seakeeping
criteria.
The method Is complemented by the suggestion that the final
assessment of seakeeping performance should include propul-sive performance In waves.
To ifiustrate the last of the above points, the powering diagrams of
both the parent and the optimum hull form of the reefer ship are
shown in Fig. 9. The iflvoluntary speed reduction curves are computed by taking, Into account the added resLstance in waves and computingthe maximum attainable ship speed on the basis of the engine and propellet characteristics (assumed to be the same for both ships in this case). From these curves It can be concluded that the reduced
added resistance of the optimum ship compensates in the higher sea
states for her slightly higher calm water resistance. The voluntary
speed reduction curves, which complement the powering diagram,
indicate that the vertical acceleration has reached a predetermined
limit. The combined Involuntary-voluntary speed reduction curve
determines the region of operation of the vessel at sea arid therefore it describes the capability of the Vessel to fulfill Its transport mission
economically. The expanded region of operation
of the
optimizedvessel Is a very strong indication of the effect of good seakeeping
characteristics on overall ship performance.
most obvious changes ifl hull fOrm geometry, which are beneficial to
seakeeping, are the Increase of the waterplane area and the shifting
of Its center of area forwards. As these changes are usually accompanied by an Increase in ship resistance, one has to be careful In specifying the amount of permissible changes In the values of these parameters. More generally, all constraints should be specified by an
experienced Naval Architect., since creative ship design cannot be done
by the computer alone.
All optimization examples were performed with respect. to vertical
motions only. This is adequate because lateral motions, especially roll, can be treated by blldge keel design, rudder and skeg design,
anti-rolling devices, changes in GM etc.
Finally, it seems that the optifliization procedure Is insensitive to ship speed and/or heading, which greatly reduces the computation effort.
On the basis of the above it can be concluded that the inclusion of
the seakeeping performance In ship design Is both desirable and possible by the use of the method presented herein.
18
is
14 12 1 C' I. nvolutitary SDeec : 11.85 kn OPTIMUM _ 0RM PARENT 0RM- .-.
_kj2
! eCk Wetness ano S1ar;
\
I=4.L1m
Absolute Vertical Acceleration at 10% of LBP aft of F.P.
(0.2 g rins)
Criteria are not eceeCe
Vo i untary
Soeeø Reudt ion
4
_6
Hi/a rrj
Fig. 9: Powering Diagram in Waves. Reefer Ship in Fully
Developed Head Seas.
6. LIST OF REFERENCES
Korvin-Kroukovsky, B.V.(1955). IEivestlgatlon of Ship Motions In
Regular Waves. Trans. SNAME, VoL 63
Bales NK. (1980). OptimIzing the Seakeeping Performance of
Destroyer-Type Hulls, 13th ONR Symp on Naval Hydrodynamics Tokyo, Japan.
Grigoropoulas G.J. and Loukakls TA. (1988). A New Method for Developing Hull Forms with Superior Seakeeping Qualltles. CADMO 88. Southampton. Great Britain.
Report of the Seakceping Committee. 17th I.T.T.C. (1984)
Gdteborg, Sweden.
Grigoropoulos GJ. (1988). Hull Form Optimization with Respect to Seakeeping, Ph.D. Thesis,, N.TIJ.A., Athens, Greece
Lackenby H. (1950). On the Systematic Geometrical Variation of Ship Forms, Trans. INA, Vol. 92, p. 289.
Salvesen N., Tuck E.O. and Faltlnsen 0. (1970). Ship Motions and Sea Loads, Trans. SNAME, Vol. 78, pp. 250-287.
Athanassoulls GA. & Loukakis TA. (1985). An Extended-Lewis
Form Family of Ship Sections and Its. Applications to Seakeeping
Calculations, LS.P., Vol. 32, No.366, pp.33-43.
Hooke
R. & Jeeves TA.
(1961). DIrect Search Solution ofNumerical and Statistical Problems, Journal of Assoc. for Computing Machinery, VoL8, No.4, p. 212.
Wangdahl G.E. (1972). The External Penalty Function
Optimization Technique and Its Application to Ship Design, The Uzth. of Michigan, Ann Arbor, Rep. No.129.