Trans RINA, Vol 152, Part B2, Intl J Small Craft Tech, 2010 Jul-Dec
may be obtained using the Decision Support Problem Technique (DSPT) [7,8]. This technique deals with multi-objective optimisations. Goal programming and sequential linear programming are the basis of the compromise decision support problem, and adaptive linear programming algorithms for multi-objective optimisation. One such model for the design of a racing yacht was developed by Pal [9]. Some of the works of the first author and his associates on the successful application of this technique to design various types of marine vehicles at the preliminary design stage are for trawlers [10,11],
tugs [12], hatch-coverless container
ships [13,14], river catamarans [15], catamaran ferries [16,17], monohull ferries [18,19] and SWATH ferries [20].
2 HULL GEOMETRY
The model in the study is of a simplified hull configuration with keel fin (not fitted with bulb) and a rudder freely hinged at the aft end of the yacht. The keel volume is such that the required mass of ballast is fully contained in it. The sail configuration consists of a masthead rig with mainsail and headsail only. The yacht is constructed of single skin fibreglass.
3. MATHEMATICAL MODEL
A mathematical model is developed to solve the complicated design problem as a compromise decision support problem. This problem is solved by decision support problem technique (DSPT) [7,8].
The cruising sailing yacht design model is described as shown below:
Given: a) A set of owner’s requirements (Table1): • Number of cabins • Number of berths • Number of days at sea • Restriction of draught • True wind speed
b) A set of five goals • minimisation of resistance • minimisation of heel angle • minimisation of cost yacht • maximisation of velocity made good • minimisation of total mass.
Find: a) System variables (twenty nine) defined in Table 2: System variables are free variables that are chosen as non-dimensional functions of design parameters, or ratios of design parameters, that are used for defining the geometry of the vessel and rig configuration. The values of the variables vary between zero and one. The lower
and upper limits of the design parameters are chosen from the data of about 250 recently built cruising sailing yachts (data obtained from the web pages of various yacht builders in 2003).
b) Deviation variables (ten): Deviation variables are due to under-achievements ( i ( id+
d− ) and over-achievements ) of the five goals, and equalisation of displacement
and total mass. These deviation variables are: 1
d− , 2d− , 3d− , 4d− , 5d− , 1d+ , 2d+ , 3d+ , 4d+ , 5d+ .
Satisfy: a) Six system constraints: • maximum draught is less than restriction on draught
• Density of ballast material is less than that of lead • Volume of keel and rudder is less than 20 per cent of canoe body volume
• Block coefficient is greater than 0.3 • Displacement and mass must be very close within a tolerance
(0.1%) to ensure numerical
convergence. This is transformed into two inequality constraints to cover exceedance and shortfall.
b) Upper and lower bounds on the 29 system variables must be satisfied: 1.0 > Xi >0.0 for i = 1:29
(c) Five goals to be achieved as far as possible: Goals (1) = 1.0 – TRTOTR/RTOTMV (minimisation of resistance) Goals (2) = 1.0 – TRHLAN/HEELMV (minimisation of heel angle) Goals (3) = 1.0 – TRYTCS/YATCST (minimisation of construction cost) Goals (4) = VMGMAX/TRVMG – 1.0 (maximisation of
velocity made good) Goals (5) = 1.0 – TRMSTL/MASSTL (minimisation of total mass)
The aim is to minimise the objective function i.e. to reach a solution for which the goals are as close to zero as possible
The general Archimedean formulation of the objective function (deviation variables only) is:
Z ( id− + P4 ( 4d−
, i ) = [P1 ( 1d− d+
d+ , 4 ) + P5 ( 5d−
, 1 ) + P2 ( 2d− , 5d+
d+ )]
where, P is a subjectively chosen weight of each deviation.
The Archimedean formulation of the objective function is the weighted sum of the present five-goal
d− i , id+ problem, the deviation is chosen arbitrarily as 0.2.
deviation variables. For weight of each
, 2 ) + P3 ( 3d− d+ , 3d+ )
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©2010: The Royal Institution of Naval Architects
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