This document discusses the optimization of a floating platform mooring system using a genetic algorithm. It describes using Mimosa software to analyze the mooring system and calculate platform responses under different environmental conditions. An objective function is formulated to minimize platform offset, and a genetic algorithm is implemented using this objective function to optimize mooring line properties like length, size, and material. As a case study, the genetic algorithm was used to optimize the mooring system of a floating unit with 10 lines, reducing platform responses by up to 3.5 times compared to an ordinary design.

1. Optimization of a Floating
Platform Mooring System Based
on a Genetic Algorithm
Aidin Rezvani Sarabi
Nelson Szilard Galgoul
NSG Engenharia, Projetos e
Representacao Comercial Ltda.
Sesam Users Conference – 03.Dec.2012 1

2. Objective
 Optimization of the platform heading
 Optimization of the mooring pattern
 Searching for the tension or length of the
mooring lines
 Choosing the optimum line material and size
Sesam Users Conference – 03.Dec.2012
2

3. Choosing an Optimization
Method
 Many optimization problems in practical
engineering are quite hard to be solved by
conventional optimization techniques.
 So there has been an increasing interest in
solving such hard optimization problems by
imitating the behavior of living beings.
Sesam Users Conference – 03.Dec.2012
3

4. Choosing Optimization Method
 Simulating the natural evolutionary process of
living beings results in stochastic optimization
techniques called evolutionary algorithms.
 The most widely developed type of
evolutionary algorithms are known today as
Genetic Algorithms (GAs).
Sesam Users Conference – 03.Dec.2012
4

5. Genetic Algorithm Fundamentals
 GAs work with a coding of the solution set, not
the solutions themselves
 GAs search for a population of solutions, not a
single solution
 Genetic Algorithms use payoff information
(Fitness Functions), not derivatives or other
auxiliary knowledge
 GAs use probabilistic transition rules, not
deterministic rules
Sesam Users Conference – 03.Dec.2012
5

6. Analysis of Mooring System
using Mimosa
 First, Mimosa determines an equilibrium
position by applying a numerical procedure
that solves the equation below:
F (
mo 1 2 6 cu 1 wi 2
)
x ,x ,x +F x +F x + f x =0
wa 6
() ( ) ( )
 The solution to this equation is the
equilibrium position that defines the
platform coordinates and heading under
static loads
Sesam Users Conference – 03.Dec.2012
6

7. Analysis of the Mooring System
using Mimosa
 The actual platform motions are computed
by performing a dynamic analysis, where the
corresponding responses are categorized as
high frequency (HF) and low frequency (LF)
motions
 The HF responses are calculated using a
linear spectral analysis.
Sesam Users Conference – 03.Dec.2012
7

8. Analysis of Mooring System
using Mimosa
 The LF responses are horizontal motions
(Surge, Sway and Yaw) which result from the
solution of equation below:
 
M x LF + C x LF + Kx LF = FLF
Sesam Users Conference – 03.Dec.2012
8

9. Analysis of the Mooring System
using Mimosa
 In order to calculate the extreme values for
the combinations of HF and LF motions,
Mimosa uses a heuristic equation which is
based on model tests and simulation studies
as given in the equation below for one
variable
 x LF + x HF 
tot  Sign ext 
x = max  
ext HF LF
 x Sign + x ext 
 
Sesam Users Conference – 03.Dec.2012
9

10. Objective Function Formulation
 Each floating unit has six degrees of freedom
(DOF) which include surge, sway, yaw, roll,
pitch and heave. The mooring system is only
capable of controlling the surge, sway and yaw
responses i.e. horizontal responses.
 To reduce roll, pitch and heave, i.e. vertical
responses, the vessel shape and dimensions
may be optimized.
Sesam Users Conference – 03.Dec.2012
10

11. Objective Function Formulation
 Here optimization of the mooring design,
means to minimize the surge and sway
responses. Surge and sway are platform
longitudinal and transverse displacements
Sesam Users Conference – 03.Dec.2012
11

12. Objective Function Formulation
 Minimizing the horizontal translational
response (Platform Offset) is our optimization
problem objective function.
 The objective function of the mooring design
optimization problem, the optimization
parameter boundaries and the problem
constraints could be defined as:
m
i =1 i
2 m
[(
Minimize : ∑ a .∆ i (α ) = ∑ a ∆x i (α ) + ∆y i (α )
i =1 i
2 2
)]
α j min ≤ α j ≤ α j max , j = 1,...n


Subjected to : 
 g (α ) ≥ 1.67 , k = 1,... p
Sesam Users Conference – 03.Dec.2012
 k

12

13. Penalty Function Formulation
 The sequence presented in the previous slide
has led to a constrained optimization problem
which now must be solved
 The penalizing strategy is chosen to handle the
constraints. So a constrained problem is
transformed into an unconstrained problem by
penalizing unfeasible solutions. The penalty
function is described as below:
 Pi = 1 if g i, k (α ) ≥ 1.67 , i = 1...m , k = 1,..., p



0.5 ≤ P ≤ 0.9 if g < 1.67 , i = 1...m , k = 1,..., p

 i i, k
Sesam Users Conference – 03.Dec.2012
13

14. Fitness Function Formulation
 Fitness is a quality value that is a measure of
the reproducing efficiency of individuals in a
population.
 A potential solution with a higher fitness value
will have greater probability of being selected
as a parent in the reproduction process.
Therefore, the minimization problem must be
transformed into a maximization problem of a
fitness function, using the following
expressions: ∆
2
 ϕ 
ϕi =
2
i
Fi = 1 − i
 ϕ .Pi

∆ avg  max 
Sesam Users Conference – 03.Dec.2012
14

15. Genetic Algorithms
 As already mentioned above GAs differ from
conventional optimization methods and
search procedures in several fundamental
ways. A GA’s basic execution cycle can be
described by the following steps:
 Step 1: Reproduction
 Step 2: Recombination
 Step 3: Replacement
 If some convergence criteria is satisfied,
Stop
Otherwise, go to step 1
Sesam Users Conference – 03.Dec.2012
15

16. Implementation Details
 1- Coding Design Variable
 Design variables were coded using a fixed-length
binary-digit {0,1} string
 2- Decoding
 To obtain the real values of the design variables in the
domain region, each chromosome must be decoded
 3- Offset Computation
 Dynamic analyses are carried out in the frequency
domain using Mimosa
 4- Fitness Function Calculation
 The fitness value of each chromosome is computed by
considering offset values obtained from Mimosa
Sesam Users Conference – 03.Dec.2012
16

17. Implementation Details
 5- Selection
 Chromosomes are selected as parents to produce
children and this selection depends on fitness values
 6- Crossover Operator
 The two-point crossover operator (2X), has been
adopted herein, for example “000000” and “111111”
make “001100” and “110011”
 7- Mutation Operator
 This operator changes the bit from 1 to 0 or vice versa
 8- Generation Gap
 It is a parameter that controls percentage of the
population that will be replaced in each generation
Sesam Users Conference – 03.Dec.2012
17

18. Computational Procedure
 1- Start
 Initialize parameters: population size, crossover and
mutation probabilities
 2- Seeding
 Initial population is generated randomly
 Initial population is decoded
 Fitness value of each individual is computed by using
the Mimosa software applying fitness equation
 3- Reproduction
 Chromosomes are selected as parents
 Application of the crossover operator
 Application of the mutation operator
Sesam Users Conference – 03.Dec.2012
18

19. Computational Procedure
 4- Updating
 The new offspring chromosomes substitute the worst
chromosomes of the current population
 5- Evaluation
 The new chromosomes are decoded
 Fitness of the new chromosomes is computed
 6- Stopping Criterion Satisfied
 If so, then go to step 7; else, go back to step 3 (Here
maximum number of 8000 iterations is considered
 7- Repeat
 8- End
Sesam Users Conference – 03.Dec.2012
19

20. Case Study
 The procedure described in the previous
sections, has been implemented in a
computer program (based on Matlab) which
has been written to solve a mooring design
optimization problem using Mimosa.
 As a case study, a
floating unit anchored
by 10 mooring lines,
was considered.
Sesam Users Conference – 03.Dec.2012
20

21. Case Study
 The 10 lines were divided into 4 groups with
side constraints, as given in the Table below:
 The floating unit is subjected to a set of
environmental conditions that are combined
according to a collinear approach, i.e. with
currents, winds and waves acting
simultaneously in the same direction.
Sesam Users Conference – 03.Dec.2012
21

22. Case Study
 In this case study, eight combinations have
been considered. The JONSWAP spectrum for
the Caspian Sea conditions was used to
calculate wave HF responses, while the API
spectrum was used for determining the time
varying part of the wind forces.
Sesam Users Conference – 03.Dec.2012
22

23. Case Study
 The total number of iterations considered
here was 8000 and the minimum value of the
objective function was reached at the 43rd
generation in offspring 4269.
 The next table presents the final results of the
mooring design optimization problem
including azimuths of each line, anchor
position, line length, line size and line
material. Also the platform heading is 180 deg.
relative to true North.
Sesam Users Conference – 03.Dec.2012
23

24. Case Study
Sesam Users Conference – 03.Dec.2012

25. Case Study
 The optimized mooring pattern is illustrated
below. Line size and material in the ordinary
case is 3.5” chain and 4” chain in the optimized
design.
Sesam Users Conference – 03.Dec.2012
25

26. Case Study
 The responses are reduced by the optimized
mooring design to up to 3.5 times less than in an
ordinary design. This matter has a great effect on
platform workability because of the reduction of
down-time.
Sesam Users Conference – 03.Dec.2012
26