Optimization Design and Calculation of Mooring System Parameters based on Genetic Algorithm

Based on the static equilibrium model of mooring system parameters, the multi objective optimization model is established and the genetic algorithm is introduced as the optimization algorithm, which improves the crossover operator. Taking the example of a single point mooring system, concerned optimization design and calculation has been done. Compared with the general genetic algorithm, the result of this algorithm is superior, significantly improving the stability of the mooring system.


Introduction
The single point mooring system has been widely used in both ship navigation and the comprehensive utilization and development of Marine resources.The small changes of mooring system parameters can greatly affect the stability of the whole system, so a large number of experts have carried out relevant researches.Ming-wu Wang [1] established a two-dimensional model of the underwater buoy system and calculated relevant parameters according to static equilibrium; John [2] used catenary method and polygon approximation method for analysis and calculation; Xing-ping Xu [3] studied single point mooring system from the perspective of dynamics.
Genetic algorithm is a kind of random searching method which is developed by the genetic mechanism of biology.It regards the possible solution in the problem as an individual in the group, and encodes it as a chromosome.Then simulating the biological evolution process, the group receives repeated hybrid operation and chooses the better one continuously, according to the evolution of the biological sector.At the same time, the optimal individual in the optimal group can be found, which is the optimal solution for satisfying the requirements.

Improvement of the genetic algorithm of crossover operators
The basic genetic algorithm also has many shortcomings, which often can only approach the optimal solution rather than calculate the optimal solution, and sometimes find the local optimal solution.In order to solve these problems, generally beginning with genetic algorithm three basic genetic operators (select operator, crossover operator and mutation operator) of genetic algorithm.In this paper, improved crossover operator's genetic algorithm [4 ~ 5] is used to solve the multi-objective optimization problem.
To enhance the diversity of population in the early evolution period, cross-operation between the parent individuals should be expanded to generate a variety of new individuals, which can choose many excellent individuals by copying the operator.However, at the late stage of evolution, with the high frequency of evolution, the solution group gradually approaches the optimal solution.At this point, if we still use a high crossover rate, it will produce a lot of new individuals, which distribute divergently in the entire search space, leading to the low proportion of good individuals in the population.The high rate will delay the convergence process.Therefore, the crossover rate is modified as follows： Where: 0 c p -a initial crossover rate; d -the current evolutionary algebra; D -the total evolutionary number.It is not difficult to see that with the increase of the iteration times, the crossover rate decreases and the convergence process is accelerated.Genetic algorithm is the search process of every generation based on the adaptability, which is mainly composed of coding mechanism, control parameters, fitness function and genetic operators.The main calculation process of solving the multi-objective optimization problem is as follows: The process is shown in Fig. 1

Static analysis of mooring system
The single point mooring system consists of steel pipe, steel bucket, heavy ball, electric welding anchor chain and special anti-drag and shifting anchor.Its schematic diagram is shown in Figure 2.This paper uses a polygon approximation method of concentrated mass [3] to conduct two-dimensional static analysis of mooring system.

Buoy force analysis
The equation of equilibrium is as follows: cos Where: buoyancy F -the buoyancy of the buoy in the sea, buoy G -the gravity of the buoy itself, T -the tension of the steel tube, f -the resistance of the float when the buoy is swimming.The buoyancy is ,  is the angle between the tension T and the horizontal direction, D is the diameter of the buoy, D C is the resistance coefficient of the fluid to the buoy, S is the horizontal wetting area of the buoy, V is the unidirectional flow rate that represents the fluid at the buoy.

Force Analysis of Steel Pipe and Steel
The equation can be: Where: buoyancy i F -buoyancy of the steel pipe in the water, f -the water resistance, i G -the gravity of the steel tube, i T -the force of the previous steel tube, 1 i T  -the force of the next steel pipe.And we can get by derivation.It can be seen from the derivation formula that if the former tension 1 i T  is given, the following tension i T can be calculated, and the steps in the middle can also be calculated by this method.The force analysis of the steel drums is similar to that of steel pipes, and the difference is that the gravity of the steel drum will be combined with the gravity of the steel ball.

Stress analysis of the link
As the volume of the link is very small, it can be considered without buoyancy and hydrodynamic effect, that is, only bears its own gravity and the force of the previous link and the chain, we can get the equilibrium equation:

Analysis of the relevance of each component`
The total length of the projection of each member in the vertical direction should equal the depth of the seabed when the system is stable, which is can be derived from the stress analysis in the previous text.
improved crossover operator genetic algorithm has better effect on improving the stability of mooring system.

6-Mooring system parameter optimization case analysis
The parameter optimization design of the mooring system is a multi -objective optimization problem with constraints.Using the genetic algorithm of improved crossover operator, the multi -objective optimization design of each parameter is solved.The result of the example shows that the optimized parameters obtained by this method can meet the constraints and improve the stability of mooring system.Therefore, this method can be carried out in multi-parameter optimization design effectively and provides a approach for other types of mooring system parameter optimization design.

iC
as the father of the mutation and randomly generate real numbers which belong to [0,1] .If

Figure 1 :
Figure 1: Flow chart of genetic algorithm for improved crossover operator MATEC Web of Conferences fitness means the best individual.c.Selection process: select one chromosome at a time as a new subgroup.Repeat this process _ pop size times to get a new generation.d.Variation operation: supposing the probability of cross operation is m : a. Initialize the population: randomly generate _ pop size feasible chromosomes.b.Calculate the population fitness: fitness function is used to evaluate the adaptability of each chromosome.In this paper we use the objective function as fitness function, the maximum level of P .Randomly select a chromosome