## 1 Introduction
GAs are used for Linear Time Invariant (LTI) state-space helicopter model identification [22] and linear quadratic Gaussian (LQR) controller design. They also find applications in medical equipment control. [PERSON] and others [23] used GA to estimate NARMA input-output model humidification inside a newborn incubator. Modification of GA, called genetic programming (GP), is used in modeling and optimization of the direct methanol fuel cell [24]. Additionally, neural network structure, which is used for non-linear MIMO system modeling, may be determined with the use of GA. This approach is convenient when there is little or no knowledge about the object structure [25]. Genetic algorithms are also used in ship model identification procedures. [PERSON] et al. in [26] used a parallel genetic algorithm for finding high-speed ships' transmittance parameters. They state the problem of reasonably searching and determining space combined with parallelization, which allows to achieve time constraints. They propose a nonlinear model, taking into account heaves caused by sea waves. A maneuvering non-linear mathematical model for ships was presented in [27]. Model coefficients were estimated on the basis of a classic genetic algorithm, optimizing the distance between the reference and recorded time histories. The devised model was created on the basis of a simulated zig-zag trial and was verified according to turning maneuver and Dieudonne spiral. The genetic algorithm is also used in ship rolling prediction models to automatically adjust least-squares support-vector machine (LSSVM) model parameters [28]. In the LSSVM algorithm the cost function is regularized by the least-squares function with equality con straints. Based on this method, a non-linear ship rolling prediction model was devised. Parameter identification of linear vessel models using gradient and genetic algorithms was presented in [29]. They proposed a way to solve the problem of varying ship parameter values identification in linearized models. Such a possibility is important for the synthesis and realization of control algorithms. The optimized Nomoto model, based on the Kempf trial simulated data, was created and presented. Grey-box model (GBM) parameters are most often optimized with the use of evolutionary algorithms. The main advantage of this method is that all model parameters are estimated in one run. This is how the ship fuel consumption model [30] and hydraulic process of ship lock [31] were created. GA models are also used in maritime autonomous ship automatic control systems, where they are used for off-line path estimation based on stationary obstacles and on-line path modification to avoid collision [32]. Fitness function is then defined as an economic cost resulting from the shape of the ship's own route. Ship mathematical models, with parameters optimized by GA, are also used in the automatic non-linear sliding mode control. Ship collision avoidance, taking into account ship maneuverability, was presented in [33], where steering course control parameters were optimized on-line by GA. Additionally, in [34] a nonlinear ship maneuvering model is combined with GA to obtain the optimum rudder angle command and length of target trajectory. Results of the presented research show that it is justified to use the genetic algorithm in ship model identification and in autonomous ship control. In this paper, GA has been applied to optimize bias and variance error coefficients in the regularization procedure. The best trade-off between them is taken into account, which leads to the best model complexity. Combination of GA and regularization was developed, and it is presented in the paper in application to the training ship's linear model identification. Results prove that it increases the quality of the model obtained from the simulation data fit to the actual ship input-output data.