**3. The usage of genetic programming to predict woven fabric porosity parameters**

Porosity parameters based on an ideal geometrical model of porous structure give woven fabric constructor some useful information about porosity by developing a new product, but they are not in a good agreement with the experimental values. In order to balance the difference between the theoretical and experimental values of porosity parameters, genetic programming was used to develop models for predicting the following macro-porosity parameters of woven fabric: the area of macro-pore cross-section, macro-pore density, open porosity, and equivalent macro-pore diameter. The genetic programming is a variant of evolutionary algorithm methods described in many sources (e.g., [2, 3, 4]). The basic information on the evolutionary algorithms is given at the beginning of the section 4. We implemented Koza's variant of genetic programming [2]. In our research, the independent input variables (the set of terminals) were: yarn fineness *T* (tex), weave value *V*, fabric tightness *t* (%) and denting *D* (ends/dent in the reed). The set of terminals also included random floating-point numbers between –10 and +10. Variegated reed denting was treated as an average value of treads, dented in the individual reed dent. The dependent output variables were: area of macro-pore cross-section *Ap* (10-3 mm2), pore density *Np* (pores/cm2), and equivalent macro-pore diameter (µm). For all modelling, the initially set of functions included the basic mathematical operations of addition, subtraction, multiplication, and division. In the case of modelling the area of macro-pore cross-section and pore density the initially set of functions also included a power function, whereas the set of functions for modelling of equivalent macro-pore diameter included an exponential function. We then used the genetic programming system to evolve appropriate models consist of abovementioned sets of terminals and functions. Open porosity was calculated on the basis of predicted values of the area of macro-pore cross-section and macro-pore density and Equation 17. The equivalent macro-pore diameter was calculated on the basis of predicted values of the area of macro-pore cross-section using Equation 19. The fitness measure for modelling by genetic programming was exactly the same as defined by Equation 33 in section 4. The goal of the modelling was to find such a predictive model in a symbolic form, that Equation 33 would give as low an absolute deviation as possible.

The evolutionary parameters for modelling by genetic programming were: population size 2000, maximum number of generations to be run 400, probability of reproduction 0.1, probability of crossover 0.8, probability of mutation 0.1, minimum depth for initial random organisms 2, maximum depth for initial random organisms 6, maximum depth of mutation fragment 6, and maximum permissible depth of organisms after crossover 17. The generative method for the initial random population was *ramped half-and-half*. The method of selection was tournament selection with a group size of 7. For the purpose of this research 100 independent genetic programming runs were executed. Only the results of the best runs (i.e., the models with the smallest error between the measurements and predictions) are presented in the paper.
