In order to determine the bending strength of wood or wood-based panels, an experimental method is typically used to test samples of different sizes that involves bending or compression. However, such tests are expensive and time-consuming, so mathematical models are often applied that allow predicting the bending strength based on a smaller number of obtained test results. One such model is the Lagrange interpolation polynomial. The study discusses Lagrange’s interpolation model. Using the results of tests done on plywood of various thicknesses, approximates the bending strength of plywood for values that could not be tested directly and provides an estimate of strength for particular values.

The work represents the continuation of the research of the maximum bending stress force of a wooden beam up to the moment of failure, which is defined experimentally and with a corresponding mathematical model. The goal was to confirm the accuracy of the mathematical model of the breaking force using numerical simulation and the Solid Works software. Five different types of wood and five different beam thicknesses were used as input parameters whose influence was monitored trough the simulation. The stress deformation state and deflection for the calculated fracture forces were analysed separately for each variant. The breaking force model, which is defined depending on the density of the wood and the thickness of the board, proved to be adequate for defining the maximum stresses and deflections when bending beams.

The Travelling Salesman Problem is categorized as NP-complete problems called combinatorial optimization problems. For the growing number of cities it is unsolvable with the use of exact methods in a reasonable time. Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions, however they give good approximation usually in time. Studies have shown that the proposed genetic algorithm can find a shorter route in real time, compared with the existing manipulator model of path selection. The genetic algorithm depends on the selection criteria, crosses, and mutation operators described in detail in this paper. Possible settings of the genetic algorithm are listed and described, as well as the influence of mutation and crossing operators on the efficiency of the genetic algorithm. The optimization results are presented graphically in the MATLAB software package for different cases, after which a comparison of the efficiency of the genetic algorithm with respect to the given parameters is performed.

One of the most interesting and important optimization problems in graph theory is the problem of extreme flow definition in the given network. the network flow theory has developed from the need to solve some practical problems which occur most often in transportation. Such problem, for example, is the defining of optimal transportation flow on the road network of a city or its wider area. This paper analyses different types of static homogenous flows (one-side limited flow, flows in the networks with special constrains, etc.). Special attention is paid to the problem of the existence of such flows, which present one of the most important problems in the total network flow theory. The paper formulates the problems, explaining then the basic ideals of algorithms that are to be used to solve adequate optimization problem.