**5***.* **Discussion**

The optimization process is iterative, and it was demonstrated with the tests that were realized varying the parameters of the genetic algorithm to analyze the behavior of the system, which means that they can be modified until finding a system whose behavior satisfies the expectations and requirements of the designer. The parameters of the GA usually interact with each other in a nonlinear relation, that's why they cannot be optimized in an independent way, been demonstrated in the presented study cases. When existing a change in the population size, this fact will be reflected in time of convergence and accuracy in the path generation.

It was demonstrated that the diversity of individuals in the population is obtained and it remains along with the operator of crossing and the genetic mutation, since in all the analysis, they allow to find better solutions and avoid premature convergence to the maximum premises. Although also it must be mentioned that the elitism and the forced inheritance help to limit the number of individuals that will cover the imposed restrictions. On the other hand, it was observed that the GA has few possibilities of making considerable or necessary a number of reproductions for the optimal solution if it has an insufficient or small population.

Besides, the excessive population causes that the algorithm requires of a greater time of calculation to process and to obtain a new generation. In fact, there is not a limit wherein it is inefficient to increase the size of the population since it neither obtains a faster speed in the resolution of the problem, nor the convergence makes sure. For the referred study cases in this chapter, when increasing the population to 3500 individuals no acceptable results are presented and the program became extremely slow. If the population remains so large, like for example 1000 individuals, this means that it can improve the performance of the algorithm, although this is affected by slower initial responses. It is important to do emphasis on the relation that exists among the population size and the probabilistic relation in the solution space of the problem.

The study cases of this work are over determined and nonlinear type, which implies by necessity a space of multidimensional, nonlinear and non-homogenous solution, therefore, large initial values cover different regions of the solution space wherein the algorithm could converge prematurely to a solution that implies optimal premises costs, but when maintaining a low probability of mutation is not possible to assure that the population, although extensive in the number of individuals, continues being probabilistic representative of the problem solution. With this in mind and considering that the computation time to evaluate and to generate a new population of individuals from the present initial or, directly is the bound to the number of individuals of this one, requires a greater number of operations to obtain a new generation of possible solutions.
