**3. Description of the evolutionary methods used in the hybrid system**

The whole task of search and the optimization has several components, including: the search space, where they are considered all possibilities of solution of a given problem and the evaluation function (or function), a way to evaluate members of the search space. There are many methods of search and evaluation functions.

Search optimization techniques and traditional begin with a single candidate, iteratively, is manipulated using some heuristics (static) directly associated with the problem to be solved. Generally, these processes are not heuristic algorithmic and its simulation in computers can be very complex. Despite these methods were not sufficiently robust, this does not imply they are useless. In practice, they are widely used, successfully, in innumerable applications (Ross, 2010).

On the other hand, the evolutionary computation techniques operate on a population of candidates in parallel. Thus, they can search in different areas of the solution space, allocating an appropriate number of members to search in multiple regions.

Meta-heuristic methods differ from traditional methods of search and optimization, mainly in four aspects (Esmin et al., 2005; Medsker, 2005):


An Evolutionary Fuzzy Hybrid System for Educational Purposes 403

selection method used is the method of roulette, where individuals of one generation are chosen to be part of the next generation, through a raffle of roulette. Figure 6 shows the

In this method, each individual of the population is represented in roulette in proportion to its index of fitness. Thus, individuals with high fitness are given a greater portion of the wheel, while the lowest fitness is given a relatively smaller portion of roulette. Finally, the roulette wheel is rotated a certain number of times, depending on the size of the population, and are chosen, as individuals who will participate in the next generation,

A set of operations is necessary so that, given a population, to generate successive populations that (hopefully) improve your fitness with time. These operators are: crossover (crossover) and mutation. They are used to ensure that the new generation is entirely new, but has in some way, characteristics of their parents, i.e. the population diversifies and maintains adaptation characteristics acquired by previous generations. To prevent the best individuals does not disappear from the population by manipulating the genetic operators;

This cycle is repeated a specified number of times. The following is an example of genetic algorithm. During this process, the best individuals, as well as some statistical data, can be

Where *g* is the current generation; *t* is the number of generations to terminate the algorithm;

representation of the roulette to a population of 4 individuals.

Fig. 6. Individuals of a population and its corresponding check roulette

they can be automatically placed on the next generation via playing elitist.

those drawn in roulette.

collected and stored for evaluation.

*Procedure AG {g = 0;* 

*{g = g +1;* 

 *} }* 

*inicial\_population (P, g) evaluation (P, g); Repeat until (g = t)* 

 *Father\_selection (P, g); recombination (P, g); mutation (P, g); evaluation (P, g);* 

and *P* is the population.


In addition to being a strategy to generate-and-test very elegant, because they are based on social organization or biological evolution, are able to identify and explore environmental factors and converge to optimal solutions, or approximately optimal in overall levels. The better a person adapt to their environment, the greater your chance of surviving and generate descendants: this is the basic concept of social organization or biological genetic evolution. The biological area more closely linked to genetic algorithms is the genetics, and the social area is particle swarm optimization.
