**3. Adjustment in the performance of the parameters of the GA**

Some authors such as (Holland, 1975), have looked into the effect of varying GA's parameters which have to be taken into account to exploit the full potential in particular applications. Accordingly to this, for a search algorithm to perform well online, one has to decide quickly which are the most promising search regions in order to concentrate the search efforts there, the off-line performance does not penalize the search algorithm to explore poor regions of the search space, provided that this will help to achieve the best possible solutions (in terms of fitness), abig generation interval and the use of an elitist strategy also improve the performance of the GA's, in which the usual recommended mutation rates between 0.001 and 0.01 for the binary representation (Goldberg, 1989), or in general, much smaller value of the crossover probability (Cabrera et al., 2002).

The main parameters that can be adjusted, by the degree of importance within the GA are:


The design of the algorithm is limited to choose and determine the degree of control or the strategies of parameters such as the ranges and the likelihood of a mutation, crossing and extent of the population. (Sanchéz-Marín, 2000) supported their research in the

Performance of Simple Genetic Algorithm

Inserting Forced Inheritance Mechanism and Parameters Relaxation 51

With reference to the mutation, it has been deeply analyzed the value of the probability, but the results vary with each researcher, for example (De Jong, 1975) recommend *pm=0.001*, (Grefenstette, 1986, Goldberg, 1989) recommend *0.1*, (Fogarty, 1989) indicates *0.005 to 0.01*. In the research of (Fogarty, 1989) and (Coello-Coello, 2007) have been developed some formulas in order determine the mutation, where its main contribution is considering the time and making a change of this during the execution of the GA. If the mutation percent is *0*, does not exist any alteration, if is *1*, the mutation creates always add-ons of the original individual and if it is 0.5, there is a high probability of altering strongly the schema of an individual. In conclusion, it is possible to control the power of alteration of the mutation and its capabilities for exploration, to have an equivalent weight within the AG as the crossing. On the other hand for the crossing some common values for this are 0.6 indicated by (De Jong, 1975), *0.95 by* (Grefenstette, 1986), *0.75 to 0.95 by* (Fogarty, 1989). (Endre Eiben et al., 1999) specify that is more common to use the results obtained in own experimentation and is rarely used a value less than 0.6. When it is looking for locating the global optimum of a problem, the mutation may be more useful, but when it is in the cumulative gain, crossing offers greater benefits. From these research works it can be said that there are needs of large populations in the crossing, to combine effectively the necessary information, but in mutation best results are

obtained when applied to small populations in a large number of generations.

operator that were not captured by the other.

and the links dimensions.

**4. Study cases** 

presented.

Evolutionary strategies, where the mutation is the principal search operator, include several operators of mutation, as well as technical adaptation, proposed by (Lima et al., 2005, Rechenberg, 1973). (Whitley et al., 1998) reported comparative studies between the operators of crossover and mutation, demonstrating that there were important features of each

In this work is demonstrated, through experimentation, that the maximum limit for individuals have an acceptable performance of the GA is 3000, this depends completely on study cases, since as it increases the number of variables in the problem to be analyzed it is necessary an increase in the population. With this amount of individuals the process of analysis is very slow, but it is in direct function of the mechanism type, the trajectory and the precision points required, in addition to the restrictions on the domain to get the angles

The case of study is based on mechanisms synthesis, for that reason the basic concepts are

A mechanism is a set of rigid members that are jointed together in order to develop a specific function. The mechanisms design, which is described by (Varbanov et al., 2006), consists of two parts: the analysis and synthesis. The first one consists of techniques to determine position, velocities and accelerations of points onto the members of mechanisms and the angular position, velocities and accelerations of those members. The second type explains the determination of the optimal length of the bars and the spatial disposition that best reproduces the desired movement of the coupler link. The optimal dimensional synthesis problem of mechanisms can be seen as a minimization process, since it is required that the structural error being as small as possible. The point of the coupler link will have to be able to generate a trajectory defined through separate points, with a minimum error. The

determination of control parameters, experimenting with different values and selecting those that gave better results. (De Jong, 1975) recommended, after experimenting, values for the probability of the interbreeding of simple point and the movement of a bit in the mutation. In this work, the following parameters are defined: a population-based measure of 50 individuals, probability of crossing 0.6, probability of mutation of 0.001 and elitist selection; however, it presents the disadvantage that these parameters only worked for a particular problem with very specific restrictions.

(De Jong, 1975) described that the operation on-line is based on the monitoring of the best solution in every generation, while the operation off-line takes into account all the solutions in the population to obtain the optimum value. (Grefenstette, 1986) used the metaalgorithms as a method of optimization, in order to obtain values with similar parameters for the operation on-line and off-line of the algorithm.

In order to have a good performance on-line of a search algorithm, it must quickly decide where the most promising search region is and concentrate their efforts there. The performance off-line does not always penalize the search algorithm to explore poor regions of the search space, since this will contribute to achieving the best possible solutions (in terms of fitness). The best sets of parameters analyzed on and off- line were population of 30 and 80 individuals, probability of crossing 0.95 and 0.45, probability of mutation 0.01 for both, either using a strategy of elitist selection for the on-line case or not elitist for the off-line case .

(Smith, 1993) proposes a genetic algorithm which adjusts the extent of the population taking into account the likelihood of error. This is linked with the number of generations, if under the conditions of little use is determined a small value (20 to 50) to the number of evaluations, the convergence will be quick, but it is not ensured an optimum result.

(Endre Eiben et al., 1999) expose technical drawbacks of the analysis of parameters on the basis of experimentation, observing the following points:


In general, here are listed some important observations made by authors such as (Holland, 1975),with respect to the genetic algorithms that must be considered for the use of this tool, such as:


With reference to the mutation, it has been deeply analyzed the value of the probability, but the results vary with each researcher, for example (De Jong, 1975) recommend *pm=0.001*, (Grefenstette, 1986, Goldberg, 1989) recommend *0.1*, (Fogarty, 1989) indicates *0.005 to 0.01*.

In the research of (Fogarty, 1989) and (Coello-Coello, 2007) have been developed some formulas in order determine the mutation, where its main contribution is considering the time and making a change of this during the execution of the GA. If the mutation percent is *0*, does not exist any alteration, if is *1*, the mutation creates always add-ons of the original individual and if it is 0.5, there is a high probability of altering strongly the schema of an individual. In conclusion, it is possible to control the power of alteration of the mutation and its capabilities for exploration, to have an equivalent weight within the AG as the crossing.

On the other hand for the crossing some common values for this are 0.6 indicated by (De Jong, 1975), *0.95 by* (Grefenstette, 1986), *0.75 to 0.95 by* (Fogarty, 1989). (Endre Eiben et al., 1999) specify that is more common to use the results obtained in own experimentation and is rarely used a value less than 0.6. When it is looking for locating the global optimum of a problem, the mutation may be more useful, but when it is in the cumulative gain, crossing offers greater benefits. From these research works it can be said that there are needs of large populations in the crossing, to combine effectively the necessary information, but in mutation best results are obtained when applied to small populations in a large number of generations.

Evolutionary strategies, where the mutation is the principal search operator, include several operators of mutation, as well as technical adaptation, proposed by (Lima et al., 2005, Rechenberg, 1973). (Whitley et al., 1998) reported comparative studies between the operators of crossover and mutation, demonstrating that there were important features of each operator that were not captured by the other.

In this work is demonstrated, through experimentation, that the maximum limit for individuals have an acceptable performance of the GA is 3000, this depends completely on study cases, since as it increases the number of variables in the problem to be analyzed it is necessary an increase in the population. With this amount of individuals the process of analysis is very slow, but it is in direct function of the mechanism type, the trajectory and the precision points required, in addition to the restrictions on the domain to get the angles and the links dimensions.
