**1. Introduction**

42 Bio-Inspired Computational Algorithms and Their Applications

In the problems where mathematical equations have many variables and parameters, it is

To exclude this limitation it is possible to divide one network operator with a considerable number of nodes into some small network operators. We receive the multilayer network operator and some matrices of smaller dimensions. Each layer of the network operator

Further development of the network operator is a creation of a special data structure for presentation of the network operator in memory of the computer. Such structure can be

Alnovani G.H.A., Diveev A.I., Pupkov K.A., Sofronova E.A. (2011) Control Synthesis for

Callan R. (1999) *The essence of neural networks*. The Prentice Hall Europe, 1999, ISBN 0-13-

Demuth, H.; Beale, M.; Hagan, M. (2008) *Neural Network Toolbox™ User's Guide*. The

Diveev A.I. (2009) A multiobjective synthesis of optimal control system by the network

*applications»* (OPTIMA) Petrovac, Montenegro, September 21-25, pp. 21-22. Diveev A.I., Sofronova E.A. (2009) Numerical method of network operator for multi-

Diveev A.I., Sofronova E.A. (2009) The Synthesis of Optimal Control System by the Network

Kahaner, D.; Moler, C.; Nash, S. (1989) *Numerical methods and software* Prentice Hall

Koza, J.R. (1992*). Genetic Programming: On the Programming of Computers by Means of Natural* 

Koza, J.R. (1994*). Genetic Programming II: Automatic Discovery of Reusable Programs*, MIT Press.

Koza, J.R.; Bennett, F.H.; Andre, D. & Keane, M.A. (1999). *Genetic Programming III: Darwinian Invention and Problem Solving*, Morgan Kaufmann. ISBN 1-55860-543-6. 1154 p. Koza, J.R.; Keane, M.A.; Streeter, M.J.; Mydlowec, W.; Yu, J.; Lanza, G. (2003). *Genetic* 

*Programming IV: Routine Human-Competitive Machine Intelligence*, Springer. ISBN 1-

*Optimization CAO'09*, 6 - 8 May, University of Jyväskylä, Agora, Finland. Diveyev A.I., Sofronova E.A. (2008) Application of network operator method for synthesis

*Congress.* Milan (Italy) August 28 – September 2. pp. 2196-2201.

Traffic Simulation in the Urban Road Network, *Preprints of the 18-th IFAC World* 

operator method. *Proceedings of international conference «Optimization and* 

objective synthesis of optimal control system, *Proceedings of Seventh International Conference on Control and Automation* (ICCA'09) Christchurch, New Zealand,

Operator Method, *Proceedings of IFAC Workshop on Control Applications of* 

of optimal structure and parameters of automatic control system, *Proceedings of 17-*

necessary to use big network operator matrices with many zero elements.

describes a part of mathematical equation.

**12. References** 

multilayered and provide effective parallel calculation.

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*th IFAC World Congress*, Seoul, 05. - 12. July . pp. 6106 – 6113.

Genetic Algorithms (GA) are powerful tools to solve large scale design optimization problems. The research interests in GA lie in both its theory and application. On one hand, various modifications have been made to allow them to solve problems faster, more accurately and more reliably.

Genetic Algorithms are a search paradigm that applies principles of evolutionary biology (crossover, mutation, natural selection) in order to deal with intractable search spaces. The power and success of GA are mostly achieved by the diversity with the individuals of a population which evolve, in parallel, following the principle of the survival of the fittest. In general, the genetic algorithms resolve combinatorial optimization problems that in (Goldberg, 1989) are mentioned, this implies a large number of responses associated with an exponential growth in solutions potentially feasible according to the magnitude of the problem. In a standard GA the diversity of the individuals is obtained and maintained using the genetic operators crossover and mutation which allow the GA to find feasible solutions and avoid premature convergence to a local maximum (Holland, 1975).

The performance of a genetic algorithm, like any global optimization algorithm, depends on the mechanism for balancing the two conflicting objectives, which are exploiting the best solutions found so far and at the same time exploring the search space for promising solutions. The power of genetic algorithms comes from their ability to combine both exploration and exploitation in an optimal way (Holland, 1975). However, although this optimal utilization may be theoretically true for a genetic algorithm, there are problems in practice. These arise because of Holland assumed that the population size is infinite, that the fitness function accurately reflects the suitability of a solution, and that the interactions between genes are very small (Beasley et al., 1993).

The evolutionary algorithm proposed in this paper is composed by a classic genetic algorithms along with the forced inheritance mechanism proposed by (Merchán-Cruz, 2005, Merchán-Cruz et al., 2008, Merchán-Cruz et al., 2007) and the regeneration mechanisms by

Performance of Simple Genetic Algorithm

are values for the variable

function to avoid singularity problems (2):

Fig. 2. Flowchart of genetic algorithms.

1 2 22 2 , , *<sup>N</sup>* θθ

 θ

Inserting Forced Inheritance Mechanism and Parameters Relaxation 45

Where *<sup>i</sup> Cxd* is a set of specific points indicated by the designer and *<sup>i</sup> Cxg* are the points

maximizes solely, but the minimization can be made easily using the reciprocal of the

In order to improve the results, approaches such as elitism, regeneration stages and the

θ

*<sup>2</sup>*, *i* is the rest of the quotient. The genetic algorithm

<sup>1</sup> *fitnessoptimum fitness* <sup>=</sup> (2)

*0, x0, y0*, the angles

generated by the coupler of the mechanism, and *v = r1, r2, r3, r4, rcx, rcy,*

θ

forced inheritance mechanism can be inserted in the process of the algorithms:

(Ramírez-Gordillo, 2010, Lugo González, 2010), for optimizing the trajectory generation in closed chain mechanisms and planning the effects that it has on the mechanism by relaxing some parameters. The objective is to show the behavior of relaxing the parameters of the GA's, observing what advantages and disadvantages appear when varying some parameter exceeding the recommended values established in the literature.
