# SIMPLE GENETIC ALGORITHM WITH a-SELECTION - Intrinsic System Model, Fixed Points and the Fixed Point Graph

### André Neubauer

#### Abstract

Genetic algorithms (GA) are instances of random heuristic search (RHS) which mimic biological evolution and molecular genetics in simplified form. These random search algorithms can be theoretically described with the help of a deterministic dynamical system model by which the stochastic trajectory of a population can be characterized using a deterministic heuristic function and its fixed points. For practical problem sizes the determination of the fixed points is unfeasible even for the simple genetic algorithm (SGA). The recently introduced simple genetic algorithm with a-selection allows the analytical calculation of the unique fixed points of the dynamical system model. In this paper, an overview of the theoretical results for the simple genetic algorithm with a-selection and its corresponding intrinsic system model is given. Further, the connection to the fixed point graph is illustrated which describes the asymptotic behavior of the simple genetic algorithm. In addition to the theoretical analysis experimental results for the simple genetic algorithm with a-selection, uniform crossover and bitwise mutation are presented.

#### References

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#### Paper Citation

#### in Harvard Style

Neubauer A. (2010). **SIMPLE GENETIC ALGORITHM WITH a-SELECTION
- Intrinsic System Model, Fixed Points and the Fixed Point Graph** . In *Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)* ISBN 978-989-8425-31-7, pages 281-288. DOI: 10.5220/0003113802810288

#### in Bibtex Style

@conference{icec10,

author={André Neubauer},

title={SIMPLE GENETIC ALGORITHM WITH a-SELECTION
- Intrinsic System Model, Fixed Points and the Fixed Point Graph},

booktitle={Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)},

year={2010},

pages={281-288},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003113802810288},

isbn={978-989-8425-31-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)

TI - SIMPLE GENETIC ALGORITHM WITH a-SELECTION
- Intrinsic System Model, Fixed Points and the Fixed Point Graph

SN - 978-989-8425-31-7

AU - Neubauer A.

PY - 2010

SP - 281

EP - 288

DO - 10.5220/0003113802810288