# AN EXPLORATION MEASURE OF THE DIVERSITY

### G. A. Papakostas, Y. S. Boutalis, D. A. Karras, B. G. Mertzios

#### Abstract

In this paper, a novel measure of the population diversity of a Genetic Algorithm (GA) is presented. Chromosomes diversity plays a major role for the successfully operation of a GA, since it describes the number of the different candidate solutions that the algorithm evaluates, in order to find the optimal one, in respect to a performance index, called objective function. In a well defined algorithm, the diversity of the current population should be measurable, in order to estimate the performance of the algorithm. The resulted observation, that is, the measuring of the diversity, can then be used to real-time adjust the factors that determine the chromosomes variety (Pc, Pm), during the execution of the GA. It is shown, that a simple chromosomes clustering into the search space, by using the well known k-means algorithm, can give a useful picture of the population’s distribution. Thus, by translating the problem of finding the best solution to a GA-based problem into an iterative clustering process, and by using the scatter matrices (Sw, Sb), which describe completely the candidate’s solutions topology, one could define a novel formula that gives the population diversity of the algorithm.

#### References

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#### Paper Citation

#### in Harvard Style

A. Papakostas G., S. Boutalis Y., A. Karras D. and G. Mertzios B. (2005). **AN EXPLORATION MEASURE OF THE DIVERSITY** . In *Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 972-8865-29-5, pages 260-265. DOI: 10.5220/0001161702600265

#### in Bibtex Style

@conference{icinco05,

author={G. A. Papakostas and Y. S. Boutalis and D. A. Karras and B. G. Mertzios},

title={AN EXPLORATION MEASURE OF THE DIVERSITY},

booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2005},

pages={260-265},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001161702600265},

isbn={972-8865-29-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - AN EXPLORATION MEASURE OF THE DIVERSITY

SN - 972-8865-29-5

AU - A. Papakostas G.

AU - S. Boutalis Y.

AU - A. Karras D.

AU - G. Mertzios B.

PY - 2005

SP - 260

EP - 265

DO - 10.5220/0001161702600265