# A GIBBS DISTRIBUTION THAT LEARNS FROM GA DYNAMICS

### Manabu Kitagata, Jun-ichi Inoue

#### Abstract

A general procedure of average-case performance evaluation for population dynamics such as genetic algorithms (GAs) is proposed and its validity is numerically examined. We introduce a learning algorithm of Gibbs distributions from training sets which are gene configurations (strings) generated by GA in order to figure out the statistical properties of GA from the view point of thermodynamics. The learning algorithm is constructed by means of minimization of the Kullback-Leibler information between a parametric Gibbs distribution and the empirical distribution of gene configurations. The formulation is applied to a solvable probabilistic model having multi-valley energy landscapes, namely, the spin glass chain. By using computer simulations, we discuss the asymptotic behaviour of the effective temperature scheduling and the residual energy induced by the GA dynamics.

#### References

- Baluja, S. (1994). Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning. Technical Report, School of Computer Science, Carnegie Mellon University, CMU-CS-94:163.
- Geman, S. and Geman, D. (1984). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-6:721-741.
- H.Holland, J. (1975). Adaptation in natural and artificial systems. The University of Michigan Press.
- Kirkpatrick, S., D.Galatt, C., and P.Vecchi, M. (1983). Optimization by simulated annealing. Science, 220:671- 680.
- Li, T. (1981). Structure of metastable states in a random ising chain. Physical Review B, 24:6579-6587.

#### Paper Citation

#### in Harvard Style

Kitagata M. and Inoue J. (2010). **A GIBBS DISTRIBUTION THAT LEARNS FROM GA DYNAMICS** . In *Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)* ISBN 978-989-8425-31-7, pages 295-299. DOI: 10.5220/0003047102950299

#### in Bibtex Style

@conference{icec10,

author={Manabu Kitagata and Jun-ichi Inoue},

title={A GIBBS DISTRIBUTION THAT LEARNS FROM GA DYNAMICS},

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

year={2010},

pages={295-299},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003047102950299},

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 - A GIBBS DISTRIBUTION THAT LEARNS FROM GA DYNAMICS

SN - 978-989-8425-31-7

AU - Kitagata M.

AU - Inoue J.

PY - 2010

SP - 295

EP - 299

DO - 10.5220/0003047102950299