Learning in genetic algorithms
Learning in artificial neural networks is often cast as the problem of “teaching” a set of stimulus-response (or input-output) pairs to an appropriate mathematical model which abstracts certain known properties of neural networks. A paradigm which has been developed independently of neural network models are genetic algorithms (GA). In this paper we introduce a mathematical framework concerning the manner in which genetic algorithms can learn, and show that gradient descent can be used in this frameork as well. In order to develop this theory, we use a class of stochastic genetic algorithms (GA) based on a population of chromosomes with mutation and crossover, as well as fitness, which we have described earlier in .
Unable to display preview. Download preview PDF.
- 2.Kernighan, B. and Lin, S. “An efficient heuristic procedure for partitioning graphs”, The Bell System Technical Journal, (February 1970).Google Scholar
- 3.Holland, J. “Adaptation in Natural and Artificial Systems,” The University of Michigan Press, Ann Arbor, Michigan (1975).Google Scholar
- 4.De Jong, Kenneth A. “An Analysis of the Behaviour of a Class of Genetic Adaptive Systems”, Doctoral Thesis, Department of Computer and Communication Sciences, University of Michigan, Ann Arbor (1975).Google Scholar
- 6.Gelenbe, E. and Pujolle, G. “Introduction to Networks of Queues”, J. Wiley and Sons, New York and London (1988), 2nd Edition (1998).Google Scholar
- 7.Muehlenbein, H., Schleuter, G. and Kramm, D. “Evolution algorithms in combinatorial optimization”, Parallel Computing, Vol 7, No 2, (1988).Google Scholar
- 10.Talbi, E. and Bessière, P. “Un algorithme génétique massivement parallèle pour le problème de partitionement de graphes”. Rapport de recherche. Laboratoire de Génie Informatique de Grenoble (1991).Google Scholar
- 12.Vose, M.D. “Formalizing genetic algorithms”, Technical Report (CS-91-127), Department of Computer Science, The University of Tennessee (1991).Google Scholar
- 13.Vose, M.D. “Modeling simple genetic algorithms”, in Whitley, L. Darrell ed.), “Foundations of Genetic Algorithms 2”, Morgan Kaufmann, San Mateo (1993).Google Scholar