Continuous optimisation theory made easy? finite-element models of evolutionary strategies, genetic algorithms and particle swarm optimizers

Authors:
Riccardo Poli;William B. Langdon;Maurice Clerc;Christopher R. Stephens
Affiliations:
Department of Computer Science, University of Essex, UK;Department of Mathematical Sciences, University of Essex, UK;Independent Consultant, Groisy, France;Instituto de Ciencias Nucleares, UNAM, México
Venue:
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Year:
2007

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Abstract

We propose a method to build discrete Markov chain models of continuous stochastic optimisers that can approximate them on arbitrary continuous problems to any precision. We discretise the objective function using a finite element method grid which produces corresponding distinct states in the search algorithm. Iterating the transition matrix gives precise information about the behaviour of the optimiser at each generation, including the probability of it finding the global optima or being deceived. The approach is tested on a (1+1)-ES, a bare bones PSO and a real-valued GA. The predictions are remarkably accurate.