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.
These can also be studied using discrete Markov chain models that can approximate them on arbitrary continuous problems to any precision REF .
Continuous optimisation theory made easy? Finite-element models of evolutionary strategies, genetic algorithms and particle swarm optimizers
Department of Computer Science, University of Essex
Computer Science