Variable-Dimensional Optimization with Evolutionary Algorithms Using Fixed-Length Representations

This paper discusses a simple representation of variable-dimensional optimization problems for evolutionary algorithms. Although it was successfully applied to the optimization of multi-layer optical coatings, it is shown that it introduces a unintentional bias into the search process with respect to the probability of a dimension being generated by mutation and recombination. In order to examine the impact of the bias, the representation was applied to another variable-dimensional problem, the simultaneous estimation of model orders and model parameters of instances of autoregressive moving average processes (ARMA). The results of the parameter study show that quality of the estimation can be improved by removing the bias.