The migration interval is one of the fundamental parameters governing the dynamic behaviour of island models. Yet, there is little understanding on how this parameter affects performance, and how to optimally set it given a problem in hand. We propose schemes for adapting the migration interval according to whether fitness improvements have been found. As long as no improvement is found, the migration interval is increased to minimise communication. Once the best fitness has improved, the migration interval is decreased to spread new best solutions more quickly. We provide a method for obtaining upper bounds on the expected running time and the communication effort, defined as the expected number of migrants sent. Example applications of this method to common example functions show that our adaptive schemes are able to compete with, or even outperform, the optimal fixed choice of the migration interval, with regard to running time and communication effort.

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