The impact of parametrization in memetic evolutionary algorithms

Memetic (evolutionary) algorithms integrate local search into the search process of evolutionary algorithms. As computational resources have to be spread adequately among local and evolutionary search, one has to care about when to apply local search and how much computational effort to devote to local search. Often local search is called with a fixed frequency and run for a fixed number of iterations, the local search depth. There is empirical evidence that these parameters have a significant impact on performance, but a theoretical understanding as well as concrete design guidelines are missing.We initiate the rigorous theoretical analysis of memetic algorithms. To this end, we consider a simple memetic algorithm for pseudo-Boolean optimization that captures basic working principles of memetic algorithms—the interplay of genetic operators like mutation and selection with local search. We present function classes where even small changes of the parametrization have a strong impact on performance. For almost every reasonable parameter setting we construct a function that, with high probability, can be optimized in polynomial time. However, changing the local search depth by a small additive term in any direction yields a superpolynomial optimization time, with high probability. For another class of functions altering the local search frequency by a factor of 2 even yields exponential optimization times.Our results show exemplarily that parametrizing memetic evolutionary algorithms can be extremely hard. Moreover, this work yields insights into the dynamic behavior of memetic algorithms and contributes to a theoretical foundation of hybrid metaheuristics.