Lazy parameter tuning and control: Choosing all parameters randomly from a power-law distribution

Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem is a challenging task. This task becomes even more complicated when the optimal parameter values change significantly during the run of the algorithm since then a dynamic parameter choice is necessary. In this work, we propose a lazy but effective solution, namely choosing all parameter values in each iteration randomly from a suitably scaled power-law distribution. We demonstrate the effectiveness of this approach via runtime analyses of the (1 + (λ, λ)) genetic algorithm with all three parameters chosen in this manner. We show that this algorithm on the one hand can imitate simple hill-climbers like the (1+1) EA, giving the same asymptotic runtime on some simple problems. On the other hand, this algorithm is also very efficient on jump functions, where the best static parameters are very different from those necessary to optimize simple problems. We prove a performance guarantee that is comparable to, and sometimes even better than, the best performance known for static parameters. We complement our theoretical results with a rigorous empirical study confirming what the asymptotic runtime results suggest.