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 often complicated interplay of parameters, setting these right for a particular problem (parameter tuning) is challenging task. This task becomes even more when optimal parameter change significantly during run algorithm since then dynamic choice control) necessary. In this work, we propose lazy but effective solution, namely choosing all (where makes sense) in each iteration randomly from suitably scaled power-law distribution. To demonstrate effectiveness approach, perform runtime analyses $(1+(\lambda,\lambda))$ genetic with three chosen manner. We show that on one hand can imitate simple hill-climbers like $(1+1)$ EA, giving same asymptotic problems OneMax, LeadingOnes, or Minimum Spanning Tree. On other hand, also very efficient jump functions, where best static are different those necessary optimize problems. prove performance guarantee comparable known parameters. For most interesting case size $k$ constant, our asymptotically better than what be obtained any choice. complement theoretical results rigorous empirical study confirming suggest.