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 (parameter tuning) 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 (parameter control) is necessary. In this work, we propose a lazy but effective solution, namely choosing all parameter values (where this makes sense) in each iteration randomly from a suitably scaled power-law distribution. To demonstrate the effectiveness of this approach, we perform runtime analyses of the $(1+(\lambda,\lambda))$ 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 problems like OneMax, LeadingOnes, or Minimum Spanning Tree. 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 the best performance known for static parameters. For the most interesting case that the jump size $k$ is constant, we prove that our performance is asymptotically better than what can be obtained with any static parameter choice. We complement our theoretical results with a rigorous empirical study confirming what the asymptotic runtime results suggest.

翻译：大多数进化算法拥有多个参数，其数值会显著影响性能。由于参数间通常存在复杂的相互作用，为特定问题设定合适的参数值（参数调优）是一项具有挑战性的任务。当最优参数值在算法运行过程中发生显著变化时，这一任务变得更加复杂，因为此时需要动态参数选择（参数控制）。在本工作中，我们提出了一种简单但有效的解决方案：在每次迭代中，从适当缩放的幂律分布中随机选择所有参数值（在合理的情况下）。为了展示该方法的有效性，我们对采用这种方式选择所有三个参数的$(1+(\lambda,\lambda))$遗传算法进行了运行时间分析。我们证明，该算法一方面可以模仿简单的爬山算法（如$(1+1)$ EA），在OneMax、LeadingOnes或最小生成树等问题上实现相同的渐近运行时间。另一方面，该算法在跳跃函数上也十分高效，而跳跃函数的最优静态参数与优化简单问题所需的参数截然不同。我们证明其性能保证可媲美已知的静态参数最优性能。对于跳跃大小$k$为常数的最有趣情况，我们证明其性能在渐近意义上优于任何静态参数选择所能达到的效果。我们通过严格的实证研究补充了理论结果，证实了渐近运行时间分析的结论。