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:大多数进化算法都有多个参数, 并且其值会极大地影响性能。 由于参数的相互作用往往非常复杂, 将这些值设定为适合特定问题( 参数调制) 是一项艰巨的任务。 当最优参数值在算法运行期间发生重大变化时, 这个任务变得更加复杂, 因为自那时起需要动态参数选择( 参数控制) 。 在这项工作中, 我们提出一个懒惰但有效的解决方案, 即随机地从适当缩放的电源法分布中选择所有参数值( 在这样合情理的情况下) 。 由于这些参数的相互作用往往非常复杂, 我们用这个方法来对$(1+ (\ lambda,\ lambda)) 进行运行时间分析, 并且用这个方法对所有三种参数都进行这种方式选择。 我们显示, 一只手上的算法可以模仿像$(1+ 1) EA 这样的简单的坡度选择( ), 给 Onemax 运行时间, 从 Onemax, oral Astial Ameral oral oral rodudeal ass is be be be be be be be be be be be be be be be be suol as the firstal suol suol suoltiental press as to as the ex ex as the prociental pract exisol as.</s>