Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm in a certain broad class of black-box optimizers can give fruitful indications in which direction to search for good established optimization heuristics. We demonstrate this approach on the recently proposed DLB benchmark, for which the only known results are $O(n^3)$ runtimes for several classic evolutionary algorithms and an $O(n^2 \log n)$ runtime for an estimation-of-distribution algorithm. Our finding that the unary unbiased black-box complexity is only $O(n^2)$ suggests the Metropolis algorithm as an interesting candidate and we prove that it solves the DLB problem in quadratic time. Since we also prove that better runtimes cannot be obtained in the class of unary unbiased algorithms, we shift our attention to algorithms that use the information of more parents to generate new solutions. An artificial algorithm of this type having an $O(n \log n)$ runtime leads to the result that the significance-based compact genetic algorithm (sig-cGA) can solve the DLB problem also in time $O(n \log n)$ with high probability. Our experiments show a remarkably good performance of the Metropolis algorithm, clearly the best of all algorithms regarded for reasonable problem sizes.

翻译：面对一个新的优化问题时，从无数不同的搜索启发式算法中选择合适的算法非常困难。本文论证了一个纯学术问题——在某一广泛的黑箱优化器类别中，什么可能是最佳算法——能够为寻找成熟优化启发式算法的方向提供富有成效的启示。我们在最近提出的DLB基准上展示了这一方法，该基准中，几种经典进化算法的已知运行时间仅为$O(n^3)$，而一种估计分布算法的运行时间为$O(n^2 \log n)$。我们发现一元无偏黑箱复杂性仅为$O(n^2)$，这提示Metropolis算法是一个有趣的候选者，并证明它以二次时间解决了DLB问题。由于我们还证明在一元无偏算法类别中无法获得更好的运行时间，因此我们将注意力转向利用更多父代信息生成新解的算法。一种具有$O(n \log n)$运行时间的人工算法表明，基于显著性的紧凑遗传算法（sig-cGA）也能以高概率在$O(n \log n)$时间内解决DLB问题。我们的实验显示，Metropolis算法的性能异常出色，在合理问题规模下，它显然是所有考虑的算法中最好的。