从理解遗传漂变到智能重启的无参数紧凑遗传算法
From Understanding Genetic Drift to a Smart-Restart Parameter-less Compact Genetic Algorithm
AI总结：
针对分布估计算法中种群规模选择困难的问题，提出无参数紧凑遗传算法，通过智能重启机制自动适配规模并中止遗传漂变运行，在理论与实验上均证明其具备高效性与鲁棒性。
摘要：
使用分布估计算法的关键难点之一是合理选择种群规模：取值过小会导致遗传漂变，从而引发巨大困难。然而，在没有遗传漂变的情况下，运行时间通常与种群规模大致成正比，这使得过大的种群规模效率低下。基于近期关于何种种群规模会导致遗传漂变的定量分析，我们提出了一种无参数版本的紧凑遗传算法（compact genetic algorithm, cGA），该算法能够自动寻找合适的种群规模，且不会在因遗传漂变而处于不利情况的场景中耗费过多时间。我们为该算法证明了数学运行时间保证，并在四个经典基准问题上进行了广泛的实验分析，这些问题包含无噪声和带有加性中心高斯后验噪声两种情况。前者表明，在自然假设下，我们的算法性能与通过最佳问题特定种群规模获得的性能非常相似。后者证实，在原始cGA中错过正确的种群规模可能是有害的，并且先前基于理论的种群规模建议可能与正确值相去甚远；它还表明我们的算法以及先前提出的一种基于并行运行的无参数cGA变体能够避免此类陷阱。比较这两种无参数方法，我们的方法得益于其能够中止可能陷入遗传漂变情况的运行的能力。
英文摘要：
One of the key difficulties in using estimation-of-distribution algorithms is choosing the population size(s) appropriately: Too small values lead to genetic drift, which can cause enormous difficulties. In the regime with no genetic drift, however, often the runtime is roughly proportional to the population size, which renders large population sizes inefficient. Based on a recent quantitative analysis which population sizes lead to genetic drift, we propose a parameter-less version of the compact genetic algorithm that automatically finds a suitable population size without spending too much time in situations unfavorable due to genetic drift. We prove a mathematical runtime guarantee for this algorithm and conduct an extensive experimental analysis on four classic benchmark problems both without and with additive centered Gaussian posterior noise. The former shows that under a natural assumption, our algorithm has a performance very similar to the one obtainable from the best problem-specific population size. The latter confirms that missing the right population size in the original cGA can be detrimental and that previous theory-based suggestions for the population size can be far away from the right values; it also shows that our algorithm as well as a previously proposed parameter-less variant of the cGA based on parallel runs avoid such pitfalls. Comparing the two parameter-less approaches, ours profits from its ability to abort runs which are likely to be stuck in a genetic drift situation.
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