Parent selection algorithms (selection schemes) steer populations through a problem's search space, often trading off between exploitation and exploration. Understanding how selection schemes affect exploitation and exploration within a search space is crucial to tackling increasingly challenging problems. Here, we introduce an "exploration diagnostic" that diagnoses a selection scheme's capacity for search space exploration. We use our exploration diagnostic to investigate the exploratory capacity of lexicase selection and several of its variants: epsilon lexicase, down-sampled lexicase, cohort lexicase, and novelty-lexicase. We verify that lexicase selection out-explores tournament selection, and we show that lexicase selection's exploratory capacity can be sensitive to the ratio between population size and the number of test cases used for evaluating candidate solutions. Additionally, we find that relaxing lexicase's elitism with epsilon lexicase can further improve exploration. Both down-sampling and cohort lexicase -- two techniques for applying random subsampling to test cases -- degrade lexicase's exploratory capacity; however, we find that cohort partitioning better preserves lexicase's exploratory capacity than down-sampling. Finally, we find evidence that novelty-lexicase's addition of novelty test cases can degrade lexicase's capacity for exploration. Overall, our findings provide hypotheses for further exploration and actionable insights and recommendations for using lexicase selection. Additionally, this work demonstrates the value of selection scheme diagnostics as a complement to more conventional benchmarking approaches to selection scheme analysis.

中文翻译：

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An Exploration of Exploration：测量词法选择的能力，以找到通往最优性的模糊路径

父选择算法（选择方案）通过问题的搜索空间引导种群，通常在开发和探索之间进行权衡。了解选择方案如何影响搜索空间内的开发和探索对于解决越来越具有挑战性的问题至关重要。在这里，我们引入了一种“探索诊断”，用于诊断选择方案的搜索空间探索能力。我们使用我们的探索诊断来研究词法酶选择及其几种变体的探索能力：epsilon 词法酶、下采样词法酶、队列词法酶和新颖性词法酶。我们验证了词法选择超过了锦标赛选择，并且我们证明了词法选择' s 探索能力可能对人口规模与用于评估候选解决方案的测试用例数量之间的比率敏感。此外，我们发现用 epsilon lexicase 放松 lexicase 的精英主义可以进一步改善探索。下采样和队列词法酶——两种将随机子采样应用于测试用例的技术——都会降低词法酶的探索能力；然而，我们发现队列分区比下采样更好地保留了词法酶的探索能力。最后，我们发现了新奇词典添加新奇测试用例会降低词典探索能力的证据。总体而言，我们的发现为进一步探索提供了假设，并为使用词法选择提供了可行的见解和建议。此外，