NK和广义NK景观的分析
An analysis of NK and generalized NK landscapes
摘要：
几十年来，模拟景观一直被用来评估搜索策略，其目标是找到具有最大适应度的景观位置。应用包括模拟酶催化反应的能力和医学治疗的临床有效性。理解景观的属性对于理解搜索难度很重要。本文提出了一种新的和透明的表征NK景观。我们证明NK景观可以用参数线性相互作用模型来表示，其中模型系数具有有意义的解释。我们推导出模型系数的统计特性，深入了解NK算法如何解析主效应和相互作用的重要性。从线性模型表示中得出的一个重要见解是，由NK算法定义的线性模型的秩与局部最优值的数量相关，局部最优值是景观复杂性和搜索难度的重要决定因素。我们发现，NK景观的最大排名是通过上位相互作用，形成部分平衡的不完全区组设计。最后，推导出代表景观局部最优解预期数量的解析表达式，提供了一种快速计算非常大的景观局部最优解预期数量的方法。
英文摘要：
Simulated landscapes have been used for decades to evaluate search strategies whose goal is to find the landscape location with maximum fitness. Applications include modeling the capacity of enzymes to catalyze reactions and the clinical effectiveness of medical treatments. Understanding properties of landscapes is important for understanding search difficulty. This paper presents a novel and transparent characterization of NK landscapes. We prove that NK landscapes can be represented by parametric linear interaction models where model coefficients have meaningful interpretations. We derive the statistical properties of the model coefficients, providing insight into how the NK algorithm parses importance to main effects and interactions. An important insight derived from the linear model representation is that the rank of the linear model defined by the NK algorithm is correlated with the number of local optima, a strong determinant of landscape complexity and search difficulty. We show that the maximal rank for an NK landscape is achieved through epistatic interactions that form partially balanced incomplete block designs. Finally, an analytic expression representing the expected number of local optima on the landscape is derived, providing a way to quickly compute the expected number of local optima for very large landscapes.
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