In pseudo-Boolean optimization, a variable interaction graph represents variables as vertices, and interactions between pairs of variables as edges. In black-box optimization, the variable interaction graph may be at least partially discovered by using empirical linkage learning techniques. These methods never report false variable interactions, but they are computationally expensive. The recently proposed local search with linkage learning discovers the partial variable interaction graph as a side-effect of iterated local search. However, information about the strength of the interactions is not learned by the algorithm. We propose local search with linkage learning 2, which builds a weighted variable interaction graph that stores information about the strength of the interaction between variables. The weighted variable interaction graph can provide new insights about the optimization problem and behavior of optimizers. Experiments with NK landscapes, knapsack problem, and feature selection show that local search with linkage learning 2 is able to efficiently build weighted variable interaction graphs. In particular, experiments with feature selection show that the weighted variable interaction graphs can be used for visualizing the feature interactions in machine learning. Additionally, new transformation operators that exploit the interactions between variables can be designed. We illustrate this ability by proposing a new perturbation operator for iterated local search.

翻译：在伪布尔优化中，变量交互图将变量表示为顶点，变量对之间的交互关系表示为边。在黑盒优化中，变量交互图至少可以通过经验性关联学习技术部分发现。这些方法从不报告错误的变量交互，但计算成本高昂。最近提出的基于关联学习的局部搜索方法，将部分变量交互图的发现作为迭代局部搜索的副产品。然而，该算法未能学习关于交互强度的信息。我们提出基于关联学习的局部搜索2，该方法构建了一个加权变量交互图，用于存储变量间交互强度的信息。加权变量交互图能够为优化问题及优化器行为提供新的洞见。在NK景观、背包问题和特征选择上的实验表明，基于关联学习的局部搜索2能够高效构建加权变量交互图。特别是在特征选择实验中，加权变量交互图可用于可视化机器学习中的特征交互。此外，可以利用变量间的交互关系设计新的变换算子。我们通过为迭代局部搜索提出一种新的扰动算子来展示这种能力。