Iterated Local Search with Linkage Learning

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.