New Epistasis Measures for Detecting Independently Optimizable Partitions of Variables

An optimization problem is often represented with a set of variables, and the interaction between the variables is referred to as epistasis. In this paper, we propose two new measures of epistasis: internal epistasis and external epistasis. Then we show that they can quantify the decomposability of a problem, which has a theoretical meaning about how strongly the problem is independently optimizable with a partition of variables. We present examples of the problem decomposition and the results of experiments that support the consistency of the measures.