Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy

Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets.