A Bilevel Integer Programming Approach for the Synchronous Attractor Control Problem

TL;DR

This paper introduces a novel Benders decomposition approach to efficiently identify minimal gene controls in Boolean network models of disease, enhancing scalability over existing methods.

Contribution

It develops an infeasibility-based Benders framework with subspace separation for bilevel integer programming in gene control problems, improving computational performance.

Findings

Algorithms outperform state-of-the-art methods in scalability.

Subspace separation significantly enhances algorithm efficiency.

Proposed methods effectively identify critical gene controls.

Abstract

Boolean networks are dynamical models of disease development in which the activation levels of genes are represented by binary variables. Given a Boolean network, controls represent mutations or medical treatments that fix the activation levels of selected genes so that all states in every attractor (i.e., long-term recurrent states) satisfy a desired phenotype. Our goal is to enumerate all minimal controls, identifying critical gene subsets in disease development and therapy. This problem has an inherent bilevel integer programming structure and is computationally challenging. We propose an infeasibility-based Benders decomposition, a logic-based Benders framework for bilevel integer programs with multiple subproblems. In our application, each subproblem finds a forbidden attractor of a given length and yields a problem-specific feasibility cut. We also propose an auxiliary IP called subspace separation that finds a Boolean subspace that includes multiple forbidden attractors and thereby strengthens the cut. Numerical experiments show that the resulting algorithms are much more scalable than state-of-the-art methods and that subspace separation substantially improves performance.