A Bilevel Integer Programming Approach for the Synchronous Attractor Control Problem

2026-04-01

AI Summary

This study addresses the problem of enumerating minimal control strategies in Boolean networks that guarantee all attractors satisfy a desired phenotype. The authors propose a bilevel integer programming model tailored to multiple subproblems and develop an infeasibility-based logic Benders decomposition framework. A key innovation is the introduction of subspace separation techniques to generate stronger feasibility cuts, significantly accelerating convergence. The resulting method markedly enhances scalability and computational efficiency, substantially outperforming state-of-the-art approaches in numerical experiments. This advancement provides a powerful computational tool for identifying critical subsets of disease-associated genes.

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.

Problem

• Boolean networks
• attractor control
• bilevel integer programming
• minimal controls
• phenotype

Innovation

• bilevel integer programming
• Benders decomposition
• Boolean networks
• attractor control
• subspace separation