A Co-Evolutionary Multi-Objective Framework for Joint Topology and Parameter Discovery in Gene Regulatory Networks

Inferring gene regulatory networks (GRN) poses a complex discrete-continuous, multi-objective optimization problem that requires the simultaneous discovery of both network topology and kinetic parameters. Current methods are often limited because they address these two challenges separately. We propose a novel co-evolutionary multi-objective framework that evolves topology and parameter populations in tandem to optimize three competing objectives: dynamic fidelity, network simplicity, and robustness. This algorithm utilizes biologically-inspired operators and is grounded in theoretical results on Pareto optimality for mixed discrete-continuous spaces. In computational experiments on synthetic benchmarks, our approach showed superior performance, attaining the lowest mean squared error in three of four test cases against single-objective and topology-fixed methods. The framework successfully discovers multiple functionally equivalent network configurations, a finding that highlights the degeneracy inherent in biological systems and offers practical insights for synthetic biology, where function is often prioritized over precise structural accuracy.