Optimization of Kinetic--Stoichiometric Growth Bounds over Autocatalytic Subnetworks
Autocatalytic subnetworks govern sustained production and balanced growth in chemical reaction systems and can be naturally represented as directed multihypergraphs that jointly encode stoichiometric structure and reaction kinetics. Existing optimization approaches identify such subnetworks by maximizing their structural amplification, typically measured through the Maximum Amplification Factor (MAF). However, structural amplification alone does not determine growth potential, since highly amplifying subnetworks may be kinetically inefficient. Motivated by recent kinetic--stoichiometric bounds on balanced growth under scalable dynamics, we study the problem of selecting the autocatalytic subnetwork maximizing the growth bound $(α^*-1)\|\mathbb{S}|_{\mathcal A'}\|_κ$, where $α^*$ is the MAF and $\|\mathbb{S}|_{\mathcal A'}\|_κ$ is a kinetic consumption norm. We formulate the problem as a mixed-integer bilinear optimization model combining hypergraph selection with generalized fractional amplification constraints. Exploiting the discrete structure of the kinetic norm, we develop an exact parametric algorithm in which each subproblem reduces to MAF maximization and is solved through a Dinkelbach-type generalized fractional programming method. Finite convergence and global optimality are established. Applications to the Oregonator, the formose reaction, carbon-fixation cycles, and synthetic benchmark networks show when maximizing the kinetic--stoichiometric bound differs from maximizing the MAF alone, revealing the interplay between stoichiometric amplification, reaction kinetics, and balanced growth. The proposed framework provides an exact optimization methodology for identifying reaction subnetworks with the highest theoretical growth potential.