Convex optimization of bioprocesses

TL;DR

This paper develops a convex optimization approach for bioprocesses, enabling efficient and exact solutions for complex nonconvex models in wastewater treatment systems.

Contribution

It introduces a convex relaxation method for bioprocess models, with conditions for exactness and efficient solutions using second-order cone programming.

Findings

Convex relaxation is exact under certain conditions.

Second-order cone programming efficiently solves large-scale problems.

Model successfully applied to wastewater treatment system.

Abstract

We optimize a general model of bioprocesses, which is nonconvex due to the microbial growth in the biochemical reactors. We formulate a convex relaxation and give conditions guaranteeing its exactness in both the transient and steady state cases. When the growth kinetics are modeled by the Monod function under constant biomass or the Contois function, the relaxation is a second-order cone program, which can be solved efficiently at large scales. We implement the model on a numerical example based on a wastewater treatment system.