Convex Optimization of Bioprocesses

In this talk, we begin by optimizing the gradostat, in which several bioreactors are interconnected by mass flow and diffusion. The gradostat is of interest both as a classical nonlinear system and because the basic network structure and nonlinearities appear in a wide variety of bioprocesses, including wastewater treatment. We formulate a convex relaxation for optimizing the gradostat. The relaxation is exact under several conditions, for example, if the gradostat is outflow connected and its flow matrix is irreducible. When the microbial growth in the bioreactors is described by the Monod or Contois functions, the relaxation is a second-order cone program, which can be solved at scales of over 10^5 variables in minutes with industrial software. We present a numerical example based on the operation of a wastewater treatment network over a two-week period.