Stochastic Dynamic Optimization of Batch and Semicontinuous Bioprocesses

Abstract

The dynamic optimization (optimal control) of batch and semicontinuous bioprocesses, like fed‐batch fermentation and bioproduct batch separation, has received considerable attention in recent years. These constrained dynamic optimization problems are difficult to solve due to their highly nonlinear character and also due to the fact that they usually are multimodal; therefore most proposed methods may fail to find the global optima. Besides, these methods are not always easy to implement and use, mainly because a laborious preparation and/or transformation of the original problem is needed. Here we present a simple yet powerful method that requires no initial preparation stage and that is useful to solve several complex optimal control problems without convergence difficulties. Two fed‐batch bioreactor case studies, taken from the recent literature, and a third case study considering a complex bioproduct dehydration problem are successfully and efficiently solved with our new approach, and its advantages are discussed.

Interval and Possibilistic Methods for Constraint-Based Metabolic Models

“…Model-based optimisation provides an alternative to the trial-and-error methods that prevail in industry, and leads to better performance within shorter development time intervals. Optimisation strategies for bioprocesses can be classified in categories: one-time optimisation (Banga, 2003;2008b), run-to-run optimisation (Camacho, 2007) and on-line optimisation (Visser, 2000).…”

“…These can be detected by inspection of R: exactly those wm,j for which the corresponding j-th column of R contains at least one nonzero value are balanceable (20) After adjusting the measured fluxes, the non-measured fluxes can be calculated with equation (15). If the problem is determined and not redundant the unique v u fulfilling (15) can be calculated using the inverse of N u .…”

“…where v p is a particular solution, for instance, the one given by (20)(21), λ is an arbitrary vector with n-m elements, and K u is the kernel of N u . The product K u ·λ spans the space of possible flux values and represents the underdeterminacy of the system.…”

“…-Evaluate consistency to detect gross errors with (19) -Detect and adjust the balanceable fluxes with (20) (thus obtaining a consistent set of measurements)…”

“…Recalling the ideas introduced the preliminaries section, the interpretation of (19) and (20) may be the following: "vm = wm is fully possible; the more vm differs from wm, the less possible such situation is. "…”