Multi-objective optimal control of dynamic bioprocesses using ACADO Toolkit

Process simulation and evaluation of scaled-up biocatalytic systems: Advances, challenges, and future prospects

With the increased demand for bio-based products and the rapid development of biomanufacturing technologies, biocatalytic reactions including microorganisms and enzyme based, have become promising approaches. Prior to the scale-up of production process, environmental and economic feasibility analysis are essential for the development of a sustainable and intelligent bioeconomy in the context of industry 4.0. To achieve these goals, process simulation supports system optimization, improves energy and resource utilization efficiencies, and supports digital bioprocessing. However, due to the insufficient understanding of cellular metabolism and interaction mechanisms, there is still a lack of rational and transparent simulation tools to efficiently simulate, control, and optimize microbial/enzymatic reaction processes. Therefore, there is an urgent need to develop frameworks that integrate kinetic modeling, process simulation, and sustainability analysis for bioreaction simulations and their optimization. This review summarizes and compares the advantages and disadvantages of different process simulation software and models in simulating biocatalytic processes, identifies the limitations of traditional reaction kinetics models, and proposes the requirement of simulations close to real reactions. In addition, we explore the current state of kinetic modeling at the microscopic scale and how process simulation can be linked to kinetic models of cellular metabolism and computational fluid dynamics modeling. Finally, this review discusses the requirement of sensitivity analysis and how machine learning can assist with optimization of simulations to improve energy efficiency and product yields from techno-economic and life cycle assessment perspectives.

Dynamic optimization of fed-batch bioprocesses using flower pollination algorithm

There exist several optimization strategies such as sequential quadratic programming (SQP), iterative dynamic programing (IDP), stochastic-based methods such as differential evolution (DE), genetic algorithm (GA), particle swarm optimization (PSA), and ant colony optimization (ACO) for finding optimal feeding profile(s) during fed-batch fermentations. Here in the present study, flower pollination algorithm (FPA) which is inspired by the pollination process in terrestrial flowering plants has been used for the first time to find the optimal feeding profile(s) during fed-batch fermentations. Single control variable, two control variables and state variable bounded problems were chosen to test the robustness of the FPA for optimal control problems. It was observed that FPA is computationally less intensive in comparison with other stochastic strategies. Thus, obtained results were compared to other studies and it has been found that the FPA converged either to newer optima or closer to the established global optimum for the cases studied.

Production optimization for concentration and volume-limited fed-batch reactors in biochemical processes

Since a very slight violation of constraint could cause process safety and product quality problems in biochemical processes, an adaptive approach of fed-batch reactor production optimization that can strictly satisfy constraints over the entire operating time is presented. In this approach, an improved smooth function is proposed such that the inequality constraints can be transformed into smooth constraints. Based on this, only an auxiliary state is needed to monitor violations in the augmented performance index. Combined with control variable parameterization (CVP), the dynamic optimization is executed and constraint violations are examined by calculating the sensitivities of states to ensure that the inequality constraints are satisfied everywhere inside the time interval. Three biochemical production optimization problems, including the manufacturing of ethanol, penicillin and protein, are tested as illustrations. Meanwhile, comparisons with pure penalty CVP method, famous dynamic optimization toolbox DOTcvp and literature results are carried out. Research results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost.

Sensitivity-based adaptive mesh refinement collocation method for dynamic optimization of chemical and biochemical processes

Collocation on finite element (CFE) is an effective simultaneous method of dynamic optimization to increase the profitability or productivity of industrial process. The approach needs to select an optimal mesh of time interval to balance the computational cost with desired solution. A new CFE approach with non-uniform refinement procedure based on the sensitivity analysis for dynamic optimization problems is, therefore, proposed, where a subinterval is further refined if the obtained control parameters have significant effect on the performance index. To improve the efficiency, the sensitivities of state parameters with respect to control parameters are derived from the solution of the discretized dynamic system. The proposed method is illustrated by testing two classic dynamic optimization problems from chemical and biochemical engineering. The detailed comparisons among the proposed method, the CFE with uniform mesh, and other reported methods are also carried out. The research results reveal the effectiveness of the proposed approach.

Dynamic optimization of biological networks under parametric uncertainty

BACKGROUND

Micro-organisms play an important role in various industrial sectors (including biochemical, food and pharmaceutical industries). A profound insight in the biochemical reactions inside micro-organisms enables an improved biochemical process control. Biological networks are an important tool in systems biology for incorporating microscopic level knowledge. Biochemical processes are typically dynamic and the cells have often more than one objective which are typically conflicting, e.g., minimizing the energy consumption while maximizing the production of a specific metabolite. Therefore multi-objective optimization is needed to compute trade-offs between those conflicting objectives. In model-based optimization, one of the inherent problems is the presence of uncertainty. In biological processes, this uncertainty can be present due to, e.g., inherent biological variability. Not taking this uncertainty into account, possibly leads to the violation of constraints and erroneous estimates of the actual objective function(s). To account for the variance in model predictions and compute a prediction interval, this uncertainty should be taken into account during process optimization. This leads to a challenging optimization problem under uncertainty, which requires a robustified solution.

RESULTS

Three techniques for uncertainty propagation: linearization, sigma points and polynomial chaos expansion, are compared for the dynamic optimization of biological networks under parametric uncertainty. These approaches are compared in two case studies: (i) a three-step linear pathway model in which the accumulation of intermediate metabolites has to be minimized and (ii) a glycolysis inspired network model in which a multi-objective optimization problem is considered, being the minimization of the enzymatic cost and the minimization of the end time before reaching a minimum extracellular metabolite concentration. A Monte Carlo simulation procedure has been applied for the assessment of the constraint violations. For the multi-objective case study one Pareto point has been considered for the assessment of the constraint violations. However, this analysis can be performed for any Pareto point.

CONCLUSIONS

The different uncertainty propagation strategies each offer a robustified solution under parametric uncertainty. When making the trade-off between computation time and the robustness of the obtained profiles, the sigma points and polynomial chaos expansion strategies score better in reducing the percentage of constraint violations. This has been investigated for a normal and a uniform parametric uncertainty distribution. The polynomial chaos expansion approach allows to directly take prior knowledge of the parametric uncertainty distribution into account.