Optimal operation of parallel mini-bioreactors in bioprocess development using multi-stage MPC

Bioprocess development is commonly characterized by long development times, especially in the early screening phase. After promising candidates have been pre-selected in screening campaigns, an optimal operating strategy has to be found and verified under conditions similar to production. Cultivating cells with pulse-based feeding and thus exposing them to oscillating feast and famine phases has shown to be a powerful approach to study microorganisms closer to industrial bioreactor conditions. In view of the large number of strains and the process conditions to be tested, high-throughput cultivation systems provide an essential tool to sample the large design space in short time. We have recently presented a comprehensive platform, consisting of two liquid handling stations coupled with a model-based experimental design and operation framework to increase the efficiency in High Throughput bioprocess development. Using calibrated macro-kinetic growth models, the platform has been successfully used for the development of scale-down fed-batch cultivations in parallel mini-bioreactor systems. However, it has also been shown that parametric uncertainties in the models can significantly affect the prediction accuracy and thus the reliability of optimized cultivation strategies. To tackle this issue, we implemented a multi-stage Model Predictive Control (MPC) strategy to fulfill the experimental objectives under tight constraints despite the uncertainty in the parameters and the measurements. Dealing with uncertainties in the parameters is of major importance, since constraint violation would easily occur otherwise, which in turn could have adverse effects on the quality of the heterologous protein produced. Multi-stage approaches build up scenario tree, based on the uncertainty that can be encountered and computing optimal inputs that satisfy the constrains despite of such uncertainties. Using the feedback information gained through the evolution along the tree, the control approach is significantly more robust than standard MPC approaches without being overly conservative. We show in this study that the application of multi-stage MPC can increase the number of successful experiments, by applying this methodology to a mini-bioreactor cultivation operated in parallel.

Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders’ cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems.

On Multistage Multiscale Stochastic Capacitated Multiple Allocation Hub Network Expansion Planning

The hub location problem (HLP) basically consists of selecting nodes from a network to act as hubs to be used for flow traffic directioning, i.e., flow collection from some origin nodes, probably transfer it to other hubs, and distributing it to destination nodes. A potential expansion on the hub building and capacitated modules increasing along a time horizon is also considered. So, uncertainty is inherent to the problem. Two types of time scaling are dealt with; specifically, a long one (viz., semesters, years), where the strategic decisions are made, and another whose timing is much shorter for the operational decisions. Thus, two types of uncertain parameters are also considered; namely, strategic and operational ones. This work focuses on the development of a stochastic mixed integer linear optimization modeling framework and a matheuristic approach for solving the multistage multiscale allocation hub location network expansion planning problem under uncertainty. Given the intrinsic difficulty of the problem and the huge dimensions of the instances (due to the network size of realistic instances as well as the cardinality of the strategic scenario tree and operational ones), it is unrealistic to seek an optimal solution. A matheuristic algorithm, so-called SFR3, is introduced, which stands for scenario variables fixing and iteratively randomizing the relaxation reduction of the constraints and variables’ integrality. It obtains a (hopefully, good) feasible solution in reasonable time and a lower bound of the optimal solution value to assess the solution quality. The performance of the overall approach is computationally assessed by using stochastic-based perturbed well-known CAB data.

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

The effects of varying drought-heat signatures on terrestrial carbon dynamics and vegetation composition

The frequency and severity of droughts and heat waves are projected to increase under global warming. However, the differential impacts of climate extremes on the terrestrial biosphere and anthropogenic CO2 sink remain poorly understood. In this study, we analyse the effects of six hypothetical climate scenarios with differing drought-heat signatures, sampled from a long stationary climate model simulation, on vegetation distribution and land carbon dynamics, as modelled by a dynamic global vegetation model (LPX-Bern v1.4). The six forcing scenarios consist of a Control scenario representing a natural climate, a Noextremes scenario featuring few droughts and heatwaves, a Nocompound scenario which allows univariate hot or dry extremes but no co-occurring extremes, a Hot scenario with frequent heatwaves, a Dry scenario with frequent droughts, and a Hotdry scenario featuring frequent concurrent hot and dry extremes. We find that a climate with no extreme events increases tree coverage by up to 10 % compared to the Control and also increases ecosystem productivity as well as the terrestrial carbon pools. A climate with many heatwaves leads to an overall increase in tree coverage primarily in higher latitudes, while the ecosystem productivity remains similar to the Control. In the Dry and even more so in the Hotdry scenario, tree cover and ecosystem productivity are reduced by up to −4 % compared to the Control. Depending on the vegetation type, the effects from the Hotdry scenario are stronger than the effects from the Hot and Dry scenario combined, illustrating the importance of correctly simulating compound extremes for future impact assessment. Overall, our study illustrates how factorial model experiments can be employed to disentangle the effects from single and compound extremes.

Benefit–Risk Assessment of the French Surveillance Protocol of Apparently Healthy Biting Dogs and Cats for Human Rabies Prevention

In France, apparently healthy dogs and cats that bite humans must undergo an observation period of 15 days with three veterinary visits to ascertain that they remain healthy, indicating that no zoonotic transmission of rabies virus occurred via salivary presymptomatic excretion. This surveillance protocol is mandatory for all pets that have bitten humans, despite France’s rabies-free status in non-flying mammals (i.e., a very low rabies risk). In this context, we aimed to perform a benefit–risk assessment of the existing regulatory surveillance protocol of apparently healthy biting animals, as well as alternative surveillance protocols. A scenario-tree modelling approach was used to consider the possible successions of events between a dog or cat bite and a human death attributed to either rabies or to lethal harm associated with the surveillance protocol (e.g., lethal traffic accidents when traveling to veterinary clinics or anti-rabies centers). The results demonstrated that the current French surveillance protocol was not beneficial, as more deaths were generated (traffic accidents) than avoided (by prompt post-exposure prophylaxis administration). We showed here that less stringent risk-based surveillance could prove more appropriate in a French context. The results in this study could allow policy-makers to update and optimize rabies management legislation.