Robust Optimization of Nonlinear Processes under Uncertainty

Lead Research Organisation: Imperial College London
Department Name: Chemical Engineering


Many important questions and challenges in process systems design, operation and control can be typically posed as nonlinear optimization problems. To date, most optimal decision making tools for such problems are mainly based on deterministic mathematical models, where all parameter values in the model are assumed to be known precisely. In practice, however, mathematical models are merely approximate descriptions of the real system, and parameters such as future demands, prices, equipment wearout and process conditions are subject to significant uncertainty. It has been frequently shown that disregarding such uncertainty can lead to severe performance losses, increased costs, and energy/environmental penalties. We propose to develop robust, local and global optimization methods for the efficient solution of such nonlinear optimization problems in the presence of uncertainties. Depending on their nature, uncertainties can be accounted for in a static/proactive or reactive way. Two important industrial applications will be investigated and the developed methods will be applied for the integrated design, optimization and control of process systems under uncertainty.

Planned Impact

While the impact of this project is likely to be in several areas, a few key beneficiaries have been particularly identified. First, the methodologies and tools that will be developed in this project will be very important for both the UK and international chemical process industry. Many important decision problems in the chemical process industry require stochastic and robust optimization-based solution approaches, e.g., production planning, scheduling, design and control of chemical processing systems, melt control, blending problems, supply chain management, etc. All these problems are affected by significant uncertainties. In fact, chemical processes are often poorly understood because of the physicochemical complexities. Robustness with respect to model uncertainty is thus essential to ensure effective operation. Moreover, there are substantial uncertainties concerning the availability of resources, the prices and demands of products, the reliability and availability of plants or machines, etc. These are resolved using parametric and/or robust approaches as appropriate. Robustness of the models is also essential to guarantee the operational safety of chemical plants. Second, the natural resource and energy companies will be interested in using the proposed robust optimization tools to support decision making for the supply/transportation of gas, oil and energy and for business development and trading. Since companies such as oil and gas suppliers, energy marketers and traders face a growing and uncertain global energy market, where the uncertainty is caused by multiple factors such as demand and price volatility, political and regulatory developments, the emerge of new undeveloped markets etc., the optimization of the capacity, resources, cost and environmental impact requires that these uncertainties are efficiently analysed and encountered in the decision making process. Robust optimization approaches are well suited for these types of problems. Third, multiproduct and custom manufacturing industry will benefit from the use of the proposed methodologies and tools of this project for the design, optimization and control of innovative processes and products, such as polymerization and hydrogen separation as well as production planning/scheduling. These are highly nonlinear processes with the uncertainties accounting for the complexity of the process or product, model uncertainties, raw material price variability etc. Fourthly, the developers of computational optimization software tools will benefit for the methodologies and tools developed in this project as they will be able to update and improve their current optimization software products with our new methods as well as develop new ones. Finally, the tools that will be developed in this project will also be offered free for academic research and further development, thus distinctly benefiting the wider UK and international academic and research community.


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Description The main developments from this research project concern robust model-predictive control and scheduling in an explicit fashion. We combine well-known approaches from robust optimization with multi-parametric programming techniques, which enable the description of novel, efficient algorithms which explore the structure of the uncertainty to provide robust control and scheduling policies. More specifically, the key findings are:
- The impact of different types of uncertainty structure onto the robust optimization problem.
- The ability to apply the concept of robust counterparts to multi-stage processes for the continuous as well as the hybrid case.
- The consideration of multiplicative as well as additive disturbance and the consideration of both robust model-predictive control and robust scheduling approaches.
- The application to pressure swing absorption as part of a unified framework for the development of design and operational policies for process systems.

In addition, the scope was broadened to also include research into linear parameter varying systems as well as advances in robust optimization theory.
Exploitation Route The research enables the increased use of model-predictive control in industrial applications, as it enables the systematic capture of model uncertainty in a computationally efficient manner. Thus, it is able to give confidence to industrial practitioners wishing to ensure the safety of their operation in the face of such uncertainty. Additionally, the research points towards a generalized methodology for the integration of robust control and scheduling, as the ability to integrate operational policies critically relies on the reliability of each aspect of the operation. This integration enables the development of novel, more efficient processes in areas such as energy and production scheduling, heat and power integration and biomanufacturing.
Sectors Energy,Healthcare,Manufacturing, including Industrial Biotechology