This project develops novel methods for optimising operation of complex large-scale processes, such as chemical plants, bio refineries, energy consumption in buildings, and industrial clusters with heat integration.
Modern approaches for realising optimal and sustainable operation of such processes are based on using a digital twin (i.e. a mathematical representation of the process) in a numerical optimisation algorithm that is repeatedly run to find the best process settings, such as valve openings, compressor power, or heating duties result in the most efficient and economic operation.
A challenge for applying these methods is that the resulting optimisation problem must be solved in real-time such that the optimal process settings can be implemented in the plant. When the uncertain operation conditions, such as energy prices or raw material quality is taken into account in the optimization, the resulting optimization problem can be too complex to solve in real-time, because the computational time is too long.
To speed up computational time, we develop new approaches that are based on decomposing the large and complex optimization problem into smaller subproblems that are easier to solve, and we repeatedly modify the subproblems, such that the collection of the subproblem solutions resembles the solution of the original problem.
The way the smaller subproblems are set up, makes it possible to solve only a few of these subproblems, and then obtain the solution to the full set of subproblems by tracking the optimal solution paths using efficient sensitivity path-following methods.
We will further develop these sensitivity methods for a class of optimization problems that allow for switching behaviour, for which these sensitivity methods do not exist yet.

The research in this project is focused on finding innovative strategies and developing new computational tools for fast optimization of large and complex dynamic systems with uncertain models and parameters. The project is embedded in a larger activity on optimization-based methods for achieving optimal operation in chemical plants in the Jäschke research group, and in the process systems engineering group at NTNU.
Optimization-based control of large systems requires solving large nonlinear programs (NLP) in real-time. When robust approaches are used to handle uncertainty, the problem can size increase dramatically (e.g Lucia et al, 2013). This large computational effort is an important reason for why many industry sectors are currently unwilling to use these methods.
To address this issue, our first objective is to develop new and efficient algorithms for solving large-scale NLP using a decomposition approach (Marti et al. 2015). In decomposition a large NLP is broken down into several smaller NLPs that are solved separately. The innovative idea in this project is to avoid solving the NLP for the subproblems, and instead apply a recently developed path-following algorithm (Jäschke et al 2014, Kungurtsev & Jäschke 2017), to obtain efficient approximate solutions of the subproblems. This can lead to dramatic increases in efficiency for decomposition methods.
The second objective is to develop an efficient sensitivity-based path-following algorithm to track optimal
solutions of mathematical programs with complementarity constraints (MPCC). MPCC can be used to describe many interesting discrete and nonsmooth phenomena, such as phase appearance and disappearance or flow reversals in pipeline networks (Baumrucker et al. 2008). While efficient sensitivity-based fast NMPC approaches are available for standard NLP, there are none for MPCC. This project will bridge the gap by combining sensitivity concepts with special MPCC sequential quadratic programming approaches.