Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model reduction, machine-learning methodology combining principal component analysis (PCA) and artificial neural networks (ANNs) is employed to construct a reduced surrogate model, which can then be utilised by advanced deterministic global optimisation algorithms to compute global optimal solutions with theoretical guarantees. However, such optimisation would still be time-consuming due to the high non-convexity of the activation functions inside the reduced ANN structures. To develop a computationally-efficient optimization framework, we propose two alternative strategies: The first one is a piecewise-affine reformulation of the nonlinear ANN activation functions, while the second one is based on deep rectifier neural networks with ReLU activation function. The performance of the proposed framework is demonstrated through three illustrative case studies.

Process synthesis using rigorous unit operation models is highly desirable to identify the most efficient pathway for sustainable production of fuels and value-added chemicals. However, it often leads to a large-scale strongly nonlinear and nonconvex mixed integer nonlinear programming (MINLP) model. In this work, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB-FP and HCBB-RB) where the homotopy continuation method is employed to gradually approach the optimal solution of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB-RB is superior to HCBB-FP due to lower computational effort required for the same locally optimal solution.

Many engineering processes can be accurately modeled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimization. In this work, a model reduction methodology combining principal component analysis (PCA) and artificial neural networks (ANNs) is employed to construct a reduced surrogate model, which is then utilized by advanced deterministic global optimization algorithms to compute global optimal solutions with theoretical guarantees. However, the optimization framework is still time-consuming due to the high non-convexity of the activation functions inside the reduced ANN structure. To further enhance the capability of our optimization framework, two alternative strategies have been proposed. The first one is a piecewise-affine reformulation while the second one is based on deep rectifier neural networks with ReLU activation function. The performances of the two improved frameworks is demonstrated through two illustrative case studies.

In this work, we develop two generic mixed-integer linear programming formulations for scheduling of multipurpose batch plants using the unit-specific event-based modelling approach. While related non-recycling production and consumption tasks are allowed to take place at the same event points but in different real time in the first model, they are not allowed in the second model. We also introduce the concept of indirect and direct material transfer, which allows to conditionally align the operational sequence of related production and consumption tasks. Processing units are able to hold materials previously produced over multiple event points. The computational results demonstrate that the proposed models do not require a task to span over multiple event points to generate the optimal solution. As a result, the proposed models are able to generate the same or better solutions with up to one order of magnitude less computational time compared to the existing models.