A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs

We consider probabilistically constrained linear programs with general distributions for the uncertain parameters. These problems involve non-convex feasible sets. We develop a branch-and-bound algorithm that searches for a global optimal solution to this problem by successively partitioning the non-convex feasible region and by using bounds on the objective function to fathom inferior partition elements. This basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partition elements and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires solving linear programming subproblems. We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions are presented.

A strategic decision making model on global capacity management for the manufacturing industry under market uncertainty

Multi-national, large-scale and complex manufacturing systems, such as those for automotive manufacturers, often require a significant investment in production capacity, as well as great management efforts in strategic planning. Capacity-related investment decisions are often irreversible or prohibitively expensive and time-consuming to change once they are in place. Furthermore, such companies operate in uncertain business environments, which can significantly influence the optimal decisions and the systems’ performance. Therefore, a strategic question is how to globally and interactively set production resources for such systems so their optimal performance can be achieved under business uncertainty. Conventional optimisation models in this field often suffer from one or more drawbacks, such as deterministic styles, non-inclusive and non-comprehensive decision terms, non-integrated frameworks, non-empirical approaches, small size practices, local/non-global approaches or difficult-to-use methods/presentations. This research develops a new scenario-based multi-stage stochastic optimisation model, which is capable of designing and planning the production capacity for a multi-national complex manufacturing system over a long-term horizon, under demand and sales price uncertainty

A Meshless Modelling Framework for Simulation and Control of Nonlinear Synthetic Biological Systems

Synthetic biology is a relatively new discipline that incorporates biology and engineering principles. It builds upon the advances in molecular, cell and systems biology and aims to transform these principles to the same effect that synthesis transformed chemistry. What distinguishes synthetic biology from traditional molecular or cellular biology is the focus on design and construction of components (e.g. parts of a cell) that can be modelled, characterised and altered to meet specific performance criteria. Integration of these parts into larger systems is a core principle of synthetic biology. However, unlike some areas of engineering, biology is highly non-linear and less predictable. In this thesis the work that has been conducted to combat some of the complexities associated with dynamic modelling and control of biological systems will be presented. Whilst traditional techniques, such as Orthogonal Collocation on Finite Elements (OCFE) are common place for dynamic modelling they have significant complexity when sampling points are increased and offer discrete solutions or solutions with limited differentiability. To circumvent these issues a meshless modelling framework that incorporates an Artificial Neural Network (ANN) to solve Ordinary Differential Equations (ODEs) and model dynamic processes is utilised. Neural networks can be considered as mesh-free numerical methods as they are likened to approximation schemes where the input data for a design of a network consists of a set of unstructured discrete data points. The use of the ANN provides a solution that is differentiable and is of a closed analytic form, which can be further utilised in subsequent calculations. Whilst there have been advances in modelling biological systems, there has been limited work in controlling their outputs. The benefits of control allow the biological system to alter its state and either upscale production of its primary output, or alter its behaviour within an integrated system. In this thesis a novel meshless Nonlinear Model Predictive Control (NLMPC) framework is presented to address issues related to nonlinearities and complexity. The presented framework is tested on a number of case studies. A significant case study within this work concerns simulation and control of a gene metabolator. The metabolator is a synthetic gene circuit that consists of two metabolite pools which oscillate under the influence of glycolytic flux (a combination of sugars, fatty acids and glycerol). In this work it is demonstrated how glycolytic flux can be used as a control variable for the metabolator. The meshless NLMPC framework allows for both Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) control. The dynamic behaviour of the metabolator allows for both top-down control (using glycolytic flux) and bottom-up control (using acetate). The benefit of using MIMO (by using glycolytic flux and acetate as the control variables) for the metabolator is that it allows the system to reach steady state due to the interactions between the two metabolite pools. Biological systems can also encounter various uncertainties, especially when performing experimental validation. These can have profound effect on the system and can alter the dynamics or overall behaviour. In this work the meshless NLMPC framework addresses uncertainty through the use of Zone Model Predictive Control (Zone MPC), where the control profile is set as a range, rather than a fixed set point. The performance of Zone MPC under the presence of various magnitudes of random disturbances is analysed. The framework is also applied to biological systems architecture, for instance the development of biological circuits from well-characterised and known parts. The framework has shown promise in determining feasible circuits and can be extended in future to incorporate a full list of biological parts. This can give rise to new circuits that could potentially be used in various applications. The meshless NLMPC framework proposed in this work can be extended and applied to other biological systems and heralds a novel method for simulation and control