Information for prospective PhD applicants in the PSE group
The PSE group is open to accept new PhD students at any time.
For this the formal procedure of applying to Cambridge University and our Department has to be followed.
Applicants who wish to work in the PSE research area are expected to have considered the following items.
- To have provided a clear statement of purpose in the formal application, that is to explain why they wish to work in the PSE area. Specifically, it would be useful to demonstrate why they have that preference based on prior experience and exposure to related topics in their previous years of study – if any.
- A clear indication of their background related to the PSE research area: for example regarding Applied Mathematics, Computing, Computer Programming (e.g. in C++, Fortran, Python, etc.), Optimisation, Linear Algebra, Process Control, etc.
- To arrange as soon as possible a telephone interview upon successful admission, so as to both explain their interest in person as well as to be provided information about work in the PSE group.
- In general, the PSE domain is very rigorous and demanding, requiring intense theoretical and computational work, with computer programming a prerequisite, as well as strong self-motivation. Students undertaking a project in the PSE group should be prepared for this: both in terms of a very strong mathematical and computational background, as well as very strong motivation and commitment to complete the PhD degree.
Ph.D. students are also expected to demonstrate independence in organising their work, showing initiative to advance their chosen field of studies and making continuous progress by engaging their project very actively, consistently, and very vigorously. It is thus very important that the match between a student and their project area is complementary to their own interests and aspirations, as well as to their prior educational background and experience.
From the group and the supervisor there will be a fully organised provision of resources and continuous support, both in terms of computational tools as well as learning resources. There is also an initial orientation in their research topic by pointing out key publications and the advanced background required for research work to be initiated and progress smoothly. Discussions and evaluation of the student’s progress will be taking place continuously, and the supervisor will be helping the student to overcome educational difficulties should they arise.
For example, PhD students at least in the first year of studies meet regularly with their supervisor in the PSE group, on a weekly basis, at least, to exchange ideas and to discuss their projects and monitor their progress. There is also a weekly group meeting, during which students are expected to give a presentation in rotation every week, as well as to practice their presentations to the Department and other venues (such as preparation for international conference presentations, etc.).
PhD student supervisors also provide the University with reports on each PhD student’s progress on a 3-month basis (once every academic term); in the PSE group particular case there are overview discussions with the students at frequent intervals, and communications in writing with a summary of the items raised during those discussions so that they have a precise record of issues that need to be addressed.
The reward of working for the PSE group is a very competitive world-class training at the end of the PhD studies, as well as the expectation for the completion of original research work during the 3 years of studies for the PhD degree, and the hope for its successful publication via several research articles in top-quality international peer-reviewed journals. Also the students are encouraged to attend at least one international conference where they will present themselves their original work, ensuring international exposure for them and to gain experience in delivering such presentations.
Although not a prerequisite for successful completion of PhD studies in our University, in terms of putting together the PhD thesis at the conclusion of one’s studies it is particularly useful to use paper submission as an experience in structuring one’s work by exposure to the international community via the article submission peer-review process. By experience, one can see that such a practice results in improving scientific writing skills, as well as leading to a very focused PhD thesis which requires minimal corrections after the PhD viva.
Finally, any student undertaking PhD studies in our Department at Cambridge University has to also pass successfully a viva based on their first year report, at the end of the first year of studies, so that they are then registered formally for the PhD degree. The basis of this viva is:
- the presentation of the report and its clarity and scientific content,
- the originality of the work conducted in the first year,
- successful completion of an oral examination by two examiners.
The examiners would want to ensure that:
- the student has carried out the work,
- has clear understanding of his/her research domain, and
- the student is capable of carrying out the rest of their studies independently in a clearly planned way.
1. Mixed-Integer Nonlinear Programming (MINLP) and Global Optimisation (GO) algorithms
Conventional Nonlinear Programming (NLP) considers the optimisation of general process models containing only continuous decision variables. MINLP methods allow the solution of problem formulations containing also discrete variables, i.e. variables taking only integer values of which binary variables are a special case. The latter can be used to model existence of units in the optimal solution and general parts of the model that can be represented by binary logic (True/False).
The power of MINLP models is in the fact that they can model both continuous and discrete decisions simultaneously, a requirement of many realistic modeling applications. Applications can be found in the area of Process Design, e.g. by construction of models containing all possible units and routes in the same model, comprising what is known as a superstructure, in the area of Operations Scheduling, such as in batch scheduling to find the optimal sequence of tasks and units to produce multiple products, and in the scheduling of maintenance/cleaning actions as for example in the case of Heat Exchanger Networks. Novel areas of application include the optimal modification prediction for biochemical reaction pathways subject to gene knock-outs or inclusion of new genes to achieve desired production objectives.
In term of algorithms there are a number of avenues to explore, drawing knowledge from an extensive bibliography. Typically solutions procedures and solvers exist for convex MINLP's, for which solution can be guaranteed to be the globally optimal one. However, engineering practice results more often in nonconvex MINLP's, and these pose a challenge to existing technology. New algorithms have appeared over the last decade or so, each with advantages and disadvantages.
The major issue is that to solve these problem models to guaranteed global optimality requires space partitioning, as even without discrete variables nonconvex NLP's are combinatorially hard. Based on the great importance that MINLP models have in both current and evolving engineering and scientific applications, this poses a challenge that we would like to explore in our group. Both rigorous and approximation methods are to be explored; the former to contribute to the theory of such methods and extend the model sizes that can be tackled, and the latter to offer practical solutions, albeit not globally guaranteed, that are valuable in current engineering applications.
2. Dynamic modelling and optimal treatment of chronic illnesses
Dynamic modelling of chronic illnesses, such as in the case of HIV infection (which was studied in our group in the past) and cancer progression, plays an important role in the understanding of the evolution of the disease. The challenge is twofold: to derive accurate mechanistic models based on population balances and related kinetics validated against published data, and to then link these models with appropriate representations of pharmacokinetics so as to provide an accurate model for the impact treatment has on the progression of these illnesses.
Once models as described above are proven to be valid, then the next phase in such research will involve dynamic optimisation studies (optimal control) which will be aiming to discover the optimal way of administering treatment as a function of time.
The cases of HIV and cancer have been mentioned, but this is not exclusive: other illnesses fall into the category of chronically managed diseases and we would be open to all such applications in our group.
3. Biochemical Reaction Pathways: metabolic control theory, sensitivity analysis, optimal control
In this broad area of research we are interested in the application of Process Systems Engineering methods in the modelling and solution of problems arising in biochemical pathways. In particular, we would like to explore general formulations involving metabolic control and genetic regulation in tandem, in a dynamic setting. The study of such systems will be both theoretical as well as computational. The general aim is to derive sensitivities of a biochemical pathway to regulating parameters of the system so as to predict the impact of genetic modifications using a model-based approach.
There is a vast number of published works in the general area to build new directions from, as well as novel ideas we have in our group in collaboration with international researchers in the field.
4. Scheduling the cleaning actions of Heat Exchanger Networks
Fouling is a major problem in many chemical industries. It is responsible for large energy and throughput losses, resulting in financial penalties and negative environmental impact. Fouling is tied together with ageing, which is the transformation of the initial soft deposit into a more cohesive form in time, due to exposure in process conditions. Thus, the growing of two layers occurs on a heat transfer surface.
One effective mitigation strategy is the regular cleaning of the fouled heat transfer units. In this ongoing project, two cleaning modes are considered, which differ in their effectiveness in removing aged material. The first, a fast and cheap in-situ technique can only remove the soft fouling layer, while the second, a time-consuming and expensive ex-situ one is able to remove both layers.
Optimisation tools can be used to schedule the timing and the selection of cleaning actions as well as the unit or units to be cleaned at each instant, in order to minimise the cost of fouling and impact on productivity. This is a scheduling problem of combinatorial nature, hence the developed models describing the cleaning scheduling yield a Mixed Integer Non Linear Programming (MINLP) optimisation problem. The primary objectives of this project can be divided in two categories:
Firstly, it aims to provide better understanding of how this coupled fouling-ageing phenomenon affects the heat transfer process and how it can be best mitigated by applying mixed cleaning campaigns. Most importantly it aims to demonstrate the potential benefit of performing experimental studies in order to obtain kinetic data about the this phenomenon.
Secondly, this work aims to contribute to the theory and solution techniques of large MINLPs, convex or nonconvex. This can be done by proposing specific model structures that are easier to solve or by investigating different problem formulations which will reduce the number of integer variables and constraints significantly. Also, it will be useful to construct approximation methods which will offer on one hand, good starting points for rigorous solvers and on the other hand, practical solutions to engineering applications.
5. Large-Scale nonlinear optimisation algorithms
Optimisation plays a paramount role in decision making, and within Chemical Engineering it is a valuable tool for the design, operation and control of industrial processes. The ever-increasing need for more accurate and large model solution necessitates the development of new optimisation algorithms that can address large, nonlinear, nonconvex and potentially badly conditioned problems.
The aim with projects in this area is to design and investigate novel algorithms, which are currently actively researched in the PSE group, and to demonstrate their applicability to real-life complex models.