School of Mathematics

PhD opportunities

The Optimization and Operational Research PhD programme and areas with opportunity for research

The School offers a PhD Programme in Optimization and Operational Research. This is a 3-year programme with an additional year available to finalise the thesisFrom the start of their studies, PhD students are assigned a main supervisor with whom they work closely throughout their degree programme and a second supervisor who provides additional help and pastoral support. 

Why Study Optimization and Operational Research in Edinburgh?

The Optimization and Operational Research Group in the School is an international leader in the mathematical and computing aspects of optimization and operational research, with members of high repute, as evidenced by Editorial Board Memberships in major international journals, international research awards, fellowships and other peer recognitions, and memberships of prestigious international societies. The group members collaborate with several research groups in the UK and overseas, and are actively engaged in collaborations with industry and government.
Funding Opportunities
The School of Mathematics offers several fully funded PhD studentships each year. Students receiving School funding are awarded a stipend equivalent to UKRI stipend rates for a period of 4 years plus a tuition waiver.  All applicants will automatically be considered for these studentships, and they do not require a separate application. If you wish to be considered for all funding opportunities, you must submit your admission application by the application deadline (please see "Application Process" below for further information). Later applications will be considered until all positions are filled. Further information on funding opportunities is available.
Eligibility Requirements
Our minimum entry requirements are a 1st class Honours degree (or its international equivalent), or a 2:1 Honours degree (or its international equivalent) plus a Masters degree (or its international equivalent) in a relevant subject. Non-UK candidates may be required to provide evidence of English proficiency.
Application Process and Further Information
Applications are invited for PhD studies for September each year. Occasionally students are admitted at other times of the year by special arrangement. Further information on  on application deadlines and how to apply is available.

Research Opportunities

Computational Optimization and Applications

The Optimization and OR group in the School of Mathematics possesses world leading expertise in the solution of very large scale continuous and mixed-integer linear, and continuous quadratic optimization problems. The group has been awarded several EPSRC-funded research projects devoted to developing core optimization methods that led to the development of world class solvers for linear programming using the interior point method. At the UK level, the group has unmatched competences in developing theory and software for solving huge scale problems.  Amongst open source systems, the performance of the group's mixed-integer linear opimization software system, HiGHS, is the best in the world.

People: Miguel Anjos, Skarleth Carrales Escobedo, Sergio Garcia Quiles, Jacek Gondzio, Andreas Grothey, Akshay Gupte, Julian Hall, Joerg Kalcsics, Ken McKinnon, John Pearson, Lars Schewe, E. Alper Yıldırım

Continuous Optimization 

The Optimization and OR group in the School of Mathematics has extensive expertise and experience in modelling optimization problems arising from various applications, developing and implementing problem-specific algorithms, and utilising decomposition methods, interiorpoint methods, advanced numerical linear algebra tools such as preconditioners, and highperformance computing approaches for solving challenging and large-scale optimization problems. In addition, the group is actively involved in general-purpose optimization software development. The research expertise in the group encompasses several facets of continuous optimization, including linear, quadratic, nonlinear, convex, nonconvex, global, PDE-constrained, and stochastic optimization. The research experience includes the development and application of OR methodology for solving optimization problems arising from diverse applications such as data science, energy systems, truss topology design, finance, and wireless networks. In addition, the group members have secured extensive external funding from funding agencies and has strong industrial collaborations.

People: Miguel Anjos, Skarleth Carrales Escobedo, Jacek Gondzio, Andreas Grothey, Julian Hall, Ken McKinnon, John Pearson, E. Alper Yıldırım

Decision Making under Uncertainty

The Optimization and OR group of the School of Mathematics has extensive experience in modelling, analyzing and optimizing real-world problems involving uncertainty. Our group is also one of the leading research groups in the world developing methods to solve the resulting huge scale stochastic optimization problems efficiently, and our members has been funded for various projects by EPSRC and other external organizations to develop fast solution methods for these problems. The research interests of our members also include Gaussian process emulation and Bayesian decision analysis. Our members have actively collaborated with organizations from a wide-variety of sectors, including but not limited to government, service, energy, aviation and telecommunication. The group has strong ties with leading research groups at Heriot-Watt University and London Business School.

People: Burak Buke, Chris Dent, Jacek Gondzio, Andreas Grothey, Akshay Gupte, Ken McKinnon, Lars Schewe

Future Energy Networks

The Optimization and OR group of the School of Mathematics can provide both domain expertise in the modelling and optimization of energy networks, particularly electric and gas networks, as well as the methodological expertise to solve the resulting optimization models in practical applications. The group collaborates with energy researchers across the university via the Energy@Edinburgh initiative. At UK national level members of the group are part of the EPSRC-funded National Centre for Energy Systems Integration. Additionally, our members have led or been involved in numerous other externally funded projects involving the development and application of OR techniques to energy problems. The members of the group have a wide range of experience in modelling different systems’ energy markets, and in optimizing energy networks of different sizes from small-scale local smart grids to national and continental networks. There is also specialist expertise in calibration of large-scale computer models, and in probabilistic security of supply risk modelling.

People: Miguel Anjos, Chris Dent, Andreas Grothey, Ken McKinnon, Lars Schewe

Integer and Combinatorial Optimization

The Optimization and OR group in the School of Mathematics has broad expertise in the modelling and solving of integer and combinatorial optimization problems. Members of the group have had public and private funding, including EPSRC, to work on logistics problems, aircraft cockpit design problems, energy problems, and portfolio optimization problems. Members of the group have worked on both the theory and application of integer and combinatorial optimization: On the theoretical side, the group has experience in cutting plane methods, convexification techniques, and the construction of efficient algorithms both to obtain exact and heuristic solutions. Here, the group has focussed both on mixed-integer linear but also on mixed-integer nonlinear programs. As for applications, the portfolio of the group includes energy, logistics (facility location, network design, supply chain, districting), and healthcare applications (junior doctor allocation, kidney exchange).

People: Miguel Anjos, Sergio Garcia Quiles, Andreas Grothey, Akshay Gupte, Joerg Kalcsics, Lars Schewe