PhD opportunities and graduate testimonials
The Optimization and Operational Research PhD programme and areas with opportunity for research
The School offers a PhD Programme in Optimization and Operational Research. From 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. See poster
Why Study Optimization and Operational Research in Edinburgh
Funding Opportunities
Eligibility Requirements
Application Process and Further Information
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: Merve Bodur, 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, Merve Bodur, Sergio Garcia Quiles, Andreas Grothey, Akshay Gupte, Joerg Kalcsics, Lars Schewe
Recent projects
Recently completed PhD projects include
- Solution Methods for Some Variants of the Vehicle Routing Problem
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Optimal Coordination of Multiple Price-Maker Electricity Storage Units for Price Arbitrage
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Optimizing Heating and Cooling of Smart Buildings
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Regularized Interior-Point Methods for Convex Programming
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Pre-trained Solution Methods for Unit Commitment
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Multi-Period Sales Districting Problem
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Efficient Algorithms for Solving p-Median Problems with Radius Constraints and Its Application to Clustering with Feature Selection
Graduate testimonials
I joined the University of Edinburgh as an MSc student in Operational Research, and the following year I started my PhD research working on routing problems. The School of Mathematics at the University of Edinburgh has given me an opportunity to be part of an excellent community, build a wide network of brilliant friends and colleagues, and gain research and teaching experience that has been invaluable for my career.
Supervisor: Sergio Garcia Quiles
Current Position: Operational Research and Optimization Analyst, Edinburgh Airport
The University of Edinburgh is a great place to do research. During my PhD I had the chance to work not only with people from the University but with researchers at other institutions, both in academia and in industry. Attending summer schools and conferences was an integral part of the programme, and a great way to find out about new or interesting ideas closely related to my research topic. I really enjoyed the social environment too. There are always plenty of events and activities going on inside the University, and a great deal of university clubs. The city is quite lively too and offers great landscapes for outdoor activities.
Supervisor: Chris Dent
Current Position: Data Scientist, Lynceus.ai
I studied my PhD in Optimization at the School of Mathematics of the University of Edinburgh, under the supervision of Prof. Jacek Gondzio and the co-supervision of Prof. John Pearson. I worked on solution methods for convex optimization problems with applications in operational research and data science. During my studies, I had the opportunity to collaborate with experts in the field of optimization both within and outside the UoE, which resulted in several successful publications in top peer-reviewed journals in the field. At the same time, I was able to travel around the world, attending major and local conferences, and expanding my research network. Studying Optimization at the School of Mathematics of the University of Edinburgh has been an invaluable experience and played a significant role in my subsequent career development. After defending my thesis, I received an offer to pursue postdoctoral studies in stochastic optimization at the electrical engineering department of Yale University. Upon the completion of my postdoctoral studies, I was offered a lectureship position in mathematics at the University of Dundee.
Supervisor: Jacek Gondzio
Current Position: Lecturer in Mathematics, University of Dundee
I first joined University of Edinburgh for a BSc in Computer Science and Mathematics. I liked the School of Mathematics and the city of Edinburgh so much, that I completed the MSc in Operational Research with Computational Optimization and, later, a PhD in Optimization in the School of Mathematics. My time as a PhD student resulted in the creation of HiGHS, the world's best open-source software for solving large-scale linear and mixed integer programming problems. As a result, I'm happily employed in the School as the HiGHS Development and Integration manager.
Supervisor: Julian Hall
Current Position: HiGHS Development and Integration Manager, University of Edinburgh
The University of Edinburgh was an ideal place to study as a PhD student. The school has one of the largest research groups in the field, and as a member of the group, you would have opportunities to interact with a number of leading researchers on a daily basis. Outside of the research, you would find an amazing environment: an international, vibrant city and a supportive, welcoming community. I highly recommend the PhD program at the University of Edinburgh.
Supervisor: Andreas Grothey
Current Position: Postdoctoral Researcher, CIRRELT, University of Montreal
Doing a PhD at the University of Edinburgh has been a thrilling and very rewarding experience. During the first year, thanks to being part of a Centre for Doctoral Training, I was given the opportunity to explore new interests in mathematics. This led to changing my original plans, which resulted in doing a PhD in Optimization and Operations Research, with applications to power systems and the energy transition. This is an area I continue to find exciting nowadays, and where I do most of my research work. During my time as a PhD student at the University of Edinburgh, I participated in many local seminars, conferences, and courses. Being able to engage with many excellent researchers, close enough to my topics of interest, significantly enhanced my learning and improved the quality of my research. In such quality, variety, and quantity, these opportunities are not present at many universities. I would like to make a special mention to my PhD supervisors, with whom I enjoyed working with, from whom I learned a lot, and were always supportive. Finally, many other PhD students in the School were also crucial for successfully completing my PhD, since I enjoyed collaborating and doing research activities with them, learning together, and having fun with and without research
Supervisor: Miguel F. Anjos
Current Position: Postdoctoral Researcher, Polytechnic University of Catalonia