Optimization and Operational Research PhD

The work in the Operational Research and Optimization research group is in three main areas: the mathematical and computing aspects of optimization, combinatorial optimization, and energy systems.

The core technology in optimization is the solution of large sparse linear and quadratic problems, and we provide world-class expertise in the two main solution methods for these: the simplex method and the interior point method. In combinatorial optimization, we provide expertise for modelling real-world problems using integer linear programming formulations and for deriving efficient exact and heuristic algorithms to solve them.

Specialist expertise in energy includes optimization of system planning and optimization, security of supply risk analysis, and decision support for public policy. We also have interests in PDE-constrained optimization, global optimization, decomposition methods, parallel computing, industrial applications of optimization and stochastic optimization.

Specific topics which could yield PhD projects include:

• Algorithms for linear and nonlinear nonconvex smooth optimization problems
• Optimization methods for linear, integer linear, quadratic and nonlinear programming
• Decomposition methods for large-scale nonlinear nonconvex constrained optimization
• Bundle methods
• Warm starts for interior point methods
• Pooling problems
• Applications of optimization in logistics
• Parameter uncertainty in queueing theory and revenue management.
• Facility location and vehicle routing

These entry requirements are for the 2025/26 academic year and requirements for future academic years may differ. Entry requirements for the 2026/27 academic year will be published on 1 Oct 2025.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency which will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced (CAE) / C2 Proficiency (CPE): total 176 with at least 169 in each component.
• Trinity ISE: ISE II with distinctions in all four components.
• PTE Academic: total 65 with at least 59 in each component. We do not accept PTE Academic Online.
• Oxford ELLT: 7 overall with at least 6 in each component.

Unless you are a national of a majority English speaking country, your English language qualification must be no more than three and a half years old from the start of the month in which the programme you are applying to study begins. If you are using an IELTS, PTE Academic, TOEFL, Trinity ISE, or Oxford ELLT test, it must be no more than two years old on the first of the month in which the programme begins, regardless of your nationality. (Revised 14 January 2025 to include Oxford ELLT.)

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old at the beginning of your programme of study.

Find out more about our language requirements:

• English language requirements

Academic Technology Approval Scheme

If you are not an EU, EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

• Academic Technology Approval Scheme