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  Heterogenous Bayesian Optimization

   Department of Computer Science

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  Prof Richard Allmendinger, Dr Mauricio Alvarez  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

The UKRI AI Centre for Doctoral Training (CDT) in Decision Making for Complex Systems is a joint CDT between the University of Manchester and the University of Cambridge. The CDT provides funding for four years of advanced studies towards a PhD. The first year consists of a taught program at Manchester that will cover the fundamentals of Machine Learning. This year is followed by three years of research at either at Manchester or Cambridge. Please note the research element of the PhD will take place at the host institution of the supervisor listed for each project.

This is a collaborative project with Honda Research Institute (HRI) Europe, the research arm of Honda, one of the world's largest and well-known automotive companies. Efficient and sustainable vehicle design is one of HRI’s focus areas. A typical challenge here is performing costly simulations (eg through CFD), potentially combined with resource-intense physical experiments in the laboratory, resulting in optimization problems with heterogeneous objectives and/or constraints [1]. Heterogeneous objectives/constraints may differ eg in practical evaluation effort (time, costs, resources, etc), formal computational complexity, determinism (stochastic vs deterministic), or some combination of all these. A particularly challenging variety of heterogeneity may occur by the combination of a time-consuming laboratory-based objective/constraint with other objectives/constraints that are evaluated using faster computer-based calculations [2,3].

Current research on heterogeneous objectives is largely focused on problems with two objectives (typically one slow vs one fast to evaluate objective) [1]. Research on heterogeneous constraints is even more so in its infancy. Also, most existing research has only considered heterogeneity in terms of computational time of objectives/constraints.

In this PhD project, we propose to generalize recent advances in machine learning and operations search [1,4] to tackle optimization problems with heterogeneous objectives/constraint. Hybrid methods will be developed and validated on real problems provided by HRI. Furthermore, realistic synthetic benchmark problems will be proposed varying in type and level of heterogeneity. The outcome of this research will allow tackling heterogenous optimization problems more efficiently while using less resources.

For queries regarding the project, please email Richard Allmendinger ([Email Address Removed]) and Mauricio Alvarez ([Email Address Removed])

For queries regarding the AI Centre for Doctoral Training (CDT) in Decision Making for Complex Systems, please email [Email Address Removed].

Entry requirements

  • Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

Background in probabilistic GPs, Optimization, Multi-Criteria Decision Making. Previous experience in Bayesian Optimisation would be great.

English language requirements (for international/EU candidates)

You have must have one or more of the following:

  • IELTS test minimum scores - 7.0 overall, 6.5 other sections.
  • TOEFL (internet based) test minimum scores - 100 overall, 25 in all sections.
  • Pearson Test of English (PTE) UKVI/SELT or PTE Academic minimum scores - 76 overall, 76 in writing, 70 in other sections.
  • To demonstrate that you have taken an undergraduate or postgraduate degree in a majority English speaking nation within the last 5 years.
  • Other tests may be considered.

How to Apply:

As the CDT has only recently been awarded we encourage you to contact the supervisor of the project you are interested in with your CV and supporting documents. You will have a chance to meet with prospective supervisors prior to submitting an application - further details will be provided.

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact.

We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status. 


Computer Science (8) Engineering (12) Mathematics (25)

Funding Notes

Funding includes tuition fees and stipend at the UKRI minimum rate, currently £18,622/annum (see for further information). Studentship funding is for 4 years commencing 1 October 2024. This scheme is open to both the UK and international applicants. We are only able to offer a limited number of scholarships to applicants outside the UK.


[1] Allmendinger, R., Handl, J. and Knowles, J., 2015. Multiobjective optimization: When objectives exhibit non-uniform latencies. European Journal of Operational Research, 243(2), pp.497-513.
[2] Allmendinger, R. and Knowles, J., 2023. Heterogeneous objectives: state-of-the-art and future research. In Many-Criteria Optimization and Decision Analysis: State-of-the-Art, Present Challenges, and Future Perspectives (pp. 317-335). Cham: Springer International Publishing.
[3] Blank, J. and Deb, K., 2022. Handling constrained multi-objective optimization problems with heterogeneous evaluation times: proof-of-principle results. Memetic Computing, 14(2), pp.135-150.
[4] Moreno-Muñoz, P., Artés, A. and Alvarez, M., 2018. Heterogeneous multi-output Gaussian process prediction. Advances in neural information processing systems, 31.

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Research output data provided by the Research Excellence Framework (REF)

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