Self-funded PhD students only

Project code



School of Mathematics and Physics

Start dates

Closing date

Applications accepted all year round

Applications are invited for a 3 year PhD to commence in October 2020 or February 2021.

The PhD will be based in the Faculty of Technology, and will be supervised by Dr Xiang Song and Professor Dylan Jones.

The work on this project could involve:

  • Investigating machine learning techniques, e.g. single layer feed-forward neural networks, multi-layer feed forward neural networks, feed-back neural networks.
  • Pre-processing the historical data and apply suitable machine learning technique to get useful routes “independently” of the real daily demand.
  • Pre-processing the historical data and apply suitable machine learning technique to get high-quality solutions (route planning) in seconds or few minutes for very-large-scale VRPs

Motivated by a real-life application, this research considers the time-dependent Large-scale Vehicle Routing Problems with time window constraints. The problem consists of routing a number of vehicles to serve up to 10,000 or even 100,000 customers in seconds or few minutes. The cost function includes fuel, emission and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions.

Traditionally, the time dependent vehicle routing problem has been investigated using heuristic or meta-heuristic algorithms. However, it takes minutes or even hours for a good quality solution to be found for only hundreds of customers. In many large companies like Ocado, they need to schedule the routing for up to 10,000 or even 100,000 customers and the transportation time and cost need to be calculated based on real time road condition. A high quality solution needs to be found in seconds or a couple of minutes for such a large sized and complicated problem. Thus the cutting edge techniques of Machine learning and artificial intelligence are to be adopted in this research to cope with this challenge.

The PhD candidate is expected to implement a number of machine learning techniques to a complicated case study from the company by taking uncertain factors (stochastic travelling time) into consideration. The PhD candidate can collect the data through visiting the company. If the candidate has no prior knowledge about machine learning, artificial intelligence, Python and or C++ programming, it is recommended that the student take some relevant training prior to the start of the PhD study.

Fees and funding

Funding availability: Self-funded PhD students only. 

PhD full-time and part-time courses are eligible for the UK Government Doctoral Loan (UK and EU students only).

2020/2021 entry (for October 2020 and February 2021 entries)

Home/EU/CI full-time students: £4,407 p/a

Home/EU/CI part-time students: £2,204 p/a

International full-time students: £16,400 p/a

International part-time students: £8,200 p/a

PhD by Publication

External candidates £4,407 p/a

Members of staff £1,680 p/a*

2021/2022 entry (for October 2021 and February 2022 entries)

PhD and MPhil

Home/EU/CI full-time students: £4,407 p/a*

Home/EU/CI part-time students: £2,204 p/a* 

International full-time students: £17,600 p/a

International part-time students: £8,800 p/a

All fees are subject to annual increase.

PhD by Publication

External Candidates £4,407 p/a*

Members of Staff £1,720 p/a*

If you are an EU student starting a programme in 2021/22 please visit this page.

*This is the 2020/21 UK Research and Innovation (UKRI) maximum studentship fee; this fee will increase to the 2021/22 UKRI maximum studentship fee when UKRI announces this rate in Spring 2021. 

Bench fees

Some PhD projects may include additional fees – known as bench fees – for equipment and other consumables, and these will be added to your standard tuition fee. Speak to the supervisory team during your interview about any additional fees you may have to pay. Please note, bench fees are not eligible for discounts and are non-refundable.

Entry requirements

  • You'll need a good first degree from an internationally recognised university (minimum second class or equivalent, depending on your chosen course) or a Master’s degree in a relevant subject area
  • In exceptional cases, we may consider equivalent professional experience and/or Qualifications
  • English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0

The ideal candidate should have a Master’s degree in Mathematics, Computer Sciences, or related backgrounds. The knowledge or experiences of Phython and/or C++ would be an advantage.

How to apply

We’d encourage you to contact Dr. Xiang Song ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, you can use our online application form. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV. Our ‘How to Apply’ page offers further guidance on the PhD application process.

If you want to be considered for this PhD opportunity you must quote project code SMAP5350220 when applying.

October start

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February start

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