Efficient optimization algorithms for large scale interdiction problems on networks

About the project

How can we protect vital networks against disruption? This PhD develops faster matheamtically sound optimization algorithms to reveal critical weaknesses in transport, logistics and communication networks. Combining mathematical theory with computational experiments, you will investigate how networks respond to disruption and build tools that help decision makers assess vulnerabilities and improve resilience.

Networks underpin the movement of people, resources and information. When a link is disrupted, operators can reroute traffic, so the importance of a component depends on the response of the whole network. Identifying the most damaging disruptions within a limited budget is known as network interdiction. Its combination of discrete decisions and an optimising network response creates challenging bilevel/min-max problems.

Working with Dr Stefano Cipolla and Prof Alain B. Zemkoho at the University of Southampton, you will develop efficient algorithms for large networks. The project will initially study shortest-path interdiction, modelling disruption through finite increases in link costs.

You will investigate how network structure can strengthen mathematical formulations and how adaptive decomposition and sparse numerical methods can accelerate solution.

You will combine theoretical analysis with implementation and reproducible computational experiments. Algorithms will be tested on synthetic and public networks against established optimisation methods, comparing runtime, memory and solution quality. Suitable continuous relaxations will provide opportunities to explore value-function and semismooth approaches.

Depending on progress, later work may extend to maximum-flow interdiction or uncertainty in disruption effects.

The intended outcomes are new algorithmic insights, documented research software and a prototype for network vulnerability assessment. The project supports defence and security resilience planning while offering potential applications in logistics and infrastructure. You will develop expertise in operational research, optimization, graph algorithms and numerical linear algebra through research and CDT training.

Dr Stefano Cipolla

• Continuos Optimization
• Second Order Methods
• Numerical Optimization

Professor Alain Zemkoho

• Bilevel and hierarchical optimization
• First and second order numerical methods for continuous optimization
• Nonsmooth and nonconvex optimization

Entry requirements

You must have an undergraduate degree (at least UK 2:1 honours degree) or its international equivalent.

You should have a foundation in linear algebra and calculus and an interest in mathematical reasoning and analytical problem-solving.

Familiarity with, or experience in, any combination of numerical programming, for example using Python, MATLAB or Julia, optimisation, or graph algorithms would be useful.

You are not expected to have experience in all of these areas, and relevant specialist skills can be developed during the PhD.

Fees and funding

For candidates looking to complete a PhD or EngD full-time we offer an enhanced tax-free stipend of up to £30k per year, along with a substantial budget for research, travel, and centre activities.

CISDnS is committed to promoting equality, diversity and inclusivity. We welcome all applicants regardless of their gender, ethnicity, disability, sexual orientation or age, and will give full consideration to applicants seeking flexible working patterns and those who have taken a career break or are transitioning into a new role. The University has a generous maternity policy, onsite childcare facilities, and offers a range of benefits to help ensure employees’ well-being and work-life balance.

How to apply

Apply now

Please apply via the online portal and select:

Applications should include:

• Academic year: 2027/28
• If you will be full time or part time
• Faculty: Engineering and Physical Sciences
• Search for "complex integrated systems"
• Select either PhD or EngD – if you are unsure, select PhD
• Add the name of the supervisor in section 2 of the application.
• your CV (resumé)
• 2 academic references
• degree transcripts and certificates to date

Faculty of Engineering and Physical Sciences

For questions about applying, email our Doctoral College (doctoralcollege-admissions@soton.ac.uk) .

Project leader

For an initial conversation, email Dr Stefano Cipolla (s.cipolla@soton.ac.uk) .

Research areas