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.
