Vacation Scholarships Projects
Operations Research
Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Operations Research
Self-organised Criticality in Real World Systems
The phenomenon of self-organised criticality (SOC) in real world systems is where interacting components combine to cause the system to reach a “critical” state, where any small perturbation can cause a major disturbance. For example, tectonic plates in the earth’s crust may move slowly, but when pressure builds up, an earthquake occurs. The Bak-Tang-Wiesenfeld (BTW) model (or "sand-pile model") has been used to model SOC. In the two-dimensional BTW model, grains of sand are added randomly, one at a time, to cells in a rectangular grid, until any “sand-piles” that are too high topple over, potentially causing a significant cascading toppling effect. The BTW model is not only rich in mathematical properties, but can be applied to many real world phenomena, such as earthquakes, forest fires, and epidemics. In this project we apply the BTW model to describe SOC in real world systems.
Contact: Mark Fackrell fackrell@unimelb.edu.au
Continuous dynamical systems associated with iterative algorithms in optimisation
The study of continuous time dynamical systems associated with iterative algorithms for solving optimization problems has a long history which can be traced back at least to 1950s. The relationship between the continuous and discrete versions of an algorithm provides a unifying perspective which gives insights into their behavior and properties, as well as providing a tool to derive and analyse new methods. The aim of this project is to investigate continuous version of recently discovered gradient-based methods with adaptive stepsize rules.
Contact: Matthew Tam matthew.tam@unimelb.edu.au
Floods, fires and explosions: how to design survivable networks in the modern age
Much of society’s critical infrastructure takes the form of large-scale networks. Think of examples such as the power grid, the NBN, gas and water pipelines, and transportation networks. All such networks are potentially vulnerable to natural disasters, or even terrorist attacks. Significant interruption to these networks can wreak havoc. So the question is: how do we design these networks to be robust against local, regional destruction, without blowing the national budget?
In this project we will use planar geometric graph models for this problem and analyse survivability when the destruction region is modelled as a circular disk. In particular, we would like to find algorithms for optimally designing networks that are survivable against failures of a given maximum radius. The project will use mathematical tools from graph theory, optimisation, computer science and just a little bit of Euclidean geometry.
Contact: Charl Ras cjras@unimelb.edu.au
Charging coordination for plug-in electric vehicle fleets
With an increasing uptake of Plug-in Electric Vehicles (PEVs), it is becoming increasingly important for aggregate charging behaviour to be coordinated in way that does not place undue stress on electricity distribution infrastructure. On the other hand, PEV owners typically make charging decisions based on individual factors (such as minimising electricity costs) rather than factors affecting electricity distribution infrastructure as a whole. To reconcile these competing interests, this project will examine decentralised algorithms based on game theory for making coordinated optimal charging decisions in fleets of non-cooperation PEVs.
Contact: Matthew Tam matthew.tam@unimelb.edu.au