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The University of Southampton
Mathematical Sciences

Research Group: Computational Optimisation

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Computational optimisation is widely used in science, engineering, economics, and industry. Researchers in our group develop cutting-edge theories and algorithms that push the limits in optimisation. Much of the work is supported by various outside organisations and carried out with their collaboration. Recent examples include the European Space Agency, EPSRC, Boeing Defense, ThyssenKrupp, Alcatel-Lucent, Bell Labs, Qualcomm, Brussels Capital-Region, EPSRC etc. Our current research interests include: decision making under uncertainty, optimisation in data dimension reduction and visualization, multi-objective and bi-level optimisation, discrete optimisation, non-smooth optimisation, optimisation methods in game theory and optimisation in finance.

Computational Optimisation
Decision Making Under Uncertainty

Decision Making Under Uncertainty

Our work includes developing and/or investigating new mathematical models which capture the uncertainty and other features such as competition, equilibrium and hierarchical relationships between decision makers. Typical examples are stochastic principal agent models (Stackelberg leader follower models), stochastic Nash equilibrium models, stochastic bilevel programming models, stochastic mathematical programs with equilibrium constraints (SMPEC) models and stochastic equilibrium programs with equilibrium constraints (SEPEC) models.

Discrete Optimisation

Discrete Optimisation

Our work in discrete optimisation mainly focuses on combinatorial optimisation, especially scheduling in production and transport. For train, vehicle and production scheduling problems, we design models and develop algorithms that are more closely related to industry practice. For example, we have applied our work on air traffic management resulting in scheduling of airport runways to improve throughput while maintaining minimum separation times between aircraft.

Multilevel Optimisation

Multilevel Optimisation

Multilevel optimisation problems are optimisation problems with a hierarchical structure involving multiple levels of decision making, respectively controlled by leaders (upper-level players) and followers (lower-level players). They represent a very powerful tool for modelling a large number of real-world problems, but are however very difficult to solve, and most of the attention is still focus on problems with two-level structure. Our work here is mainly devoted to the development of exact and approximate solution approaches that can handle both the optimistic and pessimistic cases of the problem.

Nonlinear Optimisation

Numerical Methods for Nonlinear Optimisation

The focus of our research here is to develop numerical optimization methods for problems presenting multiple objectives and problems with a bi-level hierarchical structure, respectively. These problems have attracted a lot interest from the optimization continuity because of the mathematical challenges they present and the powerful framework they provide to model decision making problems with conflicting objectives or featuring two levels of decision making. We apply our research in these areas on space engineering, web science and transportation.

Optimisation in Data Dimension Reduction

Optimisation in Data Dimension Reduction and Visualization

The fundamental problem of dimensionality reduction arises from analysing and visualizing very high dimensional data. Fast optimization methods are becoming an indispensable tool in deriving high-quality low-dimensional embedding. Our research focuses on distance embedding methods, especially for large scale data that is incomplete or has missing values.  Applications include sensor network localization, classification of high-dimensional images and visualizing social networks.

Trajectory Optimisation

Trajectory Optimisation

We are interested in trajectory optimisation problems especially those with combinatorial aspects, merging classical approaches from optimal control theory and nonlinear optimisation with techniques from mixed-integer programming and discrete optimisation. Our work is supported by the European Space Agency (ESA), the Clean Sky Initiative of the Horizon 2020 European Union Funding Programme, and the Brazilian "Science without Borders" scheme. Our partners include Thales Aerospace, the University of Federal Armed Forces Munich, the University of Bremen and the Technical University Munich.

Image credit: (c) ESA

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