Computational and Optimisation Modelling
The group has been active in research for over 25 years within the Department of Mathematical Sciences. Interests focus on computational optimisation and mathematical modelling. Investigations undertaken by the group include design of sequential and parallel optimisation algorithms, development of software systems and applications to business and industrial problems. Substantial experience has been accumulated in solving large-scale linear and integer programming problems. Recently the group has developed in innovative Masters degree course in Decision Modelling and Information Systems.
Efficiency and robustness issues relating to algorithm performance have played a central role in research. In addition to work on traditional serial computers, the group has explored methods of efficiency exploiting parallel computing platforms. The modelling work has been extended to cover the confluence of interest in knowledge systems, mathematical programming modelling and models of uncertainty and randomness. The research activities can be categorised into four main areas set out below:
- Solution of large-scale linear programming problems using sparse simplex and interior point method. Investigation of these methods in relation to course grain parallel shared memory machines and massively parallel machines.
- Integration of tree search methods, cutting plane methods and graph theoretic algorithms for the solution of integer and mixed integer programming problems. Combinatorial and network optimisation.
- Tools for constructing and analysing mathematical programming models. Integration of knowledge representation techniques from AI and Constraint Logic Programming with optimisation models to construct decision support systems. Application specific methods for scheduling problems.
- Optimum decision making under uncertainty. This includes, quadratic programming and E-V models, stochastic programming and their applications in financial planning problems including portfolio analytics and asset and liability management.
- The group has around fourteen research students and has received support for the above research from various grant giving bodies, such as EPSRC, BBSRC, EU, DTI, US Army's European Research Office, Scientific Affairs Division of NATO, Numerical Algorithms Group (NAG) Ltd, US Coast Guard R & D Center, Ministry of Defence, Southern Electric, Unilever, Advanced Portfolio Technologies(APT), UBS Warburg, INQUIRE, Fidelity Investment Services and DRA.