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Research by Gondzio (Maxwell Institute) on algorithms for large-scale optimization has led to major advances in the design of interior point methods (IPMs). The advances include new ways of exploiting centrality (1996-2008) as well as special preconditioning (2004) and warmstarting (2003, 2008) techniques. These techniques make it possible to solve more difficult optimization problems more quickly. Some of these have been implemented by all major commercial providers of optimization software including IBM, Gurobi, Mosek and FICO. The techniques have therefore had an economic impact on these companies and on thousands of their customers worldwide who now benefit from faster, more reliable methods to solve their challenging optimization tasks.
New optimization routines have been commercialised as a product by the Numerical Algorithms Group (NAG). These routines are based on research in the School of Mathematics at the University of Birmingham. NAG has confirmed that their expectation is that they will release this new product, under licence, in Mark 24 of the NAG C Library, to be made available in February 2014. The product is based on the PENNON software code developed by Michal Kocvara (Birmingham) and Michael Stingl (Erlangen). NAG are an international benchmark provider of numerical algorithms and software in mathematics, and as optimization becomes ubiquitous, the novel routines for nonlinear optimization will help NAG attract new customers and bring further benefits to industrial and commercial end users. Inclusion in the NAG Library will mean that this product is actively marketed to the company's worldwide client base which includes many major corporations in the finance sector and engineering industries (44% of NAG's £8.2m turnover in 2012/2013 was outside of the UK).
Designs for complex structures like cars, aeroplanes and modern buildings suffer from unpredictable vibrations that lead to anything from irritating noises to dangerous structural failures. Predicting the distribution of vibrational energy in large coupled systems is an important and challenging task of major interest to industry. Until recently there was no reliable method to predict vibrations at the important mid-to-high frequency ranges.
There is a need to gain accurate predictions of vibrations at the design stage. However, previous techniques developed in the context of Quantum Chaos are too cumbersome to be used in a fast-moving commercial design setting. Bandtlow has used his expertise to develop a novel method that computes a very close approximation to these predictions but in a reasonable time. Bandtlow's method of constructing an efficient mathematical model for spectral vibrations has informed inuTech's latest product and led to enhanced performance of automobiles and aircraft.
This research has profoundly influenced the practice of pharmacoepidemiology in 2008-13. The self-controlled case series (SCCS) method is particularly well-suited for working with computerised databases, which are increasingly used in epidemiology. The method has been recommended by international agencies (WHO, ECDC) and is now widely used by health practitioners within national public health agencies, including the CDC (USA), Public Health England (UK) and many other national and regional public health bodies. It has influenced practice within the private sector (notably the pharmaceutical and the healthcare industries). Use of the SCCS method has impacted on health by reducing costs, improving timeliness and improving the quality of evidence upon which policy decisions are based.
Spatial decomposition methods have been extended to apply to spatial, scale, and temporal domains as a result of work at the Numerical and Applied Mathematics Research Unit (NAMU) at the University of Greenwich. This work has led to a numerical framework for tackling many nonlinear problems which have been key bottlenecks in software design and scientific computing. The work has benefitted the welding industry in the UK because these concepts are now embedded, with parallel computing, in the industry's modern welding design process software.
In response to the deficiencies in bank risk management revealed following the 2008 financial crisis, one of the mandated requirements under the Basel III regulatory framework is for banks to backtest the internal models they use to price their assets and to calculate how much capital they require should a counterparty default. Qiwei Yao worked with the Quantitative Analyst — Exposure team at Barclays Bank, which is responsible for constructing the Barclays Counterpart Credit Risk (CCR) backtesting methodology. They made use of several statistical methods from Yao's research to construct the newly developed backtesting methodology which is now in operation at Barclays Bank. This puts the CCR assessment and management at Barclays in line with the Basel III regulatory capital framework.
Many operations in daily life, from manufacturing to running a hospital, need to optimise the return on use of resources where volume and value are conditions. Scheduling theory tackles some of the hardest practical optimisation problems, not known to be solvable in reasonable computation time. Strusevich and Kellerer have been able to reformulate practical scheduling challenges as `knapsack problems' - dealing with volume and value constraints - and then design approximation algorithms which can be applied back to the original challenge. The work has attracted EPSRC funding, stimulated a new field of research which is developing fast, been widely published, led to presentations at international conferences including the 2009 Computers and Industrial Engineering conference attended by industry practitioners and is impacting on Combinatorial Optimisation research.
Through close collaboration with scientists at the European Space Agency (ESA), research at the University of Southampton has developed new algorithms and an associated software tool that have contributed to more efficient spacecraft design. Now a standard component of the ESA's design technology, the tools have doubled the speed in which crucial design processes can be completed, resulting in increased efficiency over the REF period of 20 person-years — equivalent to €1 million in monetary terms — and maintaining the ESA's manufacturing competitiveness. The success of this work led to a €480,000 EU grant to adapt the tools for the avionics industry as part of efforts to meet ambitious environmental targets under the EU Clean Sky Initiative.
This case study demonstrates the benefits achieved when the mathematical and computational aspects of a computational fluid dynamics (CFD) problem were brought together to work on real-world aerodynamic applications. While earlier insight on the solution reconstruction problem was purely based on empirical intuition, research in the School of Mathematics at the University of Birmingham by Dr Natalia Petrovskaya has resulted in the development of the necessary synthetic judgement in which the importance of accurate reconstruction on unstructured grids has been fully recognised by the CFD researchers at the Boeing Company. Boeing has confirmed that the research has led to substantial resultant improvements in their products as well as gains in engineering productivity. For instance, wing body fairing and winglets optimization for the Boeing 787 has been done by means of CFD only. Implementation of CFD in the design of their new aircraft allowed Boeing to reduce the testing time in the wind tunnel for the 787 aircraft by 30% in comparison with testing carried out for Boeing 777. Efficient use of CFD in the design of new aircrafts has helped the Boeing Company to further strengthen their core operations, improve their execution and competitiveness and leverage their international advantage.
Professor Wright has developed practical scheduling implementations for sports fixtures and officials, with regular clients at both professional and amateur level in the UK and abroad, including the England and Wales Cricket Board and the New Zealand Rugby Union. His expertise also supports `what if' exercises, enabling clients to experiment with new ideas and announce changes with confidence that they will work in practice. His work has resulted in financial gains, substantial savings in skilled administrative time and high satisfaction for stakeholders. His research has potential reach across numerous sports, at all levels across the world.