A paper describing work in this area for EDF Energy has been published in the Journal of the Royal Statistical Society (Statistical Modelling of Graphite Brick Cracking in Advanced Gas-Cooled Reactors by Philip R Maul, Peter C Robinson and Paul Northrop, JRSS, Series C, 60(3), 1-15).
Another technique that we have applied in several projects is Genetic Algorithms. For many problems this powerful approach to optimisation makes searching through huge numbers of possible cases practicable. A particular area that we have developed is Portfolio Analysis, where the optimisation involves searching for a best combination of items rather than a single one. There is a large literature on this topic in the financial sector, but there are also wider applications to problems in the energy and environment sectors.
In addition to applying these approaches for our existing clients, we have recently entered several competitions advertised on the internet. Peter Robinson was announced as an Award Winner by Innocentive after submitting a solution to the challenge “Algorithms Optimized for Efficiency and Speed for Exploring and Testing Large Model Spaces”. Innocentive brings together companies with problems and innovators across the world in Open Innovation. Challenges cover a wide range of technical problems and innovators from across the world take part (200,000+ from 200 countries are registered). This success followed an earlier successful submission to Société de Calcul Mathématique in France for an efficient algorithm to calculate some high-dimensional integrals used in a novel approach to modelling extreme events (in this case high summer temperatures in Paris).