The application of multilevel refinement to the vehicle routing problem

We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL heuristic, termed the combined node-exchange composite heuristic (CNCH), is developed first to solve instances of the VRP. A ML version (the ML-CNCH) is then created, using the construction and improvement heuristics of the CNCH at each level. Experimentation is used to find a suitable combination, which extends the global view of these heuristics. Results comparing both SL and ML are presented.

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Multilevel approaches applied to the capacitated clustering problem

This paper presents two multilevel refinement algorithms for the capacitated clustering problem. Multilevel refinement is a collaborative technique capable of significantly aiding the solution process for optimisation problems. The central methodologies of the technique are filtering solutions from the search space and reducing the level of problem detail to be considered at each level of the solution process. The first multilevel algorithm uses a simple tabu search while the other executes a standard local search procedure. Both algorithms demonstrate that the multilevel technique is capable of aiding the solution process for this combinatorial optimisation problem.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

Accelerating innovation in the social housing sector in UK

The UK government has been promoting innovation in the construction sector to improve the sustainability of the built environment. It has the potential and strength in developing construction research in design and engineering, but the impact of these processes seems to be slow in reaching the residential sector. While funding remains a major constraint research show that a number of detrimental issues including; organisation, risk, mind sets of the stakeholders, planning constraints,reluctance to accept change and the unexploited markets are major contributing factors. Most of these barriers can be overcome with research, development and information and knowledge transfer techniques. Educating all stakeholders can act as an accelerator for innovation. Given the large stock of existing dwellings, the situation is compounded, by issues related to climate change, to the point that this problem can no longer be ignored and requires an urgent response from all sectors involved. This paper attempts to highlight some of the key issues that are important in accelerating innovation in the housing sector. It briefly looks at the process of innovation in housing and presents lessons learnt from two research projects. The drivers and barriers and the role played by the government are examined in relation to the housing context.

Depth gradients of benthic standing stock and diversity on the continental margin at a high-latitude ice-free site (off Spitsbergen 79 degrees N)

High-latitude seas are mostly covered by multi-year ice, which impacts processes of primary production and sedimentation of organic matter. Because of the warming effect of West Spitsbergen Current (WSC), the waters off West Spitsbergen have only winter ice cover. That is uncommon for such a high latitude and enables to separate effects of multiyear-ice cover from the latitudinal patterns. Macrofauna was sampled off Kongsfjord (79°N) along the depth gradient from 300 to 3000 m. The density, biomass and diversity at shallow sites situated in a canyon were very variable. Biomass was negatively correlated with depth (R=-0.86R=-0.86, p<0.001), and ranged from 61 g ww m−2 (212 m) to 1 g ww m−2 (2025 m). The biomasses were much higher than in the multiyear-ice covered High Arctic at similar depths, while resembling those from temperate and tropical localities. Species richness (expressed by number of species per sample and species–area accumulation curves) decreased with depth. There was no clear depth-related pattern in diversity measures: Hurbert rarefaction, Shannon–Wiener or Pielou. The classic increase of species richness and diversity with depth was not observed. Species richness and diversity of deep-sea macrofauna were much lower in our study than in comparable studies of temperate North Atlantic localities. That is related to geographic isolation of Greenland–Icelandic–Norwegian (GIN) seas from the Atlantic pool of species.

Recruitment in a changing environment: the 2000s North Sea herring recruitment failure

Environmentally induced change appears to be impacting the recruitment of North Sea herring (Clupea harengus). Despite simultaneously having a large adult population, historically low exploitation, and Marine Stewardship Council accreditation (implying sustainability), there have been an unprecedented 6 sequential years of poor juvenile production (recruitment). Analysis suggests that the poor recruitment arises during the larval overwintering phase, with recent survival rates greatly reduced. Contemporary warming of the North Sea has caused significant changes in the plankton community, and a recently identified regime shift around 2000 shows close temporal agreement with the reduced larval survival. It is, therefore, possible that we are observing the first consequences of this planktonic change for higher trophic levels. There is no indication of a recovery in recruitment in the short term. Fishing mortality is currently outside the agreed management plan, and forecasts show a high risk of the stock moving outside safe biological limits soon, potentially precipitating another collapse of the stock. However, bringing the realized fishing mortality back in line with the management plan would likely alleviate the problem. This illustrates again that recruitment is influenced by more than just spawning-stock biomass, and that changes in other factors can be of equal, or even greater, importance. In such dynamically changing environments, recent management success does not necessarily guarantee future sustainability.