Multilevel refinement for the vehicle routing problem

Multilevel approaches to computational problems are pervasive across many areas of applied mathematics and scientific computing. The multilevel paradigm uses recursive coarsening to create a hierarchy of approximations to the original problem, then an initial solution is found for the coarsest problem and iteratively refined and improved at each level, coarsest to finest. The solution process is aided by the global perspective (or `global view') imparted to the optimisation by the coarsening. This paper looks at their application to the Vehicle Routing Problem.

A study of modelling approaches for rail vehicle collision behaviour

A rigid wall model has been used widely in the numerical simulation of rail vehicle impacts. Finite element impact modelling of rail vehicles is generally based on a half-width and full-length or half-length structure, depending on the symmetry. The structure and components of rail vehicles are normally designed to cope with proof loading to ensure adequate ride performance. In this paper, the authors present a study of a rail vehicle with driving cab focused on improving the modelling approach and exploring the intrinsic structural weaknesses to enhance its crashworthiness. The underpinning research used finite element analysis and compared the behaviour of the rail vehicle in different impact scenarios. It was found that the simulation of a rigid wall impact can mask structural weaknesses; that even a completely symmetrical impact may lead to an asymmetrical result; that downward bending is an intrinsic weakness of conventional rail vehicles and that a rigid part of the vehicle structure, such as the body bolster, may cause uncoordinated deformation and shear fracture between the vehicle sections. These findings have significance for impact simulation, the full-scale testing of rail vehicles and rail vehicle design in general.

Multilevel refinement strategies for the capacity 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 algorithm, which uses a combination of standard VRP heuristics, is developed first to solve instances of the VRP. A ML version, which extends the global view of these heuristics, is then created, using variants of the construction and improvement heuristics at each level. Finally some multilevel enhancements are developed. Experimentation is used to find suitable parameter settings and the final version is tested on two well-known VRP benchmark suites. Results comparing both SL and ML algorithms are presented.

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.

Analysis of the structural characteristics of an intermediate rail vehicle and their effect on vehicle crash performance

In the current paper, the authors present an analysis of the structural characteristics of an intermediate rail vehicle and their effects on crash performance of the vehicle. Theirs is a simulation based analysis involving four stages. First, the crashworthiness of the vehicle is assessed by simulating an impact of the vehicle with a rigid wall. Second, the structural characteristics of the vehicle are analysed based on the structural behaviour during this impact and then the structure is modified. Third, the modified vehicle is tested again in the same impact scenario with a rigid wall. Finally, the modified vehicle is subjected to a modelled head-on impact which mirrors the real-life impact interface between two intermediate vehicles in a train impact. The emphasis of the current study is on the structural characteristics of the intermediate vehicle and the differences compared to an impact of a leading vehicle. The study shows that, similar to a leading vehicle, bending, or jackknifing is a main form of failure in this conventionally designed intermediate vehicle. It has also been found that the location of the door openings creates a major difference in the behaviour of an intermediate vehicle. It causes instability of the vehicle in the door area and leads to high stresses at the joint of the end beam with the solebar and shear stresses at the joint of the inner pillar with the cantrail. Apart from this, the shapes of the vehicle ends and impact interfaces are also different and have an effect on the crash performance of the vehicles. The simulation results allow the identification of the structural characteristics and show the effectiveness of relevant modifications. The conclusions have general relevance for the crashworthiness of rail vehicle design