Martin Reed

An ant colony algorithm for the multi-compartment vehicle routing problem

We demonstrate the use of Ant Colony System (ACS) to solve the capacitated vehicle routing problem associated with collection of recycling waste from households, treated as nodes in a spatial network. For networks where the nodes are concentrated in separate clusters, the use of k-means clustering can greatly improve the efficiency of the solution. The ACS algorithm is extended to model the use of multi-compartment vehicles with kerbside sorting of waste into separate compartments for glass, paper, etc. The algorithm produces high-quality solutions for two-compartment test problems.

ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES

SUMMARY This paper deals with two forms of preconditioner which can be easily used with a Conjugate Gradient solver to replace a direct solution subroutine in a traditional engineering nite element package; they are tested in such a package (FINAL) over a range of 2-D and 3-D elasticity problems from geotechnical engineering. Quadratic basis functions are used. A number of modications to the basic Incomplete Choleski [IC(0)] factorization preconditioner are considered. An algorithm to reduce positive o-diagonal entries is shown in numerical experiments to ensure stability, but at the expense of slow convergence. An alternative algorithm of Jennings and Malik is more successful, and a relaxation parameter ! is introduced which can make a further signicant improvement in performance while maintaining stability. A heuristic for determining a near-optimal value of ! is proposed. A second form of preconditioning, symmetrically scaled element by element, due to Bartelt, is also shown to perform robustly over a range of problems; it does not require assembly of the global stiness matrix, and has great potential for parallelization. ? 1997 by John Wiley & Sons, Ltd.

Convergence analysis for an element-by-element finite element method

Abstract This paper describes an element-by-element iterative finite element algorithm for linear elasticity problems. While it does not claim to compete with conventional finite element solvers on a serial computer, it is very suitable for parallelization. It is constructed in a manner very similar to the Static Relaxation algorithm used in the Discrete Element Method, thus facilitating the development of a unified FEM/DEM analysis. The convergence properties of the algorithm are analysed, and illustrated on a model problem.

A finite element method to model progressive fracturing

Abstract In this paper, a theoretical basis is established for a finite element iterative algorithm for load-displacement analysis of elasticity problems in which the elastic body fractures under load. Location of fractures is determined by testing a Coulomb friction criterion along inter-element edges. Convergence of the algorithm to a physically-meaningful solution is proved, and is illustrated by results for a cantilever-type problem.

IMPROVEMENT OF ROCK PROPERTIES BY BOLTING IN THE PLASTIC ZONE AROUND A TUNNEL: A NUMERICAL STUDY

This paper describes i) the modelling of grouted rockbolts in a plane strain elasto-viscoplastic finite element analysis and ii) the use of the model to demonstrate the effect of rockbolting in restricting the growth of the zone of yielded rock in a circular tunnel problem. Practical aspects of rockbolting are outlined and the basis for numerical modelling of rockbolts described. A circular cross-section tunnel, 5m in radius, excavated in a pre- stressed rock mass of infinite extent is then condsidered. The use of no rockbolts, 11 long bolts, 11 short bolts and 6 long bolts in conditions of ideal plasticity and brittle plasticity are considered. The finite element analysis programme FESTA is used. The results are presented with diagrams. A significant reduction in deformation of the tunnel wall and size of the zone of yielded rock is demonstrated. An important conclusion is that the optimum length of rockbolt is one which places the tip of the bolt in intact unyielded rock.

Language competence in mathematics

This paper asks whether particular problems exist in mathematics for students who have to learn their discipline in a language which is not their mother tongue. One possible problem area is considered—the relationship between performance in mathematics and the understanding of mathematical text.

L-Broyden methods: a generalization of the L-BFGS method to the limited-memory Broyden family

The paper derives a multiplicative update equation for the convex Broyden family of quasi-Newton (QN) updates. The well-known multiplicative Broyden-fletcher-Goldfarb-Shanno (BFGS) update is a special case of this. Using a self-scaling parameter, the formula is extended to the SR1 update. It is shown that for each Broyden update, a pair of multiplicative update formulae can be defined (coincident in the case of Davidon-fletcher-Powell (DFP)). The multiplicative updates are used to define limited-memory QN algorithms, denoted the L-Broyden methods, of which L-BFGS is a special case. Numerical results show that the L-Broyden methods are competitive with extensions of the variable storage conjugate gradients limited memory QN method to other Broyden updates, but that L-BFGS with Shanno scaling remains the most efficient and reliable method in the L-Broyden family.

A hybrid algorithm for continuous optimisation

An effective particle swarm - quasi-Newton hybrid for the optimisation of continuous functions is developed, which is shown to work well on a range of test problems. This method exploits the global exploration abilities of the PSO algorithm and the fast convergence of the quasi-Newton method. New switching heuristics between the quasi-Newton and PSO methods are introduced, with the update pairs being used to generate new particles. The new hybrid, called L-PSO, is shown to be effective in obtaining the global minimum on a range of test problems, and outperforms previous hybrids with which it is compared.