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.
SUMMARYA smoothing technique is developed to remove the oscillatory errors in initial nodal pore pressures, associated with the use of quadratic isoparametric elements to model soil consolidation. Numerical results using this technique are compared with the performance of other types of element in problems of oneand two-dimensional consolidation.
This paper analyses the stresses and displacements in a uniformly prestressed Mohr-Coulomb continuum, caused by the excavation of an infinitely long cylindrical cavity. It is shown that the solution to this axisymmetric problem passes through three stages as the pressure at the cavity wall is progressively reduced. In the first two stages it is possible to determine the stresses and displacements in the r θ -plane without consideration of the out-of plane stress . In the third stage it is shown that an inner plastic zone develops in which, so that the stress states lie on a singularity of the plastic yield surface. Using the correct flow rule for this situation, an analytic solution for the radial displacements is obtained. Numerical examples are given to demonstrate that a proper consideration of this third stage can have a significant effect on the cavity wall displacements.
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 ÿnite 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 modiÿcations 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 signiÿcant 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 sti ness matrix, and has great potential for parallelization. ? 1997 by John Wiley & Sons, Ltd.
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