A Component Based Heuristic Search Method with AdaptivePerturbations for Hospital Personnel Scheduling

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with adaptive perturbations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then mimic a natural evolutionary process on these components to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs a dynamic evaluation function which evaluates how well each component contributes towards the final objective. Two perturbation steps are then applied: the first perturbation eliminates a number of components that are deemed not worthy to stay in the current schedule; the second perturbation may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.

An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations

In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) An adjoint consistent imposition of the boundary conditions; (ii) An adjoint consistent reformulation of the underlying target functional of practical interest; (iii) Design of appropriate interior-penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L_2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi & Rebay, cf. [11], the standard SIPG method outlined in [25], and an NIPG variant of the new scheme will be undertaken.