Modeling laboratory data from clinical trials

Laboratory data from clinical trials are considered precursors of potential organ dysfunctions. The routine analysis of these data focusses on the occurrence of extremely high or low values relative to normal ranges, the change of these incidences compared to baseline, or the worst values from each individual patient. However, only rarely is an attempt made to model the dynamics of the measurements over time. In this paper we propose to model laboratory measurements by stochastic processes, specifically by Ornstein-Uhlenbeck processes. The aim is to estimate parameters of these processes in order to characterize a potential effect of drugs or other medical treatments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-Skilled Workforce Optimisation

This paper describes a problem faced by CS Energy's Swanbank Power Station in the Australian state of Queensland. It involved the personnel scheduling (rostering) of staff with multiple skill levels at the power station. Such a problem can be classified using the six stage construction process proposed by Ernst et al. We assume that the three processes of ‘demand modelling,’ ‘shift starting times’ and ‘task scheduling’ are specified. We are concerned with the essential processes of ‘day off scheduling,’ ‘line of work construction’ and ‘shift assignment to staff’ with requirements to maintain multiple skills. Several other authors have reported results for staff with hierarchical skills while the methods proposed in this paper are for non-hierarchical skill sets. The paper describes a set covering approach to the multi-skilled rostering problem. We propose a number of solution strategies for the set covering approach and give a comparison of the results.     

Supply Chain Optimisation in the Paper Industry

We describe the formulation and development of a supply-chain optimisation model for Fletcher Challenge Paper Australasia (FCPA). This model, known as Paper Industry Value Optimisation Tool (PIVOT), is a large mixed integer program that finds an optimal allocation of supplier to mill, product to paper machine, and paper machine to customer, while at the same time modelling many of the supply chain details and nuances which are peculiar to FCPA. PIVOT has assisted FCPA in solving a number of strategic and tactical decision problems, and provided significant economic benefits for the company.     

Optimisation under hybrid uncertainty

Fuzzy Stochastic Optimisation is emerging as a subfield of Mathematical programming, the disciplinary matrix of which consists of analysis of mathematical programs under fuzziness and randomness along with methods for solving them. The “primum movens” of this paper is to describe a unifying methodological approach, that is suitable for finding a satisfying solution of a mathematical program in the presence of fuzzy data and random variables. Properties of fuzzy random variables (FRVs) serve as the backdrop to this approach which also lends itself better to handling mathematical programs with fuzzy random coefficients. For the paper to be somewhat self-contained, the notion of FRV is briefly discussed and a synopsis of Fuzzy Stochastic Optimisation provided. A systematically solved example aimed at illustrating the proposed approach is also included.     

Optimisation of Structures with Inelastic Deformations

In context of design optimisation, the treatment of inelastic, path-dependent materials is a topic of interest. As opposed to purely elastic materials, it is necessary to store and analyse the deformation history in order to appropriately describe inelastic material behaviour. For design optimisation of structures sensitivities of all quantities of influence have to be computed so as to use gradient based optimisation algorithms. Considering path-dependent materials the sensitivities of internal variables that represent the deformation history have to be additionally calculated. A numerical effective way of determining sensitivities is the variational sensitivity analysis. This approach is applied to develop a powerful and effective algorithm to compute sensitivities of the structural response with respect to their geometric design. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Light Refraction is Nonlinear Optimisation

In this paper, we show that the near field light refraction can be formulated as a nonlinear optimisation problem, both for a point light source and for a parallel light source.     

Optimisation of the vibrational response of ultrasonic cutting systems

^** Email: m.cartmell{at}mech.gla.ac.uk This paper provides an account of an investigation into possibledynamic interactions between two coupled non-linear sub-systems,each possessing opposing non-linear overhang characteristicsin the frequency domain in terms of positive and negative cubicstiffnesses. This system is a two-degree-of-freedom Duffingoscillator in which certain non-linear effects can be advantageouslyneutralised under specific conditions. This theoretical vehiclehas been used as a preliminary methodology for understandingthe interactive behaviour within typical industrial ultrasoniccutting components. Ultrasonic energy is generated within apiezoelectric exciter, which is inherently non-linear, and whichis coupled to a bar- or block-horn, and to one or more materialcutting blades, for example. The horn/blade configurations arealso non-linear, and within the whole system there are responsefeatures which are strongly reminiscent of positive and negativecubic stiffness effects. The two-degree-of-freedom model isanalysed and it is shown that a practically useful mitigatingeffect on the overall non-linear response of the system canbe created under certain conditions when one of the cubic stiffnessesis varied. It has also been shown experimentally that couplingof ultrasonic components with different non-linear characteristicscan strongly influence the performance of the system and thatthe general behaviour of the hypothetical theoretical modelis indeed borne out in practice. Further experiments have shownthat a multiple horn/blade configuration can, under certaincircumstances, display autoparametric responses based on theforced response of the desired longitudinal mode parametricallyexciting an undesired lateral mode. Typical autoparametric responsephenomena have been observed and are presented at the end ofthe paper.     

Quasi-linear production systems: Optimisation of the transportation system

This paper is devoted to the quasi-linear production systems under the following additional hypothesis:

• 1.1. There exists a loading sequence which gives the input order of the parts of the system.
• 2.2. There exists, for each machine, a processing sequence which gives the order for manufacturing the parts.
• 3.3. The transportation system uses carts. A cart is a transportation unit able to carry one part for a machine to another. The parts are loaded on the carts before entering the system and unloaded when the manufacture of the part is finished.

We give an algorithm which leads to the minimal number of carts needed in order to reach the maximal production rate, the loading and processing sequences being known. We also characterize the optimal solution in the case of equal processing times.     

Optimisation of sludge treatment and transport

In this paper we describe some work carried out in the UK into improving the effectiveness of a waste treatment and distribution network. Sludge is the name given to (treated) waste water and sewage. It is collected at small facilities and requires further treatment before it can be disposed of. We develop a linear programming model for the problem of effectively treating and distributing sludge. This model has been implemented in a large UK regional water company, Yorkshire Water.     

Optimisation of road vehicle passive suspension systems. Part 1. Optimisation algorithm and vehicle model

Numerous problems have in the past been experienced during the development of military vehicle suspension systems. In order to solve some of these problems a two-dimensional multi-body vehicle dynamics simulation model has been developed for computer implementation. This model is linked to a mathematical optimisation algorithm in order to enable the optimisation of vehicle design parameters through the minimisation of a well defined objective function. In part 1 of this paper the concept of multi-disciplinary design optimisation is discussed. This is followed by the presentation of the up to six degrees of freedom vehicle model developed for this study, and a discussion of the specific gradient-based optimisation algorithm selected for the optimisation. In particular the derivation of the set of second-order differential equations, describing the acceleration of the different solid bodies of the vehicle model, is presented. In order to perform the optimisation of the non-linear suspension component characteristics, a six piece-wise continuous and linear approximation is used which is also described in this paper. Part 2 of this study will outline the simulation programme and the qualification of the programme. It will also present a typical case study where the proposed optimisation methodology is applied to improve the damper characteristics of a specific vehicle.     

A Review of the Report of the Committee on Policy Optimisation

When the Government Committee on Policy Optimisation published its report, the Committee of Professors in Operational Research was concerned to discover that there had been no formal input from the Operational Research community into the evidence which was taken. As a first stage in deciding what should be done, the Committee of Professors invited Professor S. L. Cook to write an appreciation and a criticism of the report. The Associate Editor, as a member of the Committee of Professors, was impressed by the outstanding quality of Professor Cook's note and suggested to him that, subject to minor editing changes such as rewriting his appreciation in the third person, Professor Cook might wish to have his note published in this journal.On the day that the Associate Editor received Professor Cook's acceptance of this invitation, he also heard of his untimely death. This paper, therefore, is published posthumously and is as Steve Cook wrote it, apart from the minor changes referred to above. The compassion and breadth of vision of Steve Cook shines through in every sentence.     

Conjugate Grids for Unconstrained Optimisation

Several recent papers have proposed the use of grids for solving unconstrained optimisation problems. Grid-based methods typically generate a sequence of grid local minimisers which converges to stationary points under mild conditions.In this paper the location and number of grid local minimisers is calculated for strictly convex quadratic functions in two dimensions with certain types of grids. These calculations show it is possible to construct a grid with an arbitrary number of grid local minimisers. The furthest of these can be an arbitrary distance from the quadratic's minimiser. These results have important implications for the design of practical grid-based algorithms.Grids based on conjugate directions do not suffer from these problems. For such grids only the grid points closest (depending on the choice of metric) to the minimiser are grid local minimisers. Furthermore, conjugate grids are shown to be reasonably stable under mild perturbations so that in practice, only approximately conjugate grids are required.     

Optimisation of multi-position machines and transfer lines

A new optimisation problem for design of multi-position machines and automatic transfer lines is considered. To reduce the number of pieces of equipment, machining operations are grouped into blocks. The operations of the same block are performed simultaneously by one piece of equipment (multi-spindle head). At the studied design stage, constraints related to the design of blocks and workstations, as well as precedence constraints for operations are known. The problem consists in an optimal grouping of the operations into blocks minimizing the total number of blocks and workstations while reaching a given cycle time (productivity). A constrained shortest path algorithm is developed and tested.     

Multilevel Refinement for Combinatorial Optimisation Problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.