Scheduling techniques to optimise rail operations

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is very complex and uses daily schedules, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. There are several benefits to formulating the train scheduling problem as a blocking parallel-machine job shop scheduling (BPMJSS) problem, namely to prevent two trains passing in one section at the same time; to keep the train activities (operations) in sequence during each run (trip) by applying precedence constraints; to pass the trains on one section in the correct order (priorities of passing trains) by applying disjunctive constraints; and, to ease passing trains by solving rail conflicts by applying blocking constraints and Parallel Machine Scheduling. Therefore, the sugarcane rail operations are formulated as BPMJSS problem. A mixed integer programming and constraint programming approaches are used to describe the BPMJSS problem. The model is solved by the integration of constraint programming, mixed integer programming and search techniques. The optimality performance is tested by Optimization Programming Language (OPL) and CPLEX software on small and large size instances based on specific criteria. A real life problem is used to verify and validate the approach. Constructive heuristics and new metaheuristics including simulated annealing and tabu search are proposed to solve this complex and NP-hard scheduling problem and produce a more efficient scheduling system. Innovative hybrid and hyper metaheuristic techniques are developed and coded using C# language to improve the solutions quality and CPU time. Hybrid techniques depend on integrating heuristic and metaheuristic techniques consecutively, while hyper techniques are the complete integration between different metaheuristic techniques, heuristic techniques, or both.

Experiences with implementing common mathematical operations using field programmable gate arrays

Many computationally intensive scientific applications involve repetitive floating point operations other than addition and multiplication which may present a significant performance bottleneck due to the relatively large latency or low throughput involved in executing such arithmetic primitives on commod- ity processors. A promising alternative is to execute such primitives on Field Programmable Gate Array (FPGA) hardware acting as an application-specific custom co-processor in a high performance reconfig- urable computing platform. The use of FPGAs can provide advantages such as fine-grain parallelism but issues relating to code development in a hardware description language and efficient data transfer to and from the FPGA chip can present significant application development challenges. In this paper, we discuss our practical experiences in developing a selection of floating point hardware designs to be implemented using FPGAs. Our designs include some basic mathemati cal library functions which can be implemented for user defined precisions suitable for novel applications requiring non-standard floating point represen- tation. We discuss the details of our designs along with results from performance and accuracy analysis tests.

Visualisation of complex flows using texture-based techniques

Detailed representations of complex flow datasets are often difficult to generate using traditional vector visualisation techniques such as arrow plots and streamlines. This is particularly true when the flow regime changes in time. Texture-based techniques, which are based on the advection of dense textures, are novel techniques for visualising such flows. We review two popular texture based techniques and their application to flow datasets sourced from active research projects. The techniques investigated were Line integral convolution (LIC) [1], and Image based flow visualisation (IBFV) [18]. We evaluated these and report on their effectiveness from a visualisation perspective. We also report on their ease of implementation and computational overheads.

Preface to the proceedings of the 16th Computational Techniques and Applications Conference

CTAC2012 was the 16th biennial Computational Techniques and Applications Conference, and took place at Queensland University of Technology from 23 - 26 September, 2012. The ANZIAM Special Interest Group in Computational Techniques and Applications is responsible for the CTAC meetings, the first of which was held in 1981.

Frontier Techniques for Measuring and Estimating Airport Efficiency : An Empirical Review with Practical Guidelines for Analysis and Future Research

Airport efficiency is important because it has a direct impact on customer safety and satisfaction and therefore the financial performance and sustainability of airports, airlines, and affiliated service providers. This is especially so in a world characterized by an increasing volume of both domestic and international air travel, price and other forms of competition between rival airports, airport hubs and airlines, and rapid and sometimes unexpected changes in airline routes and carriers. It also reflects expansion in the number of airports handling regional, national, and international traffic and the growth of complementary airport facilities including industrial, commercial, and retail premises. This has fostered a steadily increasing volume of research aimed at modeling and providing best-practice measures and estimates of airport efficiency using mathematical and econometric frontiers. The purpose of this chapter is to review these various methods as they apply to airports throughout the world. Apart from discussing the strengths and weaknesses of the different approaches and their key findings, the paper also examines the steps faced by researchers as they move through the modeling process in defining airport inputs and outputs and the purported efficiency drivers. Accordingly, the chapter provides guidance to those conducting empirical research on airport efficiency and serves as an aid for aviation regulators and airport operators among others interpreting airport efficiency research outcomes.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Examples illustrating the use of renormalization techniques for singularly perturbed differential equations

With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Multi-objective models and techniques for analysing the absolute capacity of railway networks

Railway capacity determination and expansion are very important topics. In prior research, the competition between different entities such as train services and train types, on different network corridors however have been ignored, poorly modelled, or else assumed to be static. In response, a comprehensive set of multi-objective models have been formulated in this article to perform a trade-off analysis. These models determine the total absolute capacity of railway networks as the most equitable solution according to a clearly defined set of competing objectives. The models also perform a sensitivity analysis of capacity with respect to those competing objectives. The models have been extensively tested on a case study and their significant worth is shown. The models were solved using a variety of techniques however an adaptive E constraint method was shown to be most superior. In order to identify only the best solution, a Simulated Annealing meta-heuristic was implemented and tested. However a linearization technique based upon separable programming was also developed and shown to be superior in terms of solution quality but far less in terms of computational time.

Techniques to effectively buffer schedules in the face of uncertainties

Resource assignment and scheduling is a difficult task when job processing times are stochastic, and resources are to be used for both known and unknown demand. To operate effectively within such an environment, several novel strategies are investigated. The first focuses upon the creation of a robust schedule, and utilises the concept of strategically placed idle time (i.e. buffering). The second approach introduces the idea of maintaining a number of free resources at each time, and culminates in another form of strategically placed buffering. The attraction of these approaches is that they are easy to grasp conceptually, and mimic what practitioners already do in practice. Our extensive numerical testing has shown that these techniques ensure more prompt job processing, and reduced job cancellations and waiting time. They are effective in the considered setting and could easily be adapted for many real life problems, for instance those in health care. This article has more importantly demonstrated that integrating the two approaches is a better strategy and will provide an effective stochastic scheduling approach.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Hybrid metaheuristic techniques for optimising sugarcane rail operations

Mixed integer programming and parallel-machine job shop scheduling are used to solve the sugarcane rail transport scheduling problem. Constructive heuristics and metaheuristics were developed to produce a more efficient scheduling system and so reduce operating costs. The solutions were tested on small and large size problems. High-quality solutions and improved CPU time are the result of developing new hybrid techniques which consist of different ways of integrating simulated annealing and Tabu search techniques.

A mathematical framework for expanding a railway’s theoretical capacity

Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.