Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication i ....Efficient Computational Methods for Constrained Path Problems. We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The region may be a continuous space or the path may be restricted to the edges of a network. The path must optimise a prescribed criterion such
as risk, reliability or cost and satisfy a number of constraints.
Problems of this type readily arise in the defence, transport and
communication industries. In addition to efficient solution methods
for these problems the project will produce computational tools for
a wide range of related network routing problems.Read moreRead less
Economic Scheduling for Efficient Management of Clusters and their Cooperative Federation. Clusters of commodity computers have emerged as mainstream parallel and distributed platforms for high-performance computing. They are presented together as a single, unified resource to the end users by middleware technologies such as resource management and scheduling (RMS) systems. However, existing cluster RMS systems continue to use system centric models rather than utility models for the management a ....Economic Scheduling for Efficient Management of Clusters and their Cooperative Federation. Clusters of commodity computers have emerged as mainstream parallel and distributed platforms for high-performance computing. They are presented together as a single, unified resource to the end users by middleware technologies such as resource management and scheduling (RMS) systems. However, existing cluster RMS systems continue to use system centric models rather than utility models for the management and allocation of resources. There is also little emphasis on the construction of a cooperative federation of clusters to facilitate transparent sharing of resources. To enhance the value delivered by shared clusters, we propose the use of computational economy metaphor in resource management. This project aims to develop (A) computational economy based scheduling policies for allocation of resources and (B) a software infrastructure for creation of cooperative federation of distributed clusters.Read moreRead less
Effective computational methods for nonlinear cone optimisation with industrial applications. This project brings together a number of national and international researchers whose combined expertise will focus on solving optimisation problems arising in a range of industries. The work will result in new cutting edge optimisation technology that can benefit industry and the community.
Discovery Early Career Researcher Award - Grant ID: DE150100240
Funder
Australian Research Council
Funding Amount
$315,000.00
Summary
Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolv ....Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolved problems in real complexity: there is no known algorithm that solves conic problems with real data in polynomial time. The project aims to develop a deep understanding of the geometry of conic problems, aiming for the resolution of this fundamental problem in computational theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120101761
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Solving intractable problems: from practice to theory and back. By analysing how theoretically intractable problems are solved in practice by highly optimised software solvers, this project aims at a better theoretical understanding of these problems. The gained mathematical insights will then be used to stimulate the development of new and improved software solvers.
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less
Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to ....Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to improve the performance and quality of many practical signal reconstruction methods. These are used by varied Australian industries from telecommunication to mining and by researchers in the digital arts and fields such as astronomy, physics, chemistry, bioscience, geoscience, engineering and medicine.Read moreRead less
Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelli ....Optimal Transforms of Random Vectors. This proposal focusses on development of optimal transforms to describe and model nonlinear phenomena when only statistical information is known. An optimal transform is a mathematical procedure that enables us to process information in a way that is most suited to the task in hand. These transforms have been successfully used in approximation, information theory, communications, control theory and signal and image processing. Applications include modelling of physical, chemical and biological systems, filtering and compression of signals and data classification and clustering. We propose two new hybrid models for realistic transforms in a general structural framework.
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Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can g ....Algorithms for hard graph problems based on auxiliary data. When solving computational problems, algorithms usually access only the data that is absolutely necessary to define the problem. However, much more data is often readily available. Especially for important or slowly evolving data, such as road networks, social graphs, company rankings, or molecules, more and more auxiliary data becomes available through computational processes, sensors, and simple user entries. This auxiliary data can greatly speed up an algorithm and improve its accuracy. This project aims to design improved algorithms that harness auxiliary data to solve selected high-impact NP-hard graph problems, and will build a new empowering theory to discern when auxiliary data can be used to improve algorithms.Read moreRead less
Integrated, interactive and systematic Marine Protected Area design for sustainability of South Australian marine environments: A GIS-based, spatial optimisation approach. This project aims to enhance MPA design in SA by integrating systematic conservation plannning (SCP), spatial optimisation and Geographic Information Systems (GIS). New, integrated Integer Programming (IP) models will be built based on established SCP principles and nationally agreed marine conservation criteria. The IP models ....Integrated, interactive and systematic Marine Protected Area design for sustainability of South Australian marine environments: A GIS-based, spatial optimisation approach. This project aims to enhance MPA design in SA by integrating systematic conservation plannning (SCP), spatial optimisation and Geographic Information Systems (GIS). New, integrated Integer Programming (IP) models will be built based on established SCP principles and nationally agreed marine conservation criteria. The IP models will be tightly coupled with the GIS to create an interactive Spatial Decision Support Tool (SDSS) for systematic MPA design - the first of its kind. The SDSS will enable real-time, systematic MPA design and will provide flexible design options for a comprehensive, adequate, representative and efficient MPA system for SA.Read moreRead less