Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this ear ....Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this early stage no algorithm capable of tracking many targets has emerged from this framework. We are confident that efficient algorithms can be developed by exploiting the insights and mathematical tools of stochastic geometryRead moreRead less
Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by ....Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by the role of fast, secure and reliable communications in modern information and communication technology. Expected outcomes include new efficient algorithms and commercial modules available for symbolic computation systems with applications in telecommunications industry.
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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
Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowl ....Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowledge in modelling interdependencies of decision criteria using recent advances in the theory of capacities. The expected outcomes are sophisticated but tractable models in which mutual dependencies of decision rules and criteria are treated explicitly and can be thoroughly evaluated. Read moreRead less
HYBRID METHODS FOR SOLVING LARGE-SCALE OPTIMISATION PROBLEMS. Mathematical modelling and optimisation plays a crucial role in the advancement of modern business, science and technology. A significant benefit of this project is the development of a range of powerful computational tools for improving the productivity of Australian industry, including: agriculture; communications; defence; manufacturing; mining and petroleum; transport and logistics. These tools will be built upon advances in the f ....HYBRID METHODS FOR SOLVING LARGE-SCALE OPTIMISATION PROBLEMS. Mathematical modelling and optimisation plays a crucial role in the advancement of modern business, science and technology. A significant benefit of this project is the development of a range of powerful computational tools for improving the productivity of Australian industry, including: agriculture; communications; defence; manufacturing; mining and petroleum; transport and logistics. These tools will be built upon advances in the fundamental theory developed by the research team. The resulting high quality publications and associated algorithms will greatly enhance Australia's international scientific reputation and provide Australian industry with new cutting-edge optimisation technology.Read moreRead less
Optimal Control Computation and Analysis of Switched Systems with State and Control Constraints. DC/DC converters are widely used in power supply systems and hybrid power systems generate cleaner energy. Achieving optimum performance in these applications has high commercial and environmental impacts. New optimal control problems for such practical problems will be formulated and new unified optimization theory and methods for these optimal control problems will be obtained. The outcomes will en ....Optimal Control Computation and Analysis of Switched Systems with State and Control Constraints. DC/DC converters are widely used in power supply systems and hybrid power systems generate cleaner energy. Achieving optimum performance in these applications has high commercial and environmental impacts. New optimal control problems for such practical problems will be formulated and new unified optimization theory and methods for these optimal control problems will be obtained. The outcomes will enhance Australia's reputation in this cutting edge research, and contribute to achieving optimal performance of high commercial and environmental value applications. It will also facilitate international collaboration, and provide an excellent opportunity for research training.Read moreRead less
Robust methods for hard optimization problems. Highly advanced industrial and information-based societies depend on complex systems that underpin their infrastructure and technologies. Mathematical modelling and optimization techniques are most frequently deployed for the development and refinement of these systems. This project focuses on an important class of difficult optimization problems that arise in many applications. A significant benefit of this project is the development of a number of ....Robust methods for hard optimization problems. Highly advanced industrial and information-based societies depend on complex systems that underpin their infrastructure and technologies. Mathematical modelling and optimization techniques are most frequently deployed for the development and refinement of these systems. This project focuses on an important class of difficult optimization problems that arise in many applications. A significant benefit of this project is the development of a number of robust methods for these hard optimization problems. These methods will be built upon advances in the fundamental theory developed by the research team. The resulting high quality publications and associated algorithms will greatly enhance Australia's international scientific reputation.Read moreRead less
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
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an inte ....Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an international collaboration which will improve Australia's ability to participate effectively in international research and innovation and to produce globally competitive mathematical technologiesRead moreRead less