Rapid optimisation in underground mining network design. This project represents a major advance in the problem of optimising the infrastructure of underground mines and providing powerful planning tools for management. The software tools we are developing will prove important to the mining industry because of their accuracy, flexibility and generality. Not only can they be used for benchmarking in the design of specific mines, but they also provide a reliable method for testing the cost-benefi ....Rapid optimisation in underground mining network design. This project represents a major advance in the problem of optimising the infrastructure of underground mines and providing powerful planning tools for management. The software tools we are developing will prove important to the mining industry because of their accuracy, flexibility and generality. Not only can they be used for benchmarking in the design of specific mines, but they also provide a reliable method for testing the cost-benefit of emerging technologies. This is an important project for ensuring that Australia's mining industry remains efficient and internationally competitive. Given our economic dependence on mineral resources, it will also benefit Australia as a whole.Read moreRead less
Stationarity and regularity in variational analysis with applications to optimization. This project will significantly develop the theoretical basis of variational analysis and optimization. Improving the understanding of regularity and stationarity issues in optimization theory will lead to major national benefits in increasing efficiencies and reducing costs in many fields of human endeavour on a national and international level.
Integrating dynamic and optimization models for efficient pipeline system operations in an evolving water and energy market. Developing an integrated dynamical and optimisation model for a piped water distribution system will advance Australia's capacity to deploy the most recent optimisation approaches to achieve the high level of efficiency required in the delivery of water to dryland regions. The outcomes of this project will be readily transferable to other regions and indeed other water d ....Integrating dynamic and optimization models for efficient pipeline system operations in an evolving water and energy market. Developing an integrated dynamical and optimisation model for a piped water distribution system will advance Australia's capacity to deploy the most recent optimisation approaches to achieve the high level of efficiency required in the delivery of water to dryland regions. The outcomes of this project will be readily transferable to other regions and indeed other water distribution systems. This will provide capability in securing Australia's water supplies and delivery systems. There may also be associated benefits to other pipeline operators in the oil and gas industries.Read moreRead less
GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative featur ....GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative features of certain ODE's exactly (in contrast to traditional methods), leading to crucial stability improvements. Extending concepts from dynamical systems theory and traditional numerical ODEs, this project will improve, extend and systematize this new field of geometric integration.Read moreRead less
Designing minimum-cost networks that are robust and avoid obstacles. The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical ....Designing minimum-cost networks that are robust and avoid obstacles. The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical considerations such as surviving local connectivity failures and avoiding pre-existing obstacles. These are recognised as mathematically challenging problems. Current approaches employ restrictive models that do not capture the flexibility of modern infrastructure networks. This project aims to develop geometric design methods using variable ‘Steiner points’, leading to fast algorithms for optimally solving these problems.Read moreRead less
Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expect ....Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expected outcomes may have an impact in enhancing the convergence of numerical methods and facilitating the post-optimal analysis of solutions. It may also generate new tools for increasing efficiencies and cost reductions in engineering, logistics, economics, financial systems, and environmental science.Read moreRead less
Maximisation of value in underground mine access design. This project represents a major advance in the problem of optimising the mine value associated with the access infrastructure of underground mines and providing powerful planning tools for management. The usefulness to the mining industry of the methods and algorithms the project is pioneering lies in their accuracy, flexibility and generality. Not only can they be used for benchmarking value in the design of specific mines, but they can ....Maximisation of value in underground mine access design. This project represents a major advance in the problem of optimising the mine value associated with the access infrastructure of underground mines and providing powerful planning tools for management. The usefulness to the mining industry of the methods and algorithms the project is pioneering lies in their accuracy, flexibility and generality. Not only can they be used for benchmarking value in the design of specific mines, but they can also determine the profitability or viability of mines under the use of new technologies. This is an important project for ensuring that Australia's mining industry remains efficient and internationally competitive. Given Australia’s economic dependence on mineral resources, it will also benefit the country as a whole.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101056
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explain ....Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explaining the power and limitations of these methods when compared with existing approaches. Possible benefits include safer and more reliable complex engineered systems, such as the power grid or interacting autonomous vehicles, verified by methods built on those developed in the project.Read moreRead less
Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
Decision tools for underground mine development. The aim of this project is to develop innovative new strategic tools to assist senior mine management in planning underground mine operations. It will be based on modelling underground mine layouts using the theory of abstract mathematical networks. For many years, there have been well-developed methods of modelling and optimising the operation of open-cut mines. The design of the infrastructure of underground mines has a similar potential for opt ....Decision tools for underground mine development. The aim of this project is to develop innovative new strategic tools to assist senior mine management in planning underground mine operations. It will be based on modelling underground mine layouts using the theory of abstract mathematical networks. For many years, there have been well-developed methods of modelling and optimising the operation of open-cut mines. The design of the infrastructure of underground mines has a similar potential for optimisation and strategic modelling. This design optimisation will lead to huge savings in the costs of underground mines. Similar methods will be used to plan drilling programs, which are major cost items.Read moreRead less