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Anglia Ruskin University ARU Featured PhD Programmes
Anglia Ruskin University ARU Featured PhD Programmes

Novel approaches for complex nonlinear equation systems


Computer Science

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Dr C Grosan Applications accepted all year round Self-Funded PhD Students Only

About the Project

In this project we aim to investigate a novel method that works by transforming a system of equations into a multiobjective optimisation problem (MOO). The method tries to overcome the following issues: (i) deal with a large number of equations; (ii) find a large number of distinct solutions; (iii) scale to larger systems; (iv) adapt to systems from different areas. The goal is to design and develop a methodology efficient from both the computational resources required as well as the quality of solutions found aspects. It is well known that the larger the system of equations the more challenging it is for the MOO algorithms as the number of objectives in optimisation increases accordingly. Another problem is that there are solutions that are better with respect with a single objective, but much worse with respect to all the others, but they are still considered as they are nondominated (in the sense of Pareto dominance). The higher the number of equations, the larger the number of such fake nondominated solutions. In this project, we aim to investigate four ways by which a population-based algorithm can contribute to improving the results while solving large systems of equations that have a significantly large number of roots: (i) the way in which the system of equations is transformed into a multiobjective optimisation problem; (ii) the way in which an iterative or population-based algorithm is applied; (iii) the way in which the exploration of the search space is performed; the way in which the final population of potential solutions is extended.

Strong computer science and mathematics is required as well as strong programming skills.

Funding Notes

Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. See more information here: https://www.brunel.ac.uk/research/Research-degrees/Research-degree-funding. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.)
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