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Novel approaches for complex nonlinear equation systems

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 are required as well as strong programming skills.

How to apply

If you are interested in applying for the above PhD topic please follow the steps below:

  1. Contact the supervisor by email or phone to discuss your interest and find out if you woold be suitable. Supervisor details can be found on this topic page. The supervisor will guide you in developing the topic-specific research proposal, which will form part of your application.
  2. Click on the 'Apply here' button on this page and you will be taken to the relevant PhD course page, where you can apply using an online application.
  3. Complete the online application indicating your selected supervisor and include the research proposal for the topic you have selected.

Good luck!

This is a self funded topic

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. The UK Government is also offering Doctoral Student Loans for eligible 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%.

Meet the Supervisor(s)

Crina Grosan - I am a Senior Lecturer in the Department of Computer Science at Brunel University. Prior to joining Brunel, I was an academic staff member at Babes-Bolyai University Cluj-Napoca, one of the top universities in Romania. My research interests span the areas of machine learning, optimisation, and multi-relational graphs. They include both theoretical and algorithmic development as well as applications for particular classes of problems such as classification, clustering, prediction, estimation, decision-making, pattern finding, data mining, very large systems of nonlinear equations and large-scale optimisation. 

Related Research Group(s)

Intelligent Data Analysis

Intelligent Data Analysis - Concerned with effective analysis of data involving artificial intelligence, dynamic systems, image and signal processing, optimisation, pattern recognition, statistics and visualisation.