Local Optima Networks and Uncertainty Quantification: Data Analytics for Computational Biology Models

Abstract

Evolutionary Algorithms (EAs) are a class of optimisation algorithm inspired by natural selection and Darwin’s theory of evolution that are well-suited to handling complex and nonlinear optimisation problems. By mimicking the process of natural selection, EAs iteratively evolve a population of candidate solutions using variation mechanisms. This allows them to explore a wide range of solution space and find high-quality solutions that may be difficult to discover using traditional methods. EAs have numerous applications across various fields, including but not limited to engineering, finance, and bioinformatics. To successfully determine the most appropriate EA for a particular problem, it is essential to comprehend the interplay between variation mechanisms of algorithms and problems. Fitness landscape analysis is a tool in evolutionary computation, which enables the study of the interactions between solutions, their connectivity and their fitness function. Through the analysis of the fitness landscape, researchers can attain insights into the complexity of the optimisation problem, the efficacy of various search algorithms and the impact of diverse parameter values on the algorithm’s performance. A local optima network (LON) is a representation of a landscape in a compressed form. LONs are mainly graphs, in which the nodes represent local optima and the edges represent the transitions between them. In this thesis, the application domain is the circadian clock within the field of systems biology. The optimisation task is the identification of optimal parameters for the mathematical modelling of exemplary circadian clock models. This thesis contributes to the analysis of continuous fitness landscapes by utilising LONs. The research takes a pioneering step in understanding the behaviour of LONs induced by population-based algorithms, which is an aspect of evolution-based based optimisation heuristics that has not been explored in the previous LON research. The thesis highlights the importance of landscape analysis to advance our understanding of circadian clocks. To this end, population-based algorithms are utilised to optimise mathematical models of exemplary clock systems and landscape analysis is subsequently conducted. The results provide further insight into the underlying mechanisms and dynamics of circadian clocks and evaluates the suitability of specific mathematical models for these systems. Additionally, the thesis explores the feasibility of using surrogate machine learning models for landscape analysis which could provide a more cost-effective alternative to using the actual fitness function. Specifically, the research employs an uncertainty quantification model to conduct landscape analysis and leverages the uncertainty to assess the model’s suitability. The results presented indicate that landscape analysis is useful to understand the behaviour of optimisation problems when utilising population-based algorithms. The application of this approach to the mathematical modelling of the circadian clock provides promising insights into the problem space of circadian clocks. Furthermore, Gaussian Processes are proven to be useful for surrogate-based fitness analysis of optimisation problems using LONs.