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Global optimisation in Hilbert spaces using the survival of the fittest algorithm

•We present a bio-inspired global optimisation method, applicable in Hilbert spaces.•The method is based on eco-evolutionary mechanism of survival of the fittest.•The method allows a proof of convergence for generic functionals.•The method is applied to the problem of diel vertical migration of zoop...

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Published in:Communications in nonlinear science & numerical simulation 2021-12, Vol.103, p.106007, Article 106007
Main Authors: Morozov, Andrew Yu, Kuzenkov, Oleg A., Sandhu, Simran K.
Format: Article
Language:English
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Summary:•We present a bio-inspired global optimisation method, applicable in Hilbert spaces.•The method is based on eco-evolutionary mechanism of survival of the fittest.•The method allows a proof of convergence for generic functionals.•The method is applied to the problem of diel vertical migration of zooplankton.•The method shows better performance as compared to other bio-inspired techniques. Global optimisation problems in high-dimensional and infinite-dimensional spaces arise in various real-world applications such as engineering, economics and finance, geophysics, biology, machine learning, optimal control, etc. Among stochastic approaches to global optimisation, biology-inspired methods are currently very popular in the literature. Bio-inspired approaches imitate natural ecological and evolutionary processes and are reported to be efficient in a large number of practical study cases. However, many bio-inspired methods can possess some vital drawbacks. For example, due to their semi-empirical nature, convergence to the globally optimal solution cannot always be guaranteed. Another major obstacle is that the existing methods often struggle with higher dimensionality of the space of parameters, which results in a slow convergence. Moreover, it is often difficult to adjust the dimensionality of the space of parameters in the corresponding computer code for a practical realisation of the optimisation method. Here, we present a bio-inspired global stochastic optimisation method applicable in Hilbert function spaces. The proposed method is an evolutionary algorithm inspired by the Darwin’s famous idea of survival of the fittest and is, therefore, referred to as the ‘Survival of the Fittest Algorithm’ (SoFA). Mathematically, the convergence of SoFA is a consequence of the fundamental property of localisation of probabilistic measure in a Hilbert space and we rigorously prove the convergence of the introduced algorithm for a generic class of functionals. The approach is simple in terms of practical coding. As an insightful, real-world problem, we apply our method to find the globally optimal trajectory for the daily vertical migration of zooplankton in the ocean and lakes, this phenomenon is considered to be the largest synchronised movement of biomass on Earth. We maximise fitness in a function space derived from a von-Foerster stage-structured population model with biologically realistic parameters. We show that for problems of fitness maximisation in high-dimensi
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2021.106007