  Global optimisation problems in high-dimensional and infinite dimensional
spaces arise in various real-world applications such as engineering, economics,
geophysics, biology, machine learning, optimal control, etc. Among stochastic
approaches to global optimisation, biology-inspired methods are currently
popular in the literature, imitating natural ecological and evolutionary
processes and reported to be efficient in many practical study cases. However,
many of bio-inspired methods have some vital drawbacks. Due to their
semi-empirical nature, convergence to the globally optimal solution cannot
always be guaranteed and struggles with the high dimensionality of space,
showing a slow convergence. Here, we present a bio-inspired global stochastic
optimisation method, applicable in Hilbert function spaces, inspired by
Darwin's' famous idea of the survival of the fittest, therefore, referred to as
the `Survival of the Fittest Algorithm' (SoFA). Mathematically, the convergence
of SoFA is a consequence of a fundamental property of localisation of
probabilistic measure in a Hilbert space, we rigorously prove the convergence
of the introduced algorithm for a generic class of functionals. As an
insightful real-world problem, we apply SoFA to find globally optimal
trajectories for daily vertical migrations of zooplankton in ocean and lakes,
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-dimensional spaces, SoFA
performs better than some other stochastic global optimisation algorithms. We
highlight the links between the new optimisation algorithm and natural
selection process in ecosystems occurring within a population via gradual
exclusion of competitive con-specific strains.
