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Global optimisation problems in high-dimensional and infinite dimensionalspaces arise in various real-world applications such as engineering, economics,geophysics, biology, machine learning, optimal control, etc. Among stochasticapproaches to global optimisation, biology-inspired methods are currentlypopular in the literature, imitating natural ecological and evolutionaryprocesses and reported to be efficient in many practical study cases. However,many of bio-inspired methods have some vital drawbacks. Due to theirsemi-empirical nature, convergence to the globally optimal solution cannotalways be guaranteed and struggles with the high dimensionality of space,showing a slow convergence. Here, we present a bio-inspired global stochasticoptimisation method, applicable in Hilbert function spaces, inspired byDarwin's' famous idea of the survival of the fittest, therefore, referred to asthe `Survival of the Fittest Algorithm' (SoFA). Mathematically, the convergenceof SoFA is a consequence of a fundamental property of localisation ofprobabilistic measure in a Hilbert space, we rigorously prove the convergenceof the introduced algorithm for a generic class of functionals. As aninsightful real-world problem, we apply SoFA to find globally optimaltrajectories for daily vertical migrations of zooplankton in ocean and lakes,considered to be the largest synchronised movement of biomass on Earth. Wemaximise fitness in a function space derived from a von-Foersterstage-structured population model with biologically realistic parameters. Weshow that for problems of fitness maximisation in high-dimensional spaces, SoFAperforms better than some other stochastic global optimisation algorithms. Wehighlight the links between the new optimisation algorithm and naturalselection process in ecosystems occurring within a population via gradualexclusion of competitive con-specific strains.

Global Optimisation in Hilbert Spaces using the Survival of the Fittest Algorithm