Evolutionary global optimization posed as a randomly perturbed martingale problem and applied to parameter recovery of chaotic oscillators

Abstract

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to a directional update term, which parallels the conventional Gateaux derivative used in a local search for the extrema of smooth cost functionals, additional layers of random perturbations referred to as 'coalescence' and 'scrambling'. A selection scheme, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method apparently provides for a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.