Hybrid Optimization Schemes for Global Optimization: Wing Modeling of Micro-Aerial Vehicles

In this paper, we present a parallel hybrid algorithm for solving global optimization problems that is based on the coupling of a stochastic global (Simultaneous-Perturbation Stochastic Approximation, Simulated Annealing, Genetic Algorithms) and a local method (Newton-Krylov Interior-Point) via a surrogate model. There exist several algorithms for finding approximate global solutions, but our technique will further guarantee that such solutions satisfy physical bounds of the problem. First, the Simultaneous-Perturbation Stochastic Approximation (SPSA) algorithm conjectures regions where a global solution may exist. Next, some data points from the regions are selected to generate a continuously differentiable surrogate model that approximates the original function. Finally, the Newton-Krylov Interior-Point (NKIP) algorithm is applied to the surrogate model subject to bound constraints for obtaining a feasible approximate global solution. The hybrid optimization code is being applied to Stanford´s UFLO Computational Fluid Dynamics (CFD) code. This code is used by the US Army High Performance Computing Research Center (AHPCRC) to develop flapping- and twisting-wing models for Micro Aerial Vehicles (MAV), hummingbird-sized airborne vehicles that can be used for sensing and surveillance. We present some preliminary numerical results of the large-scale high performance computing (HPC) hybrid optimization C code that is being run on the Department of Defense MANA machine from Maui, Hawaii.