A parallel hybrid optimization algorithm for robust airfoil design

Abstract

We present a hybrid algorithm that consists of a population based, stochastic, zero-order optimization algorithm and a gradient based optimization algorithm for robust airfoil design optimization. The gradient based optimization algorithm used in the hybrid is to repair solutions (to satisfy the equality constraints) for the problem in contrast to other hybrids where it is usually used to improve the final solution obtained by the stochastic algorithm. Approaches involving equality constraints are known to pose difficulties to existing stochastic methods. The inequality constraints in the present stochastic algorithm are handled via the concept of non-dominance, instead of scaling and aggregating the constraint violations. To demonstrate the behavior of the current proposed hybrid algorithm, we present results of two single objective and two multi-objective airfoil design optimization problems. For comparison, a result of an airfoil design using aggregation is included to highlight some of the limitations of aggregation based formulations used in robust design. To improve upon the computational cost for such computationally expensive problems, we have implemented the algorithm to run on multiple processors based on master-slave architecture.