*Article* **A New Hybrid Optimization Method, Application to a Single Objective Active Flow Control Test Case**

**Martí Coma 1,2,\* , Navid Monshi Tousi <sup>3</sup> , Jordi Pons-Prats 1,4 , Gabriel Bugeda 1,5 and Josep M. Bergada <sup>3</sup>**


**Abstract:** Genetic Algorithms (GA) are useful optimization methods for exploration of the search space, but they usually have slowness problems to exploit and converge to the minimum. On the other hand, gradient based methods converge faster to local minimums, although are not so robust (e.g., flat areas and discontinuities can cause problems) and they lack exploration capabilities. This article presents a hybrid optimization method trying to combine the virtues of genetic and gradient based algorithms, and to overcome their corresponding drawbacks. The performance of the Hybrid Method is compared against a gradient based method and a Genetic Algorithm, both used alone. The rate of convergence of the methods is used to compare their performance. To take into account the robustness of the methods, each one has been executed more than once, with different starting points for the gradient based method and different random seeds for the Genetic Algorithm and the Hybrid Method. The performance of the different methods is tested against an optimization Active Flow Control (AFC) problem over a 2D Selig–Donovan 7003 (SD7003) airfoil at Reynolds number <sup>6</sup> <sup>×</sup> <sup>10</sup><sup>4</sup> and a 14 degree angle of attack. Five design variables are considered: jet position, jet width, momentum coefficient, forcing frequency and jet inclination angle. The objective function is defined as minus the lift coefficient (−*C<sup>l</sup>* ), so it is defined as a minimization problem. The proposed Hybrid Method enables working with *N* optimization algorithms, multiple objective functions and design variables per optimization algorithm.

**Keywords:** Hybrid Methods; Genetic Algorithms; gradient-based methods; optimization; Active Flow Control; Synthetic Jets
