Martí Coma Company defends its thesis on optimization with hybrid methods

Evolutionary Algorithms (EA) are useful optimization methods for exploration of the search space, but they usually have slowness problems to exploit and converge to the minimum with accuracy. 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 thesis presents and analyze four versions of a hybrid optimization method trying to combine the virtues of Evolutionary Algorithms (EA) and gradient based algorithms, and to overcome their corresponding drawbacks. The proposed Hybrid Methods enable working with N optimization algorithms (called players), multiple objective functions and design variables, and define them differently for each player. The performance of the Hybrid Methods are compared against a gradient based method, two Genetic Algorithms (GA) and a Particle Swarm Optimization (PSO).

Tests have been conducted with mathematical benchmark problems (synthetic tests designed to specifically test optimization methods) and an engineering application with high demanding computational resources, a Synthetic Jet actuator for Active Flow Control (AFC) over a 2D Selig-Donovan 7003 (SD7003) airfoil at Reynolds number 60000 and a 14 degree angle of attack. The Active Flow control problem has been used in a single optimization problem and in a two objective optimization problem.