Optimization on industrial problems focussing on multi-player strategies

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 enables 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 6 x 10^4 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 problemEls Algoritmes Evolutius (EA) són mètodes d'optimització útils per a l'exploració de l'espai de cerca, però solen tenir problemes de lentitud per explotar-ne el mínim i convergir amb precisió. D'altra banda, els mètodes basats en gradients convergeixen més ràpidament als mínims locals, encara que no són tan robusts (per exemple, les àrees planes i les discontinuïtats poden causar problemes) i no tenen capacitats d'exploració. Aquesta tesi presenta i analitza quatre versions d'un mètode d'optimització híbrid que intenta combinar les virtuts dels Algoritmes Evolutius (EA) i els algoritmes basats en gradients, i superar-ne els inconvenients corresponents. Els Mètodes Híbrids proposats permeten treballar amb N algoritmes d'optimització (anomenats jugadors), múltiples funcions objectiu i variables de disseny, i definir-les de manera diferent per a cada jugador. El rendiment dels mètodes híbrids es compara amb un mètode basat en gradient, dos Algoritmes Genètics (GA) i un mètode d'optimització d'eixam de partícules (PSO). S'han fet proves amb problemes matemàtics de referència (proves sintètiques dissenyades per provar específicament mètodes d'optimització) i una aplicació d'enginyeria amb recursos computacionals molt exigents, un actuador de jet sintètic per a control de flux actiu (AFC) sobre un perfil aerodinàmic 2D Selig -Donovan 7003 (SD7003) al número de Reynolds 6 x 104 i un angle d'atac de 14 graus. El problema de control de flux actiu s'ha utilitzat en un problema d'optimització monoobjectiu i en un problema d'optimització de dos objectius.Postprint (published version

An adjoint for likelihood maximization

The process of likelihood maximization can be found in many different areas of computational modelling. However, the construction of such models via likelihood maximization requires the solution of a difficult multi-modal optimization problem involving an expensive O(n3) factorization. The optimization techniques used to solve this problem may require many such factorizations and can result in a significant bottle-neck. This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic differentiation. This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be utilised within a simple local search or within a hybrid global optimization to accelerate convergence and therefore reduce the cost of the likelihood optimization

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners