Study of genetic algorithm for optimization problems

Dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáThis work consists in to explore the Genetic Algorithms to solve non-linear optimization problems. The aim of this work is to study and develop strategies in order to improve the performance of the Genetic Algorithm that can be applied to solve several optimization problems, as time schedule, costs minimization, among others. For this, the behavior of a traditional Genetic Algorithm was observed and the acquired information was used to propose variations of this algorithm. Thereby, a new approach for the selection operator was proposed, considering the abilities of population individuals to generate offspring. In addition, a Genetic Algorithm that uses dynamic operators rates, controlled by the amplitude and the standard deviation of the population, is also proposed. Together with this algorithm, a new stopping criterion is also proposed. This criterion uses population and the problem information to identify the stopping point. The strategies proposed are validated by twelve benchmark optimization functions, defined in the literature for testing optimization algorithms. The dynamic rate algorithm results were compared with a fixed rate Genetic Algorithm and with the defaultMatlab Genetic Algorithm, and in both cases, the proposed algorithm presented excellent results, for all considered functions, which demonstrates the robustness of the algorithm for solving several optimization problems.Este trabalho consiste em explorar o Algoritmo Genético para resolução de problemas de otimização não-linear. O objetivo deste trabalho é estudar e desenvolver estratégias para melhorar o desempenho do Algoritmo Genético que possa ser aplicado para resolução de problemas de otimização variados, como escalonamento de horários, minimização de custos, entre outros. Para isso, foi observado o comportamento usual do Algoritmo Genético e as informações adquiridas foram usadas para propor variações deste algoritmo. Assim, uma nova abordagem para o operador de seleção é proposta, considerando a habilidade dos indivíduos da população em gerar descendentes. Além disso, também é proposto um Algoritmo Genético que utiliza taxas dinâmicas nos operadores, controladas pela amplitude e desvio padrão da população. Juntamente com este algoritmo, um novo critério de paragem também é proposto. Este critério utiliza informações da população e do problema de otimização para determinar o local de paragem. As estratégias propostas são validadas por doze funções de teste, definidas na literatura para teste de algoritmos de otimização. Os resultados do algoritmo de taxas dinâmicas foram comparados com um Algoritmo Genético de taxas fixas e com o Algoritmo Genético padrão disponível no Matlab, e em ambos os casos o algoritmo proposto apresentou excelentes resultados, para todas as funções consideradas, o que demonstra a robustez do método para resolução de problemas de otimização variados

Optimisation of a weightless neural network using particle swarms

Among numerous pattern recognition methods the neural network approach has been the subject of much research due to its ability to learn from a given collection of representative examples. This thesis is concerned with the design of weightless neural networks, which decompose a given pattern into several sets of n points, termed n-tuples. Considerable research has shown that by optimising the input connection mapping of such n-tuple networks classification performance can be improved significantly. In this thesis the application of a population-based stochastic optimisation technique, known as Particle Swarm Optimisation (PSO), to the optimisation of the connectivity pattern of such “n-tuple” classifiers is explored. The research was aimed at improving the discriminating power of the classifier in recognising handwritten characters by exploiting more efficient learning strategies. The proposed "learning" scheme searches for ‘good’ input connections of the n-tuples in the solution space and shrinks the search area step by step. It refines its search by attracting the particles to positions with good solutions in an iterative manner. Every iteration the performance or fitness of each input connection is evaluated, so a reward and punishment based fitness function was modelled for the task. The original PSO was refined by combining it with other bio-inspired approaches like Self-Organized Criticality and Nearest Neighbour Interactions. The hybrid algorithms were adapted for the n-tuple system and the performance was measured in selecting better connectivity patterns. The Genetic Algorithm (GA) has been shown to be accomplishing the same goals as the PSO, so the performances and convergence properties of the GA were compared against the PSO to optimise input connections. Experiments were conducted to evaluate the proposed methods by applying the trained classifiers to recognise handprinted digits from a widely used database. Results revealed the superiority of the particle swarm optimised training for the n-tuples over other algorithms including the GA. Low particle velocity in PSO was favourable for exploring more areas in the solution space and resulted in better recognition rates. Use of hybridisation was helpful and one of the versions of the hybrid PSO was found to be the best performing algorithm in finding the optimum set of input maps for the n-tuple network

Inverse Design of Whispering-Gallery Nanolasers with Tailored Beam Shape and Polarisation

The aim of this thesis is to design the shape of nanocavities to tailor their radiated beam in terms of intensity and polarisation distribution, and emission direction. The radiative processes behind light amplification are revised, leading to the concept of laser device as a system composed of a gain medium, an optical cavity and a pump method. Next, the optoelectronic properties of semiconductor quantum wells and modal properties of whispering-gallery mode cavities are described, justifying why they were chosen as gain medium and optical cavity for the nanolasers studied in this thesis. We engineered the cavity shape of the nanolasers with an automated inverse design method based on topology optimisation, which demonstrated to yield photonic devices with novel geometries that outperform those designed by conventional means, such as parametric sweeps, based on the intuition of the user. We prove the generality of this inverse method by designing and experimentally verifying nanolasers that produce three different beams: a gaussian-like beam with linear polarisation, and two doughnut beams with azimuthal and radial polarisation. The nanolasers are fabricated via electron-beam lithography and etching processes. The output laser beams are characterised by Fourier microscopy and k-space polarimetry, to analyse their intensity and polarisation angular distribution, and yield overlaps of up to 92%, 96% and 85% with the target modes for the azimuthal, radial and linearly polarised cases, respectively. The lasing performance of the nanolasers is studied by fitting the input power output power curve to a laser model and is compared to the literature. More power is collected from the inverse-designed nanolasers thanks to their axial emission, compared to conventional circular microdisc lasers. In summary, in this thesis we demonstrate the validity of the inverse design method in the engineering of ultra-compact lasers with tailored beams.Engineering and Physical Sciences Research Council (EPSRC