Yes / An efficient multi-object evolutionary algorithms are proposed for optimizing frequency characteristics of antennas based on an interfacing created by Matlab environment. This interface makes a link with CST Microwave studio where the electromagnetic investigation of antenna is realized. Very small, compact printed monopole antenna is optimized for ultra- wideband (UWB) applications. Two objective functions are introduced; the first function intends to increase the impedance bandwidth, and second function to tune the antenna to resonate at a particular frequency. The two functions operate in the range of 3.2 to 10.6 GHz and depend on the level of return loss. The computed results provide a set of proper design for UWB system in which the bandwidth achieved is 7.5GHz at the resonance frequency 4.48GHz, including relatively stable gain and radiation patterns across the operating band.

Over the last two decades, chip design has been conducted at the register transfer (RT) Level using Hardware Descriptive Languages (HDL), such as VHDL and Verilog. The modeling at the behavioral level not only allows for better representation and understanding of the design, but also allows for encapsulation of the sub-modules as well, thus increasing productivity. Despite these benefits, validating a RTL design is not necessarily easier. Today, design validation is considered one of the most time and resource consuming aspects of hardware design. The high costs associated with late detection of bugs can be enormous. Together with stringent time to market factors, the need to guarantee the correct functionality of the design is more critical than ever. The work done in this thesis tackles the problem of RTL design validation and presents new frameworks for functional test generation. We use branch coverage as our metric to evaluate the quality of the generated test stimuli. The initial effort for test generation utilized simulation based techniques because of their scalability with design size and ease of use. However, simulation based methods work on input spaces rather than the DUT's state space and often fail to traverse very narrow search paths in large input spaces. To encounter this problem and enhance the ability of test generation framework, in the following work in this thesis, certain design semantics are statically extracted and recurrence relationships between different variables are mined. Information such as relations among variables and loops can be extremely valuable from test generation point of view. The simulation based method is hybridized with Z3 based symbolic backward execution engine with feedback among different stages. The hybridized method performs loop abstraction and is able to traverse narrow design paths without performing costly circuit analysis or explicit loop unrolling. Also structural and functional unreachable branches are identified during the process of test generation. Experimental results show that the proposed techniques are able to achieve high branch coverage on several ITC'99 benchmark circuits and their modified variants, with significant speed up and reduction in the sequence length. / Master of Science

A dual satellite system in a Low Earth Orbit, LEO, would be beneficial to study the electromagnetic occurrences in the magnetosphere and their contributions to the development of the aurora events in the Earth's lower atmosphere. An orbit configuration is sought that would increase the total time that both satellites are inside the auroral oval. Some additional objectives include minimizing the total fuel cost and the average angle between the satellites' radius vectors. This orbit configuration is developed using a series of instantaneous burns applied at each satellite's perigee. An analysis of the optimal solutions generated by a Particle Swarm Optimization method is completed using a cost function with different weights for the time, fuel, and angle terms. Three different scenarios are presented: a single burn case, a double burn case, and a four burn case. The results are calculated using two different orbital mechanics models: an unperturbed two-body simulation and a two-body simulation with added Earth's equatorial bulge effects. It is shown that the added perturbation reduces the total event time in the optimal solutions generated. Specific weights for the cost function are recommended for further studies. / Master of Science

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T17:29:03Z No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:44:17Z (GMT) No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Made available in DSpace on 2018-01-23T13:44:17Z (GMT). No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) Previous issue date: 2017-09-15 / O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática. / The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.

Tato dizertační práce se zabývá vývojem optimalizačního nástroje, který je založen na metodě Particle swarm optimization a je poté aplikován na dva typy oběžných kol radiálních čerpadel.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. For the CPGA we show that a standard CPGA using blend crossover and standard mutation, is rotationally variant. To construct a rotationally invariant CPGA it is possible to modify the crossover operation to be rotationally invariant. This however, again results in loss of diversity. We introduce diversity in two ways: firstly using a modified mutation scheme, and secondly, following the same approach as in the PSO and the DE, by adding a self-scaling random vector to the offspring vector. This formulation is strictly invariant, albeit still in a stochastic sense only. Numerical results are presented for the variant and invariant versions of the respective algorithms. The intention of this study is not the contribution of yet another competitive and/or superior population based algorithm, but rather to present formulations that are both diverse and invariant, in the hope that this will stimulate additional future contributions, since rotational invariance in general is a desirable, salient feature for an optimization algorithm. / AFRIKAANSE OPSOMMING: In hierdie studie bestudeer ons die gebrek aan rotasionele invariansie van drie verskillende populasiegebaseerde optimeringsmetodes, met name die partikel-swerm optimerings (PSO) algoritme, die differensi¨ele evolusie (DE) algoritme en die kontinue-parameter genetiese algoritme (KPGA). Ons stel dan rotasionele invariante weergawes van hierdie algoritmes voor. Ons beginmet die PSO. Die sogenaamde klassieke PSO algoritme is bekend dat dit variant is onder rotasie, terwyl die lineˆere PSO rotasioneel invariant is. Hierdie invariansie lei tot ’n gebrek aan diversiteit in die algoritme, wat beteken dat die lineˆere PSO minder goed presteer as die klassieke PSO. Die voorheen voorgestelde sogenaamde diverse rotasionele invariante (DRI) PSO is ’n algoritme wat beoog om beide diversiteit en invariansie te kombineer. Hierdie algoritme is slegs rotasioneel invariant in ’n stogastiese sin. Boonop is die formulering afhanklik van ’n willekeurige rotasie matriks S, maar invariansie is net gewaarborg vir ’klein’ rotasies in S. In hierdie studie stel ons ’n formulering voor wat divers is en streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. In hierdie formulering, vertrek ons met die lineˆere PSO, en voeg dan ’n self-skalerende ewekansige vektor met ’n standaard normaalverdeling by, wat eenvormig van die oppervlakte van ’n n-dimensionele eenheid sfeer geneem word. Vir die DE algoritme toon ons aan dat die klassieke DE/rand/1/bin algoritme, wat gebruik maak van konstante mutasie en standaard kruising rotasioneel variant is. Ons bestudeer dan ’n voorheen voorgestelde rotasionele invarianteDE formulering waarin die kruisingsoperasie plaasvind in ’n ortogonale basis wat gekonstrueer wordmet behulp van die Gramm-Schmidt ortogonalieseringsproses. Verder stel ons dan twee nuwe formulerings voor deur eerstens ’n baie eenvoudige rotasionele invariante formulering te oorweeg, wat konstante mutasie en volledige rekenkundige kruising gebruik. Hierdie elementˆere formulering onderpresteer as gevolg van die afwesigheid van diversiteit. Ons voeg dan diversiteit by die formulering toe, deur gebruik te maak van twee afsonderlike strategie ¨e. Die eerste verander die kruisings stap deur die rigting van die lineˆere kombinasie tussen die teiken vektor en die mutasie vektor te perturbeer. Hierdie formulering is slegs invariant in ’n stogastiese sin. In die ander formulering, soos met die nuwe rotasionele invariante PSO, voeg ons bloot ’n self-skalerende ewekansige vektor by die onveranderde volledige rekenkundige kruisingsvektor. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Vir die KPGA wys ons dat die standaard KPGA wat gemengde kruising en standaard mutasies gebruik, rotasioneel variant is. Om ’n rotasionele invariante KPGA te konstrueer is dit moontlik om die kruisingsoperasie aan te pas. Dit veroorsaak weereens ’n verlies aan diversiteit. Ons maak die algoritmes divers op twee verskillende maniere: eerstens deur gebruik te maak van ’n gewysigde mutasie skema, en tweedens deur die selfde aanslag te gebruik as in die PSO en die DE, deur ’n self-skalerende ewekansige vektor by die nageslag vektor te voeg. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Numeriese resultate word vir die variante en invariante weergawe van die onderskeie algoritmes verskaf. Die doel van hierdie studie is nie die bydrae van bloot nog ’n kompeterend en/of beter populasiegebaseerde optimeringsmetode nie, maar eerder om formulerings voor te lê wat beide divers en invariant is, met die hoop dat dit in die toekoms bykomende bydraes sal stimuleer, omdat rotasionele invariansie in die algemeen ’n aantreklike, belangrike kenmerk is vir ’n optimerings algoritme.

In the literature, various Mobile Ad hoc NETwork (MANET) routing protocols proposed. Each performs the best under specific context conditions, for example under high mobility or less volatile topologies. In existing MANET, the degradation in the routing protocol performance is always associated with changes in the network context. To date, no MANET routing protocol is able to produce optimal performance under all possible conditions. The core aim of this thesis is to solve the routing problem in mobile Ad hoc networks by introducing an optimum system that is in charge of the selection of the running routing protocol at all times, the system proposed in this thesis aims to address the degradation mentioned above. This optimisation system is a novel approach that can cope with the network performance’s degradation problem by switching to other routing protocol. The optimisation system proposed for MANET in this thesis adaptively selects the best routing protocol using an Artificial Intelligence mechanism according to the network context. In this thesis, MANET modelling helps in understanding the network performance through different contexts, as well as the models’ support to the optimisation system. Therefore, one of the main contributions of this thesis is the utilisation and comparison of various modelling techniques to create representative MANET performance models. Moreover, the proposed system uses an optimisation method to select the optimal communication routing protocol for the network context. Therefore, to build the proposed system, different optimisation techniques were utilised and compared to identify the best optimisation technique for the MANET intelligent system, which is also an important contribution of this thesis. The parameters selected to describe the network context were the network size and average mobility. The proposed system then functions by varying the routing mechanism with the time to keep the network performance at the best level. The selected protocol has been shown to produce a combination of: higher throughput, lower delay, fewer retransmission attempts, less data drop, and lower load, and was thus chosen on this basis. Validation test results indicate that the identified protocol can achieve both a better network performance quality than other routing protocols and a minimum cost function of 4.4%. The Ad hoc On Demand Distance Vector (AODV) protocol comes in second with a cost minimisation function of 27.5%, and the Optimised Link State Routing (OLSR) algorithm comes in third with a cost minimisation function of 29.8%. Finally, The Dynamic Source Routing (DSR) algorithm comes in last with a cost minimisation function of 38.3%.

La résolution satisfaisante d'un problème d'optimisation difficile, qui comporte un grand nombre de solutions sous-optimales, justifie souvent le recours à une métaheuristique puissante. La majorité des algorithmes utilisés pour résoudre ces problèmes d'optimisation sont les métaheuristiques à population. Parmi celles-ci, nous intéressons à l'Optimisation par Essaim Particulaire (OEP, ou PSO en anglais) qui est apparue en 1995. PSO s'inspire de la dynamique d'animaux se déplaçant en groupes compacts (essaims d'abeilles, vols groupés d'oiseaux, bancs de poissons). Les particules d'un même essaim communiquent entre elles tout au long de la recherche pour construire une solution au problème posé, et ce en s'appuyant sur leur expérience collective. L'algorithme PSO, qui est simple à comprendre, à programmer et à utiliser, se révèle particulièrement efficace pour les problèmes d'optimisation à variables continues. Cependant, comme toutes les métaheuristiques, PSO possède des inconvénients, qui rebutent encore certains utilisateurs. Le problème de convergence prématurée, qui peut conduire les algorithmes de ce type à stagner dans un optimum local, est un de ces inconvénients. L'objectif de cette thèse est de proposer des mécanismes, incorporables à PSO, qui permettent de remédier à cet inconvénient et d'améliorer les performances et l'efficacité de PSO. Nous proposons dans cette thèse deux algorithmes, nommés PSO-2S et DEPSO-2S, pour remédier au problème de la convergence prématurée. Ces algorithmes utilisent des idées innovantes et se caractérisent par de nouvelles stratégies d'initialisation dans plusieurs zones, afin d'assurer une bonne couverture de l'espace de recherche par les particules. Toujours dans le cadre de l'amélioration de PSO, nous avons élaboré une nouvelle topologie de voisinage, nommée Dcluster, qui organise le réseau de communication entre les particules. Les résultats obtenus sur un jeu de fonctions de test montrent l'efficacité des stratégies mises en oeuvre par les différents algorithmes proposés. Enfin, PSO-2S est appliqué à des problèmes pratiques, en segmentation d'images et en électronique / The successful resolution of a difficult optimization problem, comprising a large number of sub optimal solutions, often justifies the use of powerful metaheuristics. A wide range of algorithms used to solve these combinatorial problems belong to the class of population metaheuristics. Among them, Particle Swarm Optimization (PSO), appeared in 1995, is inspired by the movement of individuals in a swarm, like a bee swarm, a bird flock or a fish school. The particles of the same swarm communicate with each other to build a solution to the given problem. This is done by relying on their collective experience. This algorithm, which is easy to understand and implement, is particularly effective for optimization problems with continuous variables. However, like several metaheuristics, PSO shows some drawbacks that make some users avoid it. The premature convergence problem, where the algorithm converges to some local optima and does not progress anymore in order to find better solutions, is one of them. This thesis aims at proposing alternative methods, that can be incorporated in PSO to overcome these problems, and to improve the performance and the efficiency of PSO. We propose two algorithms, called PSO-2S and DEPSO-2S, to cope with the premature convergence problem. Both algorithms use innovative ideas and are characterized by new initialization strategies in several areas to ensure good coverage of the search space by particles. To improve the PSO algorithm, we have also developed a new neighborhood topology, called Dcluster, which can be seen as the communication network between the particles. The obtained experimental results for some benchmark cases show the effectiveness of the strategies implemented in the proposed algorithms. Finally, PSO-2S is applied to real world problems in both image segmentation and electronics fields

Dans l'état actuel des connaissances, il est impossible de poser correctement toute la physique permettant de modéliser les hydrosystèmes dans leur ensemble, notamment à cause de la dynamique très contrastée des différents compartiments. Les modèles systémiques simplifient la représentation des hydrosystèmes en ne considérant que leurs flux d’échange. L’objet de ce travail est de proposer un outil de modélisation systémique fournissant des informations sur le fonctionnement physique des hydrosystèmes, tout en étant simple et parcimonieux. Ce modèle nommé MASH (pour Modélisation des Hydrosystèmes par Approche Systémique) est basé sur l’utilisation de fonctions de transfert paramétriques choisies en fonction de leur faible paramétrisation, leur caractère général et leur interprétation physique. Il est versatile, dans le sens que son architecture est modulable et que le nombre d’entrées, le nombre de fonctions de transfert en série et le type de fonctions de transfert utilisé est laissée à la discrétion de l’utilisateur. Ce modèle est inversé en utilisant de récentes avancées en apprentissage automatique grâce à une famille d’heuristiques basée sur l’intelligence en essaim nommé « optimisation par essaim de particule » (ou PSO pour « Particle Swarm Optimization »). Le modèle et ses algorithmes d’inversion sont testés sur un cas d’école synthétique, puis sur un cas d’application réel. / In the light of current knowledge, hydrosystems cannot be modelled as a whole since underlying physical principles are not totally understood. Systemic models simplify hydrosystem representation by considering only water flows. The aim of this work is to provide a systemic modelling tool giving information about hydrosystem physical behavior while being simple and parsimonious. This model, called HMSA (for Hydrosystem Modelling with a Systemic Approach) is based on parametric transfer functions chose for their low parametrization, their general nature and their physical interpretation. It is versatile, since its architecture is modular, and the user can choose the number of inputs, outputs and transfer functions. Inversion is done with recent machine learning heuristic family, based on swarm intelligence called PSO (Particle Swarm Optimization). The model and its inversion algorithms are tested first with a textbook case, and then with a real-world case.

presente trabalho consolida um estudo para o planejamento de trajetória livre de colisão para um robô pneumático com 5 graus de liberdade aplicando três algoritmos metaheurísticos: algoritmos metaheurísticos por vagalumes, algoritmos metaheurísticos por enxames de partículas e algoritmos genéticos. No que se refere à aplicação de algoritmos metaheurísticos ao estudo de planejamento de trajetória de robôs manipuladores na presença de obstáculos, existem diferentes tipos de técnicas para evitar colisões que consideram os efeitos cinemáticos e dinâmicos na obtenção de trajetórias com o menor tempo, torque, etc. Neste estudo, são propostas contribuições à aplicação dessas técnicas especificamente a robôs manipuladores pneumáticos, sobretudo, no que diz respeito às características específicas dos servoposicionadores pneumáticos, como, por exemplo, a modelagem do atrito desses sistemas, o cálculo da massa equivalente, etc. A metodologia utilizada é definida em duas etapas. A primeira delas consiste na obtenção de pontos intermediários, adquiridos considerando a menor distância entre os mesmos e o ponto final, gerados considerando a presença de obstáculos (cilindros, cubos e esferas) Esses obstáculos são mapeados em regiões de colisão, que constituem restrições para o problema de otimização. A segunda etapa baseia-se no estudo do planejamento de trajetórias: aplicam-se b-splines de 5º e 7º grau na interpolação dos pontos intermediários, com vistas à obtenção de trajetórias que considerem, de um lado, a menor força dos atuadores associada à dinâmica do manipulador em estudo e, de outro, restrições cinemáticas e dinâmicas, determinadas por meio das características operacionais dos servoposicionadores pneumáticos. Os resultados mostram que a metodologia proposta é adequada para tarefas de manipulação de peças na presença de obstáculos, uma vez que os pontos intermediários situam-se fora da região de colisão nos três casos aqui apresentados. Além disso, quanto à segunda etapa, observou-se que as trajetórias de 5º e 7º grau apresentaram resultados similares, de maneira que os erros obtidos poderiam ser melhorados analisando aspectos associados ao controlador do robô em estudo. / The thesis presents a study for collision-free trajectory planning for a pneumatic robot with 5 degrees of freedom applying three metaheuristic algorithms: firefly metaheuristic algorithm, particle swarm optimization and genetic algorithms. As regards the application of metaheuristic algorithms to the study of the trajectory planning of manipulating robots in the presence of obstacles, there are different types of techniques to avoid collisions that consider the kinematic and dynamic effects, obtaining trajectories with the optimal time, torque, etc. In this study, contributions are made to the application of these techniques specifically to pneumatic manipulator robots, particularly with regard to the specific characteristics of pneumatic servo-actuators, such as friction modeling of these systems, calculation of equivalent mass, etc. The methodology used is defined in two steps. The first one consists of obtaining intermediate points, acquired considering the smallest distance between the intermediate points and the final point, generated considering the presence of obstacles (cylinders, cubes and spheres) These obstacles are mapped in collision regions, which are constraints to the optimization problem. The second step is based on the study of the trajectory planning: 5th and 7th degree b-splines are applied in the interpolation of the intermediate points, in order to obtain trajectories that consider the smallest actuator force associated to the dynamics of the manipulator and the kinematic and dynamic constraints, determined by the operational characteristics of pneumatic servo-positioners. The results show that the proposed methodology is suitable for tasks of manipulating parts in the presence of obstacles because the intermediate points are outside the collision region in the three cases presented here. In addition, it was observed that the trajectories of 5th and 7th degree presented similar results, so that the errors obtained could be improved by analyzing aspects associated to the controller of the robot.