Research on multi-agent systems performing cooperative tasks has received considerable attention in recent years. Because multiple agents perform cooperative tasks in close proximity, the coordination control of multiple agents to avoid collisions holds one of the critical keys to mission success. The potential function approach has been extensively employed for collision avoidance, but it has one inherent limitation of local minimum. This dissertation proposes a new avoidance strategy for the issue of local minimum. The primary objective of this research is to construct novel potential-function-based control schemes that drive agents from their initial to the goal configurations while avoiding collision with other agents and obstacles. The control schemes enable agents to avoid being trapped at a local minimum by forcing them to exit from the regions that may contain a local minimum. This dissertation consists of three studies, each of which has different technical assumptions. In the first study, all-to-all communication ability among agents is assumed. In addition, each agent is assumed to a priori know the location of all obstacles. In the second study, all-to-all communication ability is again assumed, but each agent is assumed to determine the location of obstacles using a sensor with a limited sensing range. In the third study, limited communication ability is assumed (i.e., each agent exchanges information only with agents within its limited communication range), and each agent is assumed to determine the location of the obstacles using its sensor with a limited sensing range. Relative to existing solutions, the new control schemes presented here have three distinct advantages. First, our avoidance strategy can provide cost-efficient solutions in applications because agents will never be trapped at a local minimum. Second, our control signals are continuous, which allows agents to change their speed in a realistic manner that is consistent with their natural motion traits. Finally, our control scheme allows for setting the upper bound of the velocity of each agent, which guarantees that the speed of agents will never exceed a maximum speed limit. / text

In this dissertation, we establish existence and multiplicity of positive solutions for semilinear elliptic equations with subcritical and critical nonlinearities. We treat problems invariant under subgroups of the orthogonal group. Roughly speaking, we prove that if enough "mass " is concentrated around special orbits, then among the functions with prescribed symmetry, there is a solution for the original problem. Our results can be regarded as a further development of the work of Z.-Q. Wang, where existence of local minima in the space of symmetric functions was studied for the Schrödinger equation. We illustrate the general theory with three examples, all of which produce new results. Our method allows the construction of solutions with prescribed symmetry, and it represents a step further in the classification of positive solutions for certain nonlinear elliptic problems.

There are many combinatorial optimization problems such as traveling salesman problem, quadratic-assignment problem, flow shop scheduling, that are computationally intractable. Tabu search based simulated annealing is a stochastic search algorithm that is widely used to solve combinatorial optimization problems. Due to excessive run time, there is a strong demand for a parallel version that can be applied to any problem with minimal modifications. Existing advanced and/or parallel versions of tabu search algorithms are specific to the problem at hand. This leads to a drawback of optimization only for that particular problem. In this work, we propose a parallel version of tabu search based SA on the Graphics Processing Unit (GPU) platform. We propose two variants of the algorithm based on where the tabu list is stored (global vs. local). In the first version, the list is stored in the global shared memory such that all threads can access this list. Multiple random walks in solution space are carried out. Each walk avoids the moves made in rest of the walks due to their access to global tabu list at the expense of more time. In the second version, the list is stored at the block level and is shared by only the block threads. Groups of random walks are performed in parallel and a walk in a group avoids the moves made by the rest of the walks within that group due to their access to shared local tabu list. This version is better than the first version in terms of execution time. On the other hand, the first version finds the global optima more often. We present experimental results for six difficult optimization functions with known global optima. Compared to the CPU implementation with similar workload, the proposed GPU versions are faster by approximately three orders of magnitude and often find the global optima.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-26T18:28:31Z No. of bitstreams: 2 Dissertação - Rafael Carvalho Couto - 2013.pdf: 41193945 bytes, checksum: 74a020dad23640afb84a085b841b91aa (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T20:26:09Z (GMT) No. of bitstreams: 2 Dissertação - Rafael Carvalho Couto - 2013.pdf: 41193945 bytes, checksum: 74a020dad23640afb84a085b841b91aa (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T20:26:10Z (GMT). No. of bitstreams: 2 Dissertação - Rafael Carvalho Couto - 2013.pdf: 41193945 bytes, checksum: 74a020dad23640afb84a085b841b91aa (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2013-04-15 / This work focuses on the development of the software MGA, which aims to determine the lowest energy structures of a given molecular system, using Genetic Algorithm (GA). The GA is a method of artificial intelligence that was developed to work with finding the best solutions of the specified conditions, ie, an algorithm that seeks the best answer desired, an optimal result. The MGA uses three techniques: Random Search (RS), Noninclusive Genetic Algorithm (NGA), Inclusive Genetic Algorithm (IGA). The last one is characterized by a new type of evolutionary strategy that allows in a single calculation and a single cycle, obtain several minimum of the potential energy surface. For optimum operation of the algorithm, was made an optimization of the parameters used in MGA, through response surface methodology. Using the techniques RS, IGA and NGA, were determined 141 distinct molecular structures of the amino acid asparagine. In the electronic structure calculations were considered the semi-empirical methods PM3, AM1 and RM1; and DFT potentials, with basis sets 6-311G ** and PC1. The RS determined the Global Minimum (GM) with ease, for the different potentials used, and proved that it’s quite useful in determining molecular geometries where there is no accuracy in the determination of local minima in order of energy. The NGA is efficient in determining the GM, performing in a shorter time, if compared to RS and IGA. The IGA proved to be a more robust method than the others, because in addition to determining the GM, it can find the local minima in order of energy. Performing calculations on an intermediate time of RS and NGA, the IGA determined the GM as the NGA, and found structures that were not founded using RS. The GM’s of asparagine determined using the potentials PC1, PM3, AM1 and RM1 have a large structural difference. This demonstrates that different potencials used in the electronic structure calculations may lead to different results. By analyzing the structures obtained for potentials PC1, PM3, AM1 and RM1, using the IGA, it appears that there is a difference in the topology of the potential energy surface of these potentials. / O presente trabalho é focado no desenvolvimento do software MGA, que tem como objetivo a determinação das estruturas de menor energia de um dado sistema molecular, utilizando o Algoritmo Genético (AG). O AG é um método de inteligência artificial que foi desenvolvido para trabalhar com a procura de soluções que melhor atendam as condições especificadas, isto é, um algoritmo que procura a melhor resposta desejada, um resultado ótimo. O MGA utiliza três técnicas: Busca Aleatória (RS), Algoritmo Genético Não-inclusivo (NGA), Algoritmo Genético Inclusivo (IGA). Este último é caracterizado por um novo tipo de estratégia evolutiva que permite em um único cálculo e um único ciclo evolucionário obter diversos mínimos da superfície de energia potencial. Para o melhor funcionamento do algoritmo, foi feita uma otimização dos parâmetros utilizados do MGA, através da metodologia de superfície de resposta. Utilizando as técnicas RS, NGA e IGA, foram determinadas 141 estruturas moleculares distintas do aminoácido asparagina. Nos cálculos de estrutura eletrônica foram considerados os métodos semi-empíricos PM3, AM1 e RM1; e potenciais DFT, com os conjuntos de base 6-311G** e PC1. O RS determinou o Mínimo Global (GM) com facilidade, para os diferentes potenciais utilizados, e se mostrou bastante útil na determinação de geometrias moleculares onde não há um rigor na determinação de mínimos locais em ordem de energia. O NGA é eficiente na determinaçãoao do GM, realizando em um menor tempo, se comparado ao RS e IGA. O IGA mostrou-se um método mais robusto que os outros, pois além de determinar o GM é possível encontrar os mínimos locais em ordem de energia. Realizando cálculos em um tempo intermediário ao RS e NGA, o IGA determinou o GM assim como o NGA, e encontrou estruturas que não foram possíveis utilizando o RS. Os GM’s da asparagina determinados utilizando os potenciais PC1, PM3, AM1 e RM1 possuem uma grande diferença estrutural. Isto demonstra que diferentes potencias utilizados nos cálculos de estrutura eletrônica podem levar a diferentes resultados. Ao analisarmos as estruturas obtidas para os potenciais PC1, PM3, AM1 e RM1, utilizando o IGA, constata-se que há uma diferença na topologia de suas superfícies de energia potencial.

The Artificial Potential Fields approach is widely used in mobile robot navigation due to its easy implementation and low computational cost. In this approach, the environment is seen as a potential surface, where the goal point is modeled as an attractor point and the obstacles are considered repulsor points. A potential field function is used to model all the environment, calculating the in uence over the robot. The force that moves the robot is the descendent gradient of the field. Local minima appear when this gradient (the force) becomes equal to zero. This situation prevents the robot from arriving at the goal point. This work presents a new algorithm to escape from local minima points in the environment. This new algorithm is inspired in the deterministic annealing algorithm. A comparative study between the developed method and two known methods, simulated annealing to escape from local minima, and the method of virtual obstacle, is carried out. The results show that the proposed algorithm can be used to perform local minima escape, since this approach was capable to produce satisfactory results when compared with other classical existent solutions. / O Método dos Campos Potenciais Artificiais é amplamente utilizado para navegação de robôs móveis por sua facilidade de implementação e baixo custo computacional. Nessa abordagem, o ambiente é modelado com base em campos potenciais. Pontos de destino são modelados como atratores, ao passo que obstáculos são vistos como repulsores e uma função é usada para modelar o campo potencial gerado por cada um dos obstáculos e destinos e a sua in uência sobre o robô. Sendo o gradiente negativo do campo a força que impulsiona o movimento do robô, há a possibilidade de surgimento de pontos de mínimos, onde a forçaa se anula, diferentes do mínimo global. Este é um problema existente no método, que pode impedir que o robô chegue ao seu ponto de destino. Nesse contexto, o presente trabalho apresenta uma nova abordagem para escapar de pontos de mínimos locais por sistemas autônomos que implementam o método dos campos potenciais artificiais, inspirada no recozimento determinístico. É apresentado um estudo comparativo entre a técnica desenvolvida neste trabalho e mais dois métodos já conhecidos: recozimento simulado para escapar de mínimos locais e o método do obstáculo virtual. Os resultados obtidos mostram que o algoritmo inspirado no recozimento determinístico pode ser usado para escapar de mínimos locais, pois esse método foi capaz de produzir resultados satisfatórios quando comparado com outras soluções clássicas existentes.

This study proposes novel optimization methodologies for the optimization of problems that reveal non-physical step discontinuities. More specifically, it is proposed to use gradient-only techniques that do not use any zeroth order information at all for step discontinuous problems. A step discontinuous problem of note is the shape optimization problem in the presence of remeshing strategies, since changes in mesh topologies may - and normally do - introduce non-physical step discontinuities. These discontinuities may in turn manifest themselves as non-physical local minima in which optimization algorithms may become trapped. Conventional optimization approaches for step discontinuous problems include evolutionary strategies, and design of experiment (DoE) techniques. These conventional approaches typically rely on the exclusive use of zeroth order information to overcome the discontinuities, but are characterized by two important shortcomings: Firstly, the computational demands of zero order methods may be very high, since many function values are in general required. Secondly, the use of zero order information only does not necessarily guarantee that the algorithms will not terminate in highly unfit local minima. In contrast, the methodologies proposed herein use only first order information, rather than only zeroth order information. The motivation for this approach is that associated gradient information in the presence of remeshing remains accurately and uniquely computable, notwithstanding the presence of discontinuities. From a computational effort point of view, a gradient-only approach is of course comparable to conventional gradient based techniques. In addition, the step discontinuities do not manifest themselves as local minima. / Thesis (PhD)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

Introduction: No Fixed-Dose Combination (FDC) formulations currently exist for pediatric tuberculosis (TB) treatment. Earlier work implemented, in the software NONMEM, a rational method for optimizing design and individualization of pediatric anti-TB FDC formulations based on patient body weight, but issues with parameter estimation, dosage strata heterogeneity and representative pharmacokinetics remained. Aim: To further develop the rational model-based methodology aiding the selection of appropriate FDC formulation designs and dosage regimens, in pediatric TB treatment. Materials and Methods: Optimization of the method with respect to the estimation of body weight breakpoints was sought. Heterogeneity of dosage groups with respect to treatment efficiency was sought to be improved. Recently published pediatric pharmacokinetic parameters were implemented and the model translated to MATLAB, where also the performance was evaluated by stochastic estimation and graphical visualization. Results: A logistic function was found better suited as an approximation of breakpoints. None of the estimation methods implemented in NONMEM were more suitable than the originally used FO method. Homogenization of dosage group treatment efficiency could not be solved. MATLAB translation was successful but required stochastic estimations and highlighted high densities of local minima. Representative pharmacokinetics were successfully implemented. Conclusions: NONMEM was found suboptimal for the task due to problems with discontinuities and heterogeneity, but a stepwise method with representative pharmacokinetics were successfully implemented. MATLAB showed more promise in the search for a method also addressing the heterogeneity issue.