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[pt] Tema: Este estudo investiga o Problema de Roteamento de Inventário (IRP) no contexto do Gerenciamento de Inventário pelo Fornecedor (VMI), uma prática comum na cadeia de suprimentos onde os fornecedores assumem a responsabilidade pela reposição. O IRP, um problema combinatório estudado amplamente há quase 40 anos, engloba três subproblemas distintos: programação de entregas, gerenciamento de estoque e roteamento de veículos. Problema: Apesar de sua idade, o IRP continua a atrair a atenção da indústria e da academia. O recente décimo segundo Desafio de Implementação DIMACS dedicou uma categoria ao IRP, e entre os benchmarks comumente utilizados, 401 instâncias ainda não possuem soluções ótimas, especialmente no desafiador subconjunto de instâncias grandes. Hipótese e Justificativa: O framework HGS proposto por Vidal et al. (2012) surgiu como uma ferramenta proeminente utilizada por várias equipes de forma satisfatória na competição. No entanto, até onde sabemos, o framework HGS não foi testada para o IRP. Este estudo propõe uma solução que combina o framework HGS com uma estratégia de busca local eficiente, o método NSIRP proposto por Diniz et al. (2020), para abordar o IRP. Metodologia: Implementamos a solução proposta e comparamos seu desempenho com 21 abordagens existentes, utilizando os benchmarks da literatura. Resumo dos Resultados: Nossa abordagem identificou 79 novas Melhores Soluções Conhecidas (BKS) dentre 1100 instâncias. Se aplicada sob as mesmas regras da competição DIMACS, nossa solução teria garantido o primeiro lugar. Contribuições e Impactos: Este trabalho contribui para o desenvolvimento contínuo de soluções para o IRP, oferecendo uma abordagem eficiente e competitiva que pode inspirar futuras pesquisas e aplicações práticas no campo do gerenciamento de estoque e roteamento de veículos. / [en] Theme: This study investigates the Inventory Routing Problem (IRP) within the context of Vendor-Managed Inventory (VMI), a prevalent supply chain practice where suppliers assume responsibility for replenishment. The IRP, a combinatorial problem that has been widely studied for almost 40 years, encompasses three distinct subproblems: delivery scheduling, inventory management, and vehicle routing. Problem: Despite its age, the IRP continues to attract industry and academia attention. The recent 12th DIMACS Implementation Challenge dedicated a track to the IRP, and among the commonly used benchmarks, 401 instances still lack optimal solutions, particularly in the challenging Large instance subset. Hypothesis and Justification: The HGS framework proposed by Vidal et al. (2012) emerged as a prominent tool used successfully by numerous teams in the competition. However, to the best of our knowledge, the HGS framework has not been tested for the IRP. This study proposes a method combining the HGS framework with an efficient local search strategy, namely NSIRP proposed by Diniz et al. (2020), to tackle the IRP. Methodology: We implemented the proposed method and compared its performance to 21 existing methods using the literature benchmarks. Summary of Results: Our approach identified 79 new Best Known Solutions (BKS) out of 1100 instances. If applied under the same rules as the DIMACS competition, our method would have secured the first place. Contributions and Impacts: This work contribute to the ongoing development of IRP methods, offering an efficient and competitive approach that may inspire further research and practical applications in the realm of inventory management and vehicle routing.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The goal of this thesis is to present evolutionary algorithms, and demonstrate their applicability in quantum computing. As an introduction to evolutionary algorithms, it is applied to the simple but still challenging (from a computational viewpoint) Travelling Salesman Problem (TSP). This example is used to illustrate the e ect of various parameters like selection method, and maximum population size on the accuracy and e ciency of the evolutionary algorithms. For the sample problem, the 48 continental state capitals of the USA, solutions are evolved and compared to the known optimal solution. From this investigation tournament selection was shown to be the most e ective selection method, and that a population of 200 individuals per generation gave the most e ective convergence rates. In the next part of the thesis, evolutionary algorithms are applied to the generation of optimal quantum circuits for the following cases: The identity transformation : Picked for its simplicity as a test of the correct implementation of the evolutionary algorithm. The results of this investigation showed that the solver program functions correctly and that evolutionary algorithms can indeed nd valid solutions for this kind of problem. The work by Ding et al. [16] on optimal circuits for the two-qubit entanglement gate, controlled-S gate as well as the three qubit entanglement gate are solved by means of EA and the results compared. In all cases similar circuits are produced in fewer generations than the application of Ding et al. [16]. The three qubit quantum Fourier transform gate was also attempted, but no convergence was attained. The quantum teleportation algorithm is also investigated. Firstly the nature of the transformation that leads to quantum teleportation is considered. Next an e ective circuit is sought using evolutionary algorithms. The best result is one gate longer than Brassard [11], and seven gates longer than Yabuki [61]. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om evolusionêre algoritmes te ondersoek en hulle toepaslikheid op kwantumkomputasie te demonstreer. As 'n inleiding tot evolusionêre algoritmes is die eenvoudige, maar steeds komputasioneel uitdagende handelsreisigerprobleem ondersoek. Die invloed van die keuse van 'n seleksie metode, sowel as die invloed van die maksimum aantal individue in 'n generasie op die akkuraatheid en e ektiwiteit van die algoritmes is ondersoek. As voorbeeld is die 48 kontinentale hoofstede van die state van die VSA gekies. Die oplossings wat met evolusionêre algoritmes verkry is, is met die bekende beste oplossings vergelyk. Die resultate van hierdie ondersoek was dat toernooi seleksie die mees e ektiewe seleksie metode is, en dat 200 individue per generasie die mees e ektiewe konvergensie tempo lewer. Evolusionêre algoritmes word vervolgens toegepas om optimale oplossings vir die volgende kwantumalgoritmes te genereer: Die identiteitstransformasie: Hierdie geval is gekies as 'n eenvoudige toepassing met 'n bekende oplossing. Die resultaat van hierdie toepassing van die program was dat dit korrek funksioneer, en vinnig by die korrekte oplossings uitkom. Vervolgens is daar ondersoek ingestel na vier van die gevalle wat in Ding et al. [16] bespreek word. Die spesi eke transformasies waarna gekyk is, is 'n optimale stroombaan vir twee kwabis verstrengeling, 'n beheerde-S hek, 'n drie kwabis verstrengelings hek, en 'n drie kwabis kwantum Fourier transform hek. In die eerste drie gevalle stem die oplossings ooreen met die van Ding et al. [16], en is die konvergensie tempo vinniger. Daar is geen oplossing vir die kwantum Fourier transform verkry nie. Laastens is daar na die kwantumteleportasiealgoritme gekyk. Die eerste stap was om te kyk na die transformasie wat in hierdie geval benodig word, en daarna is gepoog om 'n e ektiewe stroombaan te evolueer. Die beste resultaat was een hek langer as Brassard [11], en sewe hekke langer as Yabuki [61].

It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems.

Many important applications in the real world that can be modelled as combinatorial optimization problems are actually dynamic in nature. However, research on dynamic optimization focuses on continuous optimization problems, and rarely targets combinatorial problems. Moreover, dynamic combinatorial problems, when addressed, are typically tackled within an application context. <br /><br /> In this thesis, dynamic combinatorial problems are addressed collectively by adopting an evolutionary based algorithmic approach. On the plus side, their ability to manipulate several solutions at a time, their robustness and their potential for adaptability make evolutionary algorithms a good choice for solving dynamic problems. However, their tendency to converge prematurely, the difficulty in fine-tuning their search and their lack of diversity in tracking optima that shift in dynamic environments are drawbacks in this regard. <br /><br /> Developing general methodologies to tackle these conflicting issues constitutes the main theme of this thesis. First, definitions and measures of algorithm performance are reviewed. Second, methods of benchmark generation are developed under a generalized framework. Finally, methods to improve the ability of evolutionary algorithms to efficiently track optima shifting due to environmental changes are investigated. These methods include adapting genetic parameters to population diversity and environmental changes, the use of multi-populations as an additional means to control diversity, and the incorporation of local search heuristics to fine-tune the search process efficiently. <br /><br /> The methodologies developed for algorithm enhancement and benchmark generation are used to build and test evolutionary models for dynamic versions of the travelling salesman problem and the flexible manufacturing system. Results of experimentation demonstrate that the methods are effective on both problems and hence have a great potential for other dynamic combinatorial problems as well.

This thesis discusses clustering related works with emphasis on Particle Swarm Optimization (PSO) principles. Specifically, we review in detail the PSO clustering algorithm proposed by Van Der Merwe & Engelbrecht, the particle swarm clustering (PSC) algorithm proposed by Cohen & de Castro, Szabo’s modified PSC (mPSC), and Georgieva & Engelbrecht’s Cooperative-Multi-Population PSO (CMPSO). In this thesis, an improvement over Van Der Merwe & Engelbrecht’s PSO clustering has been proposed and tested for standard datasets. The improvements observed in those experiments vary from slight to moderate, both in terms of minimizing the cost function, and in terms of run time.

In this thesis, I introduce two new algorithms: Ant Brood Clustering-Intelligent Ants (ABC-INTE) and Ant Brood Clustering-Polymorphic Ants (ABC-POLY) for the graph clustering problem. ABC-INTE uses techniques such as hopping ants, relaxed drop function, ants with memories, stagnation control, and addition of k-means cluster retrieval process, as an improvement of the basic ABC-KLS algorithm. ABC-POLY uses two types of ants, inspired by the division of labour between the major and minor ants in Pheidole genus, as an improvement of ABC-INTE. For comparison purpose, I also implement MMAS, an ACO clustering algorithm. When tested on the benchmark networks, ABC-POLY outperforms or achieves the same modularity values as MMAS and ABC-INTE on 7 out of 10 networks and is robust against different graphs. In practice, the speed of ABC-POLY is at least 10 times faster than MMAS, making it a scalable algorithm compared to MMAS. ABC-POLY also outputs a direct visual representation of the natural clusters on the graph that is appealing to human observation. This thesis opens an interesting research topic to apply polymorphic ants for graph clustering in the ABC-POLY algorithm. The distributive and self-organization nature of ABC-POLY makes it a candidate for analyzing clusters in more complex and dynamic graphs. / May 2016

The Ant Colony Optimization belongs into the metaheuristic methods category and it has been developing quite recently. So far it has shown its capabalities to over-perform other metaheuristic methods in quality of the solutions. This work brings analysis of the possible applications of the method on the classical optimization combinatorial problems -- traveling salesman problem, vehicle routing problem, knapsack problem, generalized assignment problem and maximal clique problem. It also deals with the practical experiments with application on several optimization problems and analysis of the time and memory complexity of such algorithms. The last part of the work is dedicated to the possibility of parallelization of the algorithm, which was result of the application of the ACO method on the traveling salesman problem. It brings analysis of the crucial operations and data synchronization issues, as well as practical example and demonstration of the parallelized version of the algorithm.

Orientador: Rubén Augusto Romero Lázaro / Banca: Anna Diva Plasencia Lotufo / Banca: Marcos Julio Rider Flores / Resumo: Neste trabalho é realizada uma análise teórica, a formulação conceitual e a implementação computacional de um algoritmo de vizinhança variável aplicado ao problema de planejamento a longo prazo de sistemas de transmissão de energia elétrica. O problema de planejamento de sistemas de transmissão é um problema muito complexo de resolver porque o modelo matemático é um problema de programação não linear inteiro misto. Por outro lado, a metaheurística de vizinhança variável é uma técnica de otimização que provou excelente desempenho na resolução de problemas complexos no campo da pesquisa operacional. Assim, neste trabalho é desenvolvido um algoritmo de vizinhança variável para o problema de planejamento de sistemas de transmissão. Um conceito importante na implementação desse algoritmo é a definição de vizinhança em relação a caminhos e a técnica de redução do tamanho da vizinhança. Testes realizados mostraram um excelente desempenho do algoritmo VNS, encontrando as melhores soluções conhecidas e mostradas na literatura especializada / Abstract: In this work a theoretical analysis is carried through, the conceptual formularization and the computational implementation of an applied algorithm of variable neighborhood to the problem of planning in the long run of systems of transmission of electric energy. The problem of planning of transmission systems is a very complex problem from solve because the mathematical model is a programming problem not linear. On the other hand, the metaheuristic of variable neighborhood is one technique of optimization that proved excellent performance in the resolution of complex problems in the field of the operational research. Thus, in this work is developed an algorithm of variable neighborhood for the problem of planning of transmission systems. An important concept in the implementation of this algorithm is the definition of neighborhood in relation the paths and the technique of reduction of the size of the neighborhood. Tests carried through had shown to an excellent performance of algorithm VNS, finding the best solutions known and shown in specialized literature / Mestre

Neste trabalho é apresentado o projeto de uma fonte de tensão de referência, um circuito capaz de prover uma tensão invariante com a temperatura, a tensão de alimentação e o processo de fabricação. São apresentadas: as equações de funcionamento, os passos para a elaboração da uma topologia final, o dimensionamento dos parâmetros de projeto com o uso de algoritmos metaheurísticos, o desenho do layout e os resultados e análises finais. O projeto emprega a tecnologia CMOS de 0,35 &#956m com quatro camadas de metal da Austria Micro Systems, em que os VTH0\'s dos transistores NMOS e PMOS, modelo típico, são, respectivamente, 0,5 V e -0,7 V. O circuito de fonte de referência é do tipo bandgap e faz a soma ponderada de correntes proporcionais a temperatura para atingir uma tensão de referência. Obteve-se um circuito típico com 0,5 V de tensão de referência, coeficiente de temperatura de 15 ppm/ºC em intervalo de temperatura de -10 a 90ºC em 1,0 V de tensão de alimentação, regulação de linha de 263 ppm/V em um intervalo de variação de 1,0 V a 2,5 V em 27ºC, 2,7 &#956A de corrente consumida e área de 0,11 mm². A introdução de um bloco de ajuste de coeficiente de temperatura, com ajuste digital, permite que mais que 90% dos circuitos produzidos tenham um coeficiente de temperatura de até 30 ppm/ºC. As medidas realizadas no trabalho são provenientes de simulações elétricas realizadas com o ELDO e modelos BSIM3v3. / In this work is presented a design of a reference voltage source, circuits capable to provide an invariant voltage regardless of the temperature, power supply and fabrication process. It\'s presented: the operation equations, the steps to elaborate a final topology, the project parameter sizing using a metaheuristic algorithm, the drawing of the layout, and the final results and its analysis. The design employs an AMS-CMOS 0.35 &#956m technology with four metal levels, whose NMOS and PMOS VTH0\'s for a typical circuit is 0.5 V and -0.7 V. The reference voltage circuit is bandgap and performs a weighted summation of proportional temperature currents to achieve the voltage reference. A typical circuit was obtained with 0.5 V reference voltage, 15 ppm/ºC temperature coefficient in the temperature range of -10 to 90ºC under 1.0 V power supply, 263 ppm/V line regulation in the range of 1.0 V to 2.5 V under 27ºC, 2.7 &#956A power consumption in a 0.11 mm² area. For a projected circuit its also possible to ensure a temperate coefficient under 30 ppm/ºC, for more than 95% of the produced circuits, employing an adjustment block which ought to be digitally calibrated for each circuit.