In real world applications such as the transporting of goods products, packing is a major issue. Goods products need to be packed such that the smallest space is wasted to achieve the maximum transportation efficiency. Packing becomes more challenging and complex when the product is circular/spherical. This thesis focuses on the best way to pack three-dimensional unit spheres into the smallest spherical and cubical space. Unit spheres are considered in lieu of non-identical spheres because the search mechanisms are more difficult in the latter set up and any improvements will be due to the search mechanism not to the ordering of the spheres. The two-unit sphere packing problems are solved by approximately using a variable neighborhood search (VNS) hybrid heuristic. A general search framework belonging to the Artificial Intelligence domain, the VNS offers a diversification of the search space by changing neighborhood structures and intensification by thoroughly investigating each neighborhood. It is exible, easy to implement, adaptable to both continuous and discrete optimization problems and has been use to solve a variety of problems including large-sized real-life problems. Its runtime is usually lower than other meta heuristic techniques. A tutorial on the VNS and its variants along with recent applications and areas of applicability of each variant. Subsequently, this thesis considers several variations of VNS heuristics for the two problems at hand, discusses their individual efficiencies and effectiveness, their convergence rates and studies their robustness. It highlights the importance of the hybridization which yields near global optima with high precision and accuracy, improving many best- known solutions indicate matching some, and improving the precision and accuracy of others. Keywords: variable neighborhood search, sphere packing, three-dimensional packing, meta heuristic, hybrid heuristics, multiple start heuristics.

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Orientador: Daniela Renata Cantane / Resumo: Originadas na década de 1970, as Infecções Hospitalares vêm cada vez mais tomando proporções colossais, acarretando óbito em cerca de 30% dos pacientes em Unidades de Terapia Intensiva (UTI). Os pacientes diagnosticados com a infecções permanecem muito tempo internados, gerando um custo muito alto para os hospitais. No ambiente hospitalar a bactéria Acinetobacter baumannii a principal responsável por tais infecções, devido a sua facilidade de sobreviver em ambientes secos e úmidos, podendo sobreviver tanto no organismo humano, quanto nos ambientes que os profissionais da saúde entram em contato (computadores, equipamentos médicos, etc). Os principais vetores desta bactéria são os próprios agentes de saúde, visto que os pacientes na UTI estão todos acamados. No entanto, medidas de higienização extremamente necessárias para conter surtos da infecções o. Por outro lado, devido as emergências nestas unidades, muitas vezes não há tempo hábil para tais procedimentos. Visto que impossível uma medida total de higienização e uma taxa nula de contato da equipe de trabalho com o ambiente em UTIs, importante conhecer quais são as mínimas medidas necessárias para a diminuição de infecções hospitalares. Neste contexto, o objetivo deste trabalho propor e analisar um modelo que descreva a dinâmica de transmissão da infecção dentro de uma UTI, considerando pacientes e profissionais da saúde, assim como, propor um modelo de otimização visando determinar quais as mínimas medidas de higienização... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Originated in the 1970s, Hospital Infections come every time more taking colossal proportions, causing death in about 30% of patients in Intensive Care Units (ICU). Patients diagnosed with infections remain long hospitalized, generating a very high cost for hospitals. In the hospital environment, Acinetobacter baumannii is the main responsible for such infections due to their ease of survival in dry and humid, and can survive both in the human body and in the environments that health workers contact (computers, medical equipment, etc.). The main vectors of this bacterium are the health agents themselves, since the patients in the ICU are all bedridden. However, hygiene measures are extremely necessary to contain outbreaks of infection. On the other hand, due to emergencies in these units, there is often no time for such procedures. Since a total sanitation measure and it is important to know the minimum measures necessary for the decrease of infections. In this context, the objective xiii of this work is to propose and analyze a model that describes the dynamics of transmission of infection within an ICU, considering patients and health professionals, as well as to propose an optimization model aiming to determine the minimum hygienic measures are needed to minimize the number of infected patients. A Variable Neighborhood Search Metaheuristic was proposed to solve the optimization model. For validation of the models were carried out computational simulations. These simulation... (Complete abstract click electronic access below) / Mestre

Bioelectronic medicine is an emerging discipline being a intersection of neu- roscience, immunology and electrical engineering. Chronic inflammation is linked to disorders such as diabetes, rheumatoid arthritis, asthma, atheroscle- rosis, obesity and inflammatory bowel disease. Chronic inflammatory diseases have been recognized as the most significant cause of death in the world today, with more than 50% of all deaths being attributable to inflammation-related diseases. To find specific parameters for the stimulation of the vagus nerve would be a major advancement in the field, since it will help restore the vagal tone optimally. A systematic review has been made to understand and explore the tissue damage, stimulation sites, FDA approved parameters and the safety and efficacy in vagus nerve stimulation (VNS). A control closed- loop system was developed based on the needs of the field and a human clinical trial protocol was proposed.    The control close-loop system is able to receive feedback from a continuous real-time measurement of the pressure of the peripheral blood flow and send a VNS based on a heart rate (HR) settled threshold. The stimulation is delivered with previously settled parameters such as, pulse width, output current, duty cycle and frequency and helps observe if the nerve has been correctly targeted or not. From the results, it becomes clear that the connection of the devices has been correctly accomplished and that the HR reduction is being measured by the control close-loop which would stimulate again when the HR threshold is surpassed. Based on the concept of this control close-loop a human protocol has been proposed to test if the hypothesis that patients have their best inflammatory response with different output current rather than all having one best performing one and that non-healthy patients will lower their HR baseline after VNS treatment showing the increase of vagus nerve activity. This report adds value on the creation of a new control close-loop device between the MouseOx and Intan devices. Controlling the stimulation parameters in VNS can be a powerful technique that will increase patient specificity and will help non respondents to different drug treatments to have a more effective alternative. The HR is a simple biomarker to detect VNS bioactivity but lots of further research on non-invasive devices and software limitations are still needed to be overcome to have clear guidance in the field. The proposal of a new human clinical trial that might give a clear and feasible solution to either find an efficient stimulation setting or the assurance of the real need for an interactive control close-loop system that would tailor the stimulation parameters for each specific patient is presented. / Bioelektronisk medicin är en framväxande disciplin som är en skärningspunkt mellan neurovetenskap, immunologi och elektroteknik. Kronisk inflamma- tion är kopplad till sjukdomar som diabetes, reumatoid artrit, astma, åder- förkalkning, fetma och inflammatoriska tarmsjukdomar som är den vanligaste dödsorsaken i världen idag. Att hitta specifika parametrar för stimulering av vagusnerven skulle vara ett stort framsteg på området, eftersom det hjälper till att återställa vagustonen optimalt. En systematisk översyn har gjorts för att förstå och utforska vävnadsskadan, stimuleringsställena, FDA-godkända parametrar och säkerheten och effekten i VNS. Ett kontrollsystem med slutet kretslopp utvecklades baserat på fältets behov och ett protokoll för kliniska prövningar för människor föreslogs. Kontrollsystemet kan ta emot feedback från en kontinuerlig realtidsmätning av trycket i det perifera blodflödet och skicka en VNS baserat på en HR-bestämd tröskel. Stimuleringen levereras med tidigare inställda parametrar såsom pulsbredd, utström, arbetscykel och frekvens. Av resultaten blir det tydligt att anslutningen av enheterna har åstadkommits korrekt och att HR-reduktionen mäts av kontrollens slutslinga som skulle stimulera igen när HR-tröskeln överskrids. Baserat på konceptet med denna kontroll close-loop har ett mänskligt protokoll föreslagits för att testa om hypotesen att patienter har sitt bästa inflammatoriska svar med olika utström snarare än att alla har en bäst presterande och att icke-friska patienter kommer att sänka sin HR baslinje efter VNS-behandling som visar ökningen av vagusnervens aktivitet. Den här rapporten ger ett mervärde när det gäller skapandet av en ny kontrollenhet mellan MouseOx- och Intan-enheterna. Att kontrollera stimuleringsparametrarna i VNS kan vara en kraftfull teknik som kommer att öka patientspecificiteten och som hjälper icke-respondenter till olika läkemedelsbehandlingar att få ett mer effektivt alternativ. HR är en enkel biomarkör för att upptäcka VNS-bioaktivitet, men massor av ytterli- gare forskning om icke-invasiva enheter och mjukvarubegränsningar behövs fortfarande för att få en tydlig vägledning på området. Förslaget om en ny klinisk prövning på människa som kan ge en tydlig och genomförbar lösning för att antingen hitta effektiva stimuleringsmiljöer eller försäkran om det verkliga behovet av ett interaktivt kontrollsystem med nära slinga som skulle skräddarsy stimuleringsparametrarna för varje specifik patient presenteras.

O problema de dimensionamento e sequenciamento de lotes vem sendo extensivamente estudado por pesquisadores da área de Pesquisa Operacional e há uma tendência de que tais trabalhos passem a cada vez mais integrar aspectos reais dos processos produtivos. Entretanto, percebe-se que os estudos conduzidos em alguns setores industriais negligenciam importantes restrições tecnológicos dos processos de produção e isso afasta esses trabalhos de Pesquisa Operacional de uma aplicação efetiva, como é o caso da indústria de embalagens de vidro. Neste contexto, propõe-se um modelo de programação inteira mista e um método de solução para o problema de dimensionamento e sequenciamentos de lotes na indústria de embalagens de vidro, sendo que este trabalho diferencia-se dos demais existentes na literatura por agregar restrições tecnológicas específicas desse processo produtivo. O modelo proposto, denominado CLSD-GCST, foi amplamente validado com base em um conjunto de testes com 40 instâncias de um problema real de uma grande empresa do setor no pacote comercial IBM ILOG CPLEX Optimization Studio Versão 12.5. A validação do modelo incluiu ainda uma análise de ganhos potenciais para o negócio de baseada no modelo SCOR. Já o método de solução proposto consiste em uma metaheurística de Busca em Vizinhança Variável (VNS) e se mostrou promissor para a solução do problema estudado, proporcionando resultados de qualidade em um baixo tempo computacional. Além disso, o VNS superou o Branch-and-Cut do CPLEX para grandes instâncias, nas quais o pacote comercial encontrou dificuldades. Por fim, o VNS proposto também foi validado por meio da análise de testes computacionais e suas principais características foram avaliadas sistematicamente, gerando um conjunto de informações que pode direcionar a utilização e, até mesmo, a evolução desse método em pesquisas futuras. / Lot sizing and scheduling problem has been extensively studied by Operations Research scientists and there is a tendency of incorporating more production processes real aspects in these researches. However, it can be noticed that studies conducted in some industrial sectors neglect important production process technological constraints and it keeps the Operations Research works away from an effective application, as happens with the glass containers industry. In this context, a mixed integer programming model and a solution method were proposed for glass containers industry lot sizing and scheduling problem, the main difference between this work and the others in literature is the inclusion of process specific technological constraints. The proposed model, named CLSD-GCST, was widely validated by a set of tests performed with 40 instances from a large company real problem using the commercial package IBM ILOG CPLEX Optimization Studio Version 12.5. The model validation also included a potential business earnings analysis based on SCOR framework. About the proposed solution method, it consists of a Variable Neighborhood Search (VNS) metaheuristic and it proved to be promising for the studied problem solution, providing good quality results in low computational time. Moreover, VNS overcame the CPLEX Branch-and-Cut for large instances, in which the commercial package found difficulties. Lastly, the proposed VNS was validated by means of computational tests analysis and its main characteristics were systematically evaluated, generating an information set that may direct this method application and even its evolution in future researches.

O problema de dimensionamento e sequenciamento de lotes vem sendo extensivamente estudado por pesquisadores da área de Pesquisa Operacional e há uma tendência de que tais trabalhos passem a cada vez mais integrar aspectos reais dos processos produtivos. Entretanto, percebe-se que os estudos conduzidos em alguns setores industriais negligenciam importantes restrições tecnológicos dos processos de produção e isso afasta esses trabalhos de Pesquisa Operacional de uma aplicação efetiva, como é o caso da indústria de embalagens de vidro. Neste contexto, propõe-se um modelo de programação inteira mista e um método de solução para o problema de dimensionamento e sequenciamentos de lotes na indústria de embalagens de vidro, sendo que este trabalho diferencia-se dos demais existentes na literatura por agregar restrições tecnológicas específicas desse processo produtivo. O modelo proposto, denominado CLSD-GCST, foi amplamente validado com base em um conjunto de testes com 40 instâncias de um problema real de uma grande empresa do setor no pacote comercial IBM ILOG CPLEX Optimization Studio Versão 12.5. A validação do modelo incluiu ainda uma análise de ganhos potenciais para o negócio de baseada no modelo SCOR. Já o método de solução proposto consiste em uma metaheurística de Busca em Vizinhança Variável (VNS) e se mostrou promissor para a solução do problema estudado, proporcionando resultados de qualidade em um baixo tempo computacional. Além disso, o VNS superou o Branch-and-Cut do CPLEX para grandes instâncias, nas quais o pacote comercial encontrou dificuldades. Por fim, o VNS proposto também foi validado por meio da análise de testes computacionais e suas principais características foram avaliadas sistematicamente, gerando um conjunto de informações que pode direcionar a utilização e, até mesmo, a evolução desse método em pesquisas futuras. / Lot sizing and scheduling problem has been extensively studied by Operations Research scientists and there is a tendency of incorporating more production processes real aspects in these researches. However, it can be noticed that studies conducted in some industrial sectors neglect important production process technological constraints and it keeps the Operations Research works away from an effective application, as happens with the glass containers industry. In this context, a mixed integer programming model and a solution method were proposed for glass containers industry lot sizing and scheduling problem, the main difference between this work and the others in literature is the inclusion of process specific technological constraints. The proposed model, named CLSD-GCST, was widely validated by a set of tests performed with 40 instances from a large company real problem using the commercial package IBM ILOG CPLEX Optimization Studio Version 12.5. The model validation also included a potential business earnings analysis based on SCOR framework. About the proposed solution method, it consists of a Variable Neighborhood Search (VNS) metaheuristic and it proved to be promising for the studied problem solution, providing good quality results in low computational time. Moreover, VNS overcame the CPLEX Branch-and-Cut for large instances, in which the commercial package found difficulties. Lastly, the proposed VNS was validated by means of computational tests analysis and its main characteristics were systematically evaluated, generating an information set that may direct this method application and even its evolution in future researches.

Made available in DSpace on 2014-12-17T15:48:01Z (GMT). No. of bitstreams: 1 EdmilsonFMOJ_DISSERT.pdf: 4310075 bytes, checksum: c753f90b3f1afd654108edecd6a3fc70 (MD5) Previous issue date: 2012-02-27 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This work seeks to propose and evaluate a change to the Ant Colony Optimization based on the results of experiments performed on the problem of Selective Ride Robot (PRS, a new problem, also proposed in this paper. Four metaheuristics are implemented, GRASP, VNS and two versions of Ant Colony Optimization, and their results are analyzed by running the algorithms over 32 instances created during this work. The metaheuristics also have their results compared to an exact approach. The results show that the algorithm implemented using the GRASP metaheuristic show good results. The version of the multicolony ant colony algorithm, proposed and evaluated in this work, shows the best results / Este trabalho tem o objetivo de propor e avaliar uma variante para o algoritmo de col?nia de formigas baseando-se no resultado de experimentos executados sobre o problema do Passeio do Rob? Seletivo (PRS, um novo problema, tamb?m proposto neste trabalho. S?o implementadas quatro metaheur?sticas, GRASP, VNS, e duas vers?es do Otimiza??o por Col?nia de Formigas, e analisados seus resultados executando-os sobre 32 inst?ncias criadas no trabalho. As metaheur?sticas tamb?m tem seu resultado comparado com o de um algoritmo exato. Os resultados mostram que o algoritmo implementado utilizando a metaheur?stica GRASP apresenta bons resultados. A vers?o multi-col?nias do algoritmo de col?nia de formigas, proposta e avaliada no trabalho, apresenta os melhores resultados

Introduction<br>Le nerf vague est un nerf mixte composé de 20% de fibres efférentes et 80% de fibres afférentes. La stimulation électrique du nerf vague (VNS) est actuellement employée comme thérapie de certaines formes d'épilepsies et de dépressions chez l'Homme. Le nerf vague a également un double rôle anti-inflammatoire : i) d'une part via la voie classique faisant intervenir les fibres vagales afférentes centripètes qui peuvent activer l'axe corticotrope, ii) d'autre part via la voie cholinergique anti-inflammatoire, plus récemment décrite. L'effet anti-inflammatoire est dans ce cas lié à l'activation des efférences vagales centrifuges. En effet, les terminaisons de ces fibres libèrent, en périphérie, de l'acétylcholine qui, en se liant au récepteur alpha 7-nicotinique exprimé en particulier par les macrophages, inhibe la sécrétion de cytokines pro-inflammatoires (TNFalpha notamment). Bien que les maladies inflammatoires chroniques de l'intestin (MICI) aient une incidence en augmentation, leur origine exacte reste méconnue et semble liée à de nombreux facteurs. Les patients atteints de MICI présentent des troubles au niveau de l'activation du système immunitaire qui vont engendrer l'apparition de lésions au niveau intestinal. Les traitements des MICI disponibles actuellement ne permettent pas une guérison totale, mais ont uniquement un rôle suspensif. <br> But <br>Les travaux réalisés ont eu pour objectif d'utiliser la VNS afin de diminuer l'inflammation dans un modèle de colite expérimentale chez le rat. Des études complémentaires ont été réalisées pour étudier les mécanismes de cet effet anti-inflammatoire ainsi que les effets centraux et digestifs moteurs de la VNS.<br> Matériels et Méthodes <br>La colite a été induite par l'instillation intra-colique d'acide trinitrobenzène sulfonique (TNBS). La VNS a été réalisée grâce à une électrode bipolaire implantée de manière chronique au niveau du nerf vague gauche (paramètres de stimulation : 1mA, 5Hz, 500µs, 10s ON, 90s OFF) ; l'animal a été stimulé pendant 3 heures le jour de l'injection du TNBS et pendant les 4 jours suivants. Les paramètres physiologiques de température corporelle et d'activité locomotrice ont été suivis en continu par télémétrie pendant cette période. L'animal a été sacrifié 5 jours après l'instillation, le côlon a été prélevé et deux zones tissulaires ont été distinguées : la partie lésée et la partie adjacente. Ces prélèvements ont ensuite été utilisés pour une analyse histologique, une quantification de la myéloperoxydase et une quantification des ARNm des cytokines par la technique de RT-PCR. L'inflammation globale induite par la colite a été étudiée par l'intermédiaire d'un index multiparamétrique global comprenant des paramètres physiologiques intégrés (température corporelle, activité locomotrice), tissulaires (surface des lésions) et moléculaires (ARNm des marqueurs d'inflammation). L'approfondissement des connaissances mécanistiques de l'effet anti-inflammatoire obtenu a été réalisé par une étude par western blot et immunohistochimie de l'expression des protéines impliquées dans les voies intracellulaires d'activation des cellules immunitaires (protéines STAT). Enfin les effets latéraux de la VNS ont été étudiés au niveau central par la technique d'immunohistochimie du c-fos et par l'analyse des électromyogrammes du jéjunum au niveau périphérique.<br>Les résultats mettent en évidence chez les animaux stimulés : une amélioration clinique significative avec une perte pondérale réduite, une tendance à la réduction des lésions intestinales, de l'expression de la myéloperoxidase et du taux d'ARNm de cytokines dans le tissu colique, ainsi qu'une diminution significative de l'index global d'inflammation. Au niveau mécanistique, la VNS induit des changements dans la signalisation intracellulaire, au niveau de la lésion et juste au-dessus de celle-ci. Enfin la VNS semble induire aussi des changements modérés au niveau de l'activation neuronale centrale et de la motricité digestive. <br> Conclusion <br>Ces données expérimentales montrent l'intérêt d'activer la voie cholinergique par la VNS pour obtenir un effet anti-inflammatoire ciblé au niveau du tube digestif. La VNS pourrait être envisagée dans le traitement des poussées ou le maintien en phase de rémission des patients atteints de MICI.

Made available in DSpace on 2014-06-11T19:22:33Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-11-30Bitstream added on 2014-06-13T18:08:29Z : No. of bitstreams: 1 martins_wa_me_ilha.pdf: 616652 bytes, checksum: e8d6346d5cc6774ab31d1538b90cb349 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / 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 / 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

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-10-02T23:37:05Z No. of bitstreams: 1 ThiagoCorreiaPereira_DISSERT.pdf: 849760 bytes, checksum: 18b8f71b02ed28bbc81789242e6e17b4 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-10-09T19:56:01Z (GMT) No. of bitstreams: 1 ThiagoCorreiaPereira_DISSERT.pdf: 849760 bytes, checksum: 18b8f71b02ed28bbc81789242e6e17b4 (MD5) / Made available in DSpace on 2017-10-09T19:56:01Z (GMT). No. of bitstreams: 1 ThiagoCorreiaPereira_DISSERT.pdf: 849760 bytes, checksum: 18b8f71b02ed28bbc81789242e6e17b4 (MD5) Previous issue date: 2017-04-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Devido ao grande volume de dados gerados pelo crescimento de aplica??es que prov?m novas informa??es, tanto em volume quanto em variedade, t?cnicas cada vez mais eficientes s?o exigidas para classific?-los e process?-los. Uma t?cnica muito utilizada ? o agrupamento de dados, cujo objetivo ? extrair conhecimento dos dados atrav?s da divis?o de entidades em subconjuntos homog?neos e/ou bem separados. Crit?rios podem ser utilizados para expressar a classifica??o dos dados. Dentre eles, um crit?rio frequentemente utilizado ? a soma m?nima das dist?ncias euclidianas quadr?ticas, do ingl?s, minimun sum-of-squares clustering (MSSC). Neste crit?rio, entidades s?o elementos no espa?o n-dimensional. O problema de agrupamento de dados pelo MSSC ? NP-?rduo, logo heur?sticas s?o t?cnicas extremamente ?teis para este tipo de problema. Este trabalho prop?e novas heur?sticas, baseadas na busca de vizinhan?as vari?veis gerais, do ingl?s, general variable neighborhood search (GVNS). Tamb?m ? proposto neste trabalho, a adapta??o da heur?stica reformulation descent (RD) para o problema MSSC, na forma de duas variantes, de forma in?dita na literatura. Os experimentos computacionais mostram que as variantes GVNS propostas neste trabalho apresentam melhores resultados, para inst?ncias grandes. / Due to the large volume of data generated by the growth of applications that provide new information, both in volume and variety, more efficient techniques are required to classify and processes them. A widely used technique is data grouping whose aim is to extract characteristics of the entities dividing them into homogeneous and/or well separated subsets. Many different criteria can be used to express the data classification. Among them, a commonly used criteria is the minimun sum-of-squares clustering (MSSC). In this criterion, entities are elements in n-dimensional Euclidean space. The data clustering problem by MSSC is NP-hard, then heuristics are extremely useful techniques for this type of problem. This work proposes new heuristics, based on the general variable neighborhood search (GVNS). Also proposed in this work is the adaptation of the heuristic reformulation descent (RD) to the MSSC problem, in the form of two variants, unapplied to this problem before in literature. The computational experiments show that the GVNS variants proposed in this work present better results, in large instances, than the current state of the art.