The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, two critical components of which are status quo analysis and coalition analysis. In stability analysis, an equilibrium is a state that is stable for all decision makers (DMs) under appropriate stability definitions or solution concepts. Status quo analysis aims to determine whether a particular equilibrium is reachable from a status quo (or an initial state) and, if so, how to reach it. A coalition is any subset of a set of DMs. The coalition stability analysis within the graph model is focused on the status quo states that are equilibria and assesses whether states that are stable from individual viewpoints may be unstable for coalitions. Stability analysis began within a simple preference structure which includes a relative preference relationship and an indifference relation. Subsequently, preference uncertainty and strength of preference were introduced into GMCR but not formally integrated. In this thesis, two new preference frameworks, hybrid preference and multiple-level preference, and an integrated algebraic approach are developed for GMCR. Hybrid preference extends existing preference structures to combine preference uncertainty and strength of preference into GMCR. A multiple-level preference framework expands GMCR to handle a more general and flexible structure than any existing system representing strength of preference. An integrated algebraic approach reveals a link among traditional stability analysis, status quo analysis, and coalition stability analysis by using matrix representation of the graph model for conflict resolution. To integrate the three existing preference structures into a hybrid system, a new preference framework is proposed for graph models using a quadruple relation to express strong or mild preference of one state or scenario over another, equal preference, and an uncertain preference. In addition, a multiple-level preference framework is introduced into the graph model methodology to handle multiple-level preference information, which lies between relative and cardinal preferences in information content. The existing structure with strength of preference takes into account that if a state is stable, it may be either strongly stable or weakly stable in the context of three levels of strength. However, the three-level structure is limited in its ability to depict the intensity of relative preference. In this research, four basic solution concepts consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined at each level of preference for the graph model with the extended multiple-level preference. The development of the two new preference frameworks expands the realm of applicability of the graph model and provides new insights into strategic conflicts so that more practical and complicated problems can be analyzed at greater depth. Because a graph model of a conflict consists of several interrelated graphs, it is natural to ask whether well-known results of Algebraic Graph Theory can help analyze a graph model. Analysis of a graph model involves searching paths in a graph but an important restriction of a graph model is that no DM can move twice in succession along any path. (If a DM can move consecutively, then this DM's graph is effectively transitive. Prohibiting consecutive moves thus allows for graph models with intransitive graphs, which are sometimes useful in practice.) Therefore, a graph model must be treated as an edge-weighted, colored multidigraph in which each arc represents a legal unilateral move and distinct colors refer to different DMs. The weight of an arc could represent some preference attribute. Tracing the evolution of a conflict in status quo analysis is converted to searching all colored paths from a status quo to a particular outcome in an edge-weighted, colored multidigraph. Generally, an adjacency matrix can determine a simple digraph and all state-by-state paths between any two vertices. However, if a graph model contains multiple arcs between the same two states controlled by different DMs, the adjacency matrix would be unable to track all aspects of conflict evolution from the status quo. To bridge the gap, a conversion function using the matrix representation is designed to transform the original problem of searching edge-weighted, colored paths in a colored multidigraph to a standard problem of finding paths in a simple digraph with no color constraints. As well, several unexpected and useful links among status quo analysis, stability analysis, and coalition analysis are revealed using the conversion function. The key input of stability analysis is the reachable list of a DM, or a coalition, by a legal move (in one step) or by a legal sequence of unilateral moves, from a status quo in 2-DM or $n$-DM ($n > 2$) models. A weighted reachability matrix for a DM or a coalition along weighted colored paths is designed to construct the reachable list using the aforementioned conversion function. The weight of each edge in a graph model is defined according to the preference structure, for example, simple preference, preference with uncertainty, or preference with strength. Furthermore, a graph model and the four basic graph model solution concepts are formulated explicitly using the weighted reachability matrix for the three preference structures. The explicit matrix representation for conflict resolution (MRCR) that facilitates stability calculations in both 2-DM and $n$-DM ($n > 2$) models for three existing preference structures. In addition, the weighted reachability matrix by a coalition is used to produce matrix representation of coalition stabilities in multiple-decision-maker conflicts for the three preference frameworks. Previously, solution concepts in the graph model were traditionally defined logically, in terms of the underlying graphs and preference relations. When status quo analysis algorithms were developed, this line of thinking was retained and pseudo-codes were developed following a similar logical structure. However, as was noted in the development of the decision support system (DSS) GMCR II, the nature of logical representations makes coding difficult. The DSS GMCR II, is available for basic stability analysis and status quo analysis within simple preference, but is difficult to modify or adapt to other preference structures. Compared with existing graphical or logical representation, matrix representation for conflict resolution (MRCR) is more effective and convenient for computer implementation and for adapting to new analysis techniques. Moreover, due to an inherent link between stability analysis and post-stability analysis presented, the proposed algebraic approach establishes an integrated paradigm of matrix representation for the graph model for conflict resolution.

The graph model for conflict resolution (GMCR) provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, two critical components of which are status quo analysis and coalition analysis. In stability analysis, an equilibrium is a state that is stable for all decision makers (DMs) under appropriate stability definitions or solution concepts. Status quo analysis aims to determine whether a particular equilibrium is reachable from a status quo (or an initial state) and, if so, how to reach it. A coalition is any subset of a set of DMs. The coalition stability analysis within the graph model is focused on the status quo states that are equilibria and assesses whether states that are stable from individual viewpoints may be unstable for coalitions. Stability analysis began within a simple preference structure which includes a relative preference relationship and an indifference relation. Subsequently, preference uncertainty and strength of preference were introduced into GMCR but not formally integrated. In this thesis, two new preference frameworks, hybrid preference and multiple-level preference, and an integrated algebraic approach are developed for GMCR. Hybrid preference extends existing preference structures to combine preference uncertainty and strength of preference into GMCR. A multiple-level preference framework expands GMCR to handle a more general and flexible structure than any existing system representing strength of preference. An integrated algebraic approach reveals a link among traditional stability analysis, status quo analysis, and coalition stability analysis by using matrix representation of the graph model for conflict resolution. To integrate the three existing preference structures into a hybrid system, a new preference framework is proposed for graph models using a quadruple relation to express strong or mild preference of one state or scenario over another, equal preference, and an uncertain preference. In addition, a multiple-level preference framework is introduced into the graph model methodology to handle multiple-level preference information, which lies between relative and cardinal preferences in information content. The existing structure with strength of preference takes into account that if a state is stable, it may be either strongly stable or weakly stable in the context of three levels of strength. However, the three-level structure is limited in its ability to depict the intensity of relative preference. In this research, four basic solution concepts consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined at each level of preference for the graph model with the extended multiple-level preference. The development of the two new preference frameworks expands the realm of applicability of the graph model and provides new insights into strategic conflicts so that more practical and complicated problems can be analyzed at greater depth. Because a graph model of a conflict consists of several interrelated graphs, it is natural to ask whether well-known results of Algebraic Graph Theory can help analyze a graph model. Analysis of a graph model involves searching paths in a graph but an important restriction of a graph model is that no DM can move twice in succession along any path. (If a DM can move consecutively, then this DM's graph is effectively transitive. Prohibiting consecutive moves thus allows for graph models with intransitive graphs, which are sometimes useful in practice.) Therefore, a graph model must be treated as an edge-weighted, colored multidigraph in which each arc represents a legal unilateral move and distinct colors refer to different DMs. The weight of an arc could represent some preference attribute. Tracing the evolution of a conflict in status quo analysis is converted to searching all colored paths from a status quo to a particular outcome in an edge-weighted, colored multidigraph. Generally, an adjacency matrix can determine a simple digraph and all state-by-state paths between any two vertices. However, if a graph model contains multiple arcs between the same two states controlled by different DMs, the adjacency matrix would be unable to track all aspects of conflict evolution from the status quo. To bridge the gap, a conversion function using the matrix representation is designed to transform the original problem of searching edge-weighted, colored paths in a colored multidigraph to a standard problem of finding paths in a simple digraph with no color constraints. As well, several unexpected and useful links among status quo analysis, stability analysis, and coalition analysis are revealed using the conversion function. The key input of stability analysis is the reachable list of a DM, or a coalition, by a legal move (in one step) or by a legal sequence of unilateral moves, from a status quo in 2-DM or $n$-DM ($n > 2$) models. A weighted reachability matrix for a DM or a coalition along weighted colored paths is designed to construct the reachable list using the aforementioned conversion function. The weight of each edge in a graph model is defined according to the preference structure, for example, simple preference, preference with uncertainty, or preference with strength. Furthermore, a graph model and the four basic graph model solution concepts are formulated explicitly using the weighted reachability matrix for the three preference structures. The explicit matrix representation for conflict resolution (MRCR) that facilitates stability calculations in both 2-DM and $n$-DM ($n > 2$) models for three existing preference structures. In addition, the weighted reachability matrix by a coalition is used to produce matrix representation of coalition stabilities in multiple-decision-maker conflicts for the three preference frameworks. Previously, solution concepts in the graph model were traditionally defined logically, in terms of the underlying graphs and preference relations. When status quo analysis algorithms were developed, this line of thinking was retained and pseudo-codes were developed following a similar logical structure. However, as was noted in the development of the decision support system (DSS) GMCR II, the nature of logical representations makes coding difficult. The DSS GMCR II, is available for basic stability analysis and status quo analysis within simple preference, but is difficult to modify or adapt to other preference structures. Compared with existing graphical or logical representation, matrix representation for conflict resolution (MRCR) is more effective and convenient for computer implementation and for adapting to new analysis techniques. Moreover, due to an inherent link between stability analysis and post-stability analysis presented, the proposed algebraic approach establishes an integrated paradigm of matrix representation for the graph model for conflict resolution.

Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.

Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.

Neste trabalho, com base em representações por matrizes de duas linhas para alguns tipos de partição (algumas já conhecidas e outras novas), identificamos propriedades sugeridas por classificá-las de acordo com a soma dos elementos de sua segunda linha. Esta soma sempre fornece alguma propriedade da partição relacionada. Se considerarmos versões sem sinal de algumas funções Mock Theta, seu termo geral pode ser interpretado como função geradora para algum tipo de partição com restrições. Para retornar aos coeficientes originais, é possível definir um peso para cada matriz e depois somá-las para contá-los. Uma representação análoga para essas partições nos permite observar propriedades sobre elas, novamente por meio de uma classificação referente à soma dos seu elementos da segunda linha. Esta seriação é feita por meio de tabelas criadas pelo software matemático Maple, as quais nos sugerem padrões e identidades relacionadas com outros tipos de partições conhecidas e, muitas vezes, encontrando uma fórmula fechada para contá-las. Tendo as conjecturas obtidas, elas são provadas por meio de bijeções entre conjuntos ou por contagem. / In this work, based on representations by matrices of two lines for some kind of partition (some already known and other new ones), we identify properties suggested by classifying them according to the sum of its second line. This sum always provides some properties of the related partition. If we consider unsigned versions of some Mock Theta Functions, its general term can be interpreted as generating function for some kind of partition with restrictions. To come back to the original coefficients, you can set a weight for each array and so add them to evaluate the coefficients. An analogous representation for partitions allows us to observe properties, again by classificating them according to the sum of its elements on the second row. This classification is made by means of tables created by mathematical software Maple, which suggest patterns, identities related to other known types of partitions and often, finding a closed formula to count them. Having established conjectured identities, all are proved by bijections between sets or counting methods.

No description available.

The project has worked with the function and structure of epicyclical automatic transmissions. The goal of the project has been to find a mathematical way of representing the transmissions setup and possible power flows. Furthermore the project has included the generation of all theoretically possible matrix representations of two simple planetary gear sets in MATLAB as the base for a future optimization model. The result of the project is a large quantity of matrix representations of the two planetary gear sets and their connections and shafts. The result from the MATLAB program has been verified by comparing the structure and the number of solutions to all manually derived setups. The result from the program can be considered to be complete for two planetary gears but to extend the analysis to more complex planetary gears and gearboxes with more than two sets, another method is suggested. The generation process in this project has been rather complex and time consuming. The conclusions drawn from this project is that it is possible to represent many epicyclical automatic transmissions in matrix form. An optimization program based on this type of matrix would simplify the design of new, more complex and more efficient epicyclical transmissions leading to more efficient vehicles. Key words: automatic transmission, planetary gear, matrix representation / Projektet har behandlat epicykliska automatväxellådor och dess uppbyggnad och funktion. Idén med projektet har varit att ta fram ett sätt för att på ett matematiskt sätt representera växellådans struktur och dess möjliga effektflöden. Utöver detta har arbetet inneburit att alla teoretiskt möjliga matrisrepresentationer för två enkla sammankopplade planetväxlar har tagits fram i MATLAB som underlag för en framtida optimeringsmodell. Resultatet av arbetet är en stor mängd uppställningar av dessa två planetväxlar och dessas sammankopplingar. Resultatet från MATLAB har jämförts och verifierats genom manuell beräkning av antalet variationer och dessas utseende. Resultatet från programmet kan anses som komplett men för en utökad analys av epicykliska automatväxellådor med fler än två planetväxlar och andra typer än den enklaste formen av planetväxel, rekommenderas en annan typ av framställning av alla möjliga variationer. Den metoden för att generera sammankopplingar som har använts i detta projekt är för komplex och tidskrävande. Slutsatsen av projektet är att det finns möjlighet att generera och representera många epicykliska automatväxellådor på matrisform. Ett optimeringsprogram baserat på denna typ av matris kan förenkla utvecklingen av nya mer avancerade och mer effektiva epicykliska automatväxelådor vilket leder till mer effektiva fordon. Nyckelord: automatisk växellåda, planetväxel, matrisrepresentation

<p dir="ltr">The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. </p><p dir="ltr">Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules.</p><p dir="ltr">This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.</p>

Uma rede de trocadores de calor pode ser definida como um grupo de trocadores de calor interligados com o objetivo de reduzir a necessidade de energia de um sistema, sendo largamente usada nas indústrias de processos. Entretanto, uma rede está sujeita à deposição, a qual causa um decréscimo na efetividade térmica dos trocadores. Este fenômeno é provocado pelo acúmulo de materiais indesejáveis sobre a superfície de troca térmica. Para compensar a redução de efetividade térmica causada pela deposição, torna-se necessário um aumento no consumo de utilidades. Isto eleva os custos de operação, assim como os custos de manutenção. Estima-se que os custos associados à deposição atinjam bilhões de dólares anualmente. Em face a este problema, vários trabalhos de pesquisa têm investigado métodos para prevenir a deposição e/ou gerenciar as operações em uma rede. Estudos envolvem desde a otimização de trocadores de calor individuais, simulação e monitoramento de redes, até a otimização da programação das paradas para limpeza de trocadores de calor em uma rede. O presente trabalho apresenta a proposição de um modelo para simulação de redes de trocadores de calor com aplicações no gerenciamento da deposição. Como conseqüência, foi desenvolvido um conjunto de códigos computacionais integrados, envolvendo a simulação estacionária de redes, a simulação pseudo-estacionária do comportamento de redes em relação à evolução da deposição, a estimação de parâmetros para diagnóstico do problema da deposição e a otimização operacional deste tipo de sistema. Com relação ao simulador estacionário, o modelo da rede foi formulado matricialmente e os balanços de massa e energia são resolvidos como sistemas de equações lineares. Do ponto de vista da otimização, o procedimento proposto redistribui as vazões, visando um melhor aproveitamento térmico dos trocadores da rede, como, por exemplo, buscando as vazões da rede que maximizem a temperatura da corrente de entrada no forno em unidades de destilação atmosférica de óleo cru. Os algoritmos foram implementados em alguns exemplos da literatura e em um problema de uma refinaria real. Os resultados foram promissores, o que sugere que a proposta deste trabalho pode vir a ser uma abordagem interessante para operações envolvendo redes de trocadores de calor / A Heat Exchanger Network (HEN) can be defined as a group of heat exchangers interconnected aiming to reduce the energy demand of a system, being widely used in the process industries. However, a HEN is subject to fouling, which causes a decrease on the thermal effectiveness of heat exchangers. This phenomenon is provoked by the accumulation of undesirable materials on thermal surface. In order to compensate the reduction of thermal effectiveness caused by fouling, it becomes necessary to increase the utility consumption. Thus, there is an increase of the operation costs, as maintenance costs. It is estimated that the costs associated to fouling reach billions of dollars annually. Facing this problem, several researches have investigated methods to prevent fouling and/or how to manage HEN operations. Studies involve since optimization of individual heat exchangers, simulation and fouling monitoring, until cleaning schedule optimization of HENs. The present work proposes a HEN simulation model, applied to fouling management. Consequently, it was developed a set of integrated computational codes, which involve a HEN stationary simulation, a pseudo-stationary simulation of HEN behavior related to fouling, a parameter estimation procedure for diagnosing fouling problems and an operational optimization procedure of this sort of system. Related to the stationary simulator, the HEN model is formulated using a matrix approach and the mass and energy balances are solved as linear equation systems. Focusing on optimization, it redistributes the HEN flows in order to improve the heat exchangers thermal efficiency, for example, searching for the HEN flows that maximize the inlet furnace stream temperature in crude distillation units. The algorithm was implemented to some literature examples and on a problem of a real refinery. All results show to be promising, which suggests that the proposal of this work may be an interesting approach for operations involving HENs

Uma rede de trocadores de calor pode ser definida como um grupo de trocadores de calor interligados com o objetivo de reduzir a necessidade de energia de um sistema, sendo largamente usada nas indústrias de processos. Entretanto, uma rede está sujeita à deposição, a qual causa um decréscimo na efetividade térmica dos trocadores. Este fenômeno é provocado pelo acúmulo de materiais indesejáveis sobre a superfície de troca térmica. Para compensar a redução de efetividade térmica causada pela deposição, torna-se necessário um aumento no consumo de utilidades. Isto eleva os custos de operação, assim como os custos de manutenção. Estima-se que os custos associados à deposição atinjam bilhões de dólares anualmente. Em face a este problema, vários trabalhos de pesquisa têm investigado métodos para prevenir a deposição e/ou gerenciar as operações em uma rede. Estudos envolvem desde a otimização de trocadores de calor individuais, simulação e monitoramento de redes, até a otimização da programação das paradas para limpeza de trocadores de calor em uma rede. O presente trabalho apresenta a proposição de um modelo para simulação de redes de trocadores de calor com aplicações no gerenciamento da deposição. Como conseqüência, foi desenvolvido um conjunto de códigos computacionais integrados, envolvendo a simulação estacionária de redes, a simulação pseudo-estacionária do comportamento de redes em relação à evolução da deposição, a estimação de parâmetros para diagnóstico do problema da deposição e a otimização operacional deste tipo de sistema. Com relação ao simulador estacionário, o modelo da rede foi formulado matricialmente e os balanços de massa e energia são resolvidos como sistemas de equações lineares. Do ponto de vista da otimização, o procedimento proposto redistribui as vazões, visando um melhor aproveitamento térmico dos trocadores da rede, como, por exemplo, buscando as vazões da rede que maximizem a temperatura da corrente de entrada no forno em unidades de destilação atmosférica de óleo cru. Os algoritmos foram implementados em alguns exemplos da literatura e em um problema de uma refinaria real. Os resultados foram promissores, o que sugere que a proposta deste trabalho pode vir a ser uma abordagem interessante para operações envolvendo redes de trocadores de calor / A Heat Exchanger Network (HEN) can be defined as a group of heat exchangers interconnected aiming to reduce the energy demand of a system, being widely used in the process industries. However, a HEN is subject to fouling, which causes a decrease on the thermal effectiveness of heat exchangers. This phenomenon is provoked by the accumulation of undesirable materials on thermal surface. In order to compensate the reduction of thermal effectiveness caused by fouling, it becomes necessary to increase the utility consumption. Thus, there is an increase of the operation costs, as maintenance costs. It is estimated that the costs associated to fouling reach billions of dollars annually. Facing this problem, several researches have investigated methods to prevent fouling and/or how to manage HEN operations. Studies involve since optimization of individual heat exchangers, simulation and fouling monitoring, until cleaning schedule optimization of HENs. The present work proposes a HEN simulation model, applied to fouling management. Consequently, it was developed a set of integrated computational codes, which involve a HEN stationary simulation, a pseudo-stationary simulation of HEN behavior related to fouling, a parameter estimation procedure for diagnosing fouling problems and an operational optimization procedure of this sort of system. Related to the stationary simulator, the HEN model is formulated using a matrix approach and the mass and energy balances are solved as linear equation systems. Focusing on optimization, it redistributes the HEN flows in order to improve the heat exchangers thermal efficiency, for example, searching for the HEN flows that maximize the inlet furnace stream temperature in crude distillation units. The algorithm was implemented to some literature examples and on a problem of a real refinery. All results show to be promising, which suggests that the proposal of this work may be an interesting approach for operations involving HENs