183 research outputs found

    Framework for Optimal Selection Using Meta‐Heuristic Approach and AHP Algorithm

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    Many real‐life decisions are focused on selecting the most preferable combination of available options, by satisfying different kinds of preferences and internal or external constraints and requirements. Focusing on the well‐known analytical hierarchical process (AHP) method and its extension CS‐AHP for capturing different kinds of preferences over two‐layered structure (including conditionally defined preferences and preferences about dominant importance), we propose a two‐layered framework for identifying stakeholders’ decision criteria requirements and employ meta‐heuristic algorithms (i.e., genetic algorithms) to optimally make a selection over available options. The proposed formal two‐layered framework, called OptSelectionAHP, provides the means for optimal selection based on specified different kinds of preferences. The framework has simultaneously proven optimality applied in software engineering domain, for optimal configuration of business process families where stakeholders’ preferences are defined over quality characteristics of available services (i.e., QoS attributes). Furthermore, this domain of application is characterized with uncertainty and variability in selection space, which is proven and does not significantly violate the optimality of the proposed framework

    Methodological review of multicriteria optimization techniques: aplications in water resources

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    Multi-criteria decision analysis (MCDA) is an umbrella approach that has been applied to a wide range of natural resource management situations. This report has two purposes. First, it aims to provide an overview of advancedmulticriteriaapproaches, methods and tools. The review seeks to layout the nature of the models, their inherent strengths and limitations. Analysis of their applicability in supporting real-life decision-making processes is provided with relation to requirements imposed by organizationally decentralized and economically specific spatial and temporal frameworks. Models are categorized based on different classification schemes and are reviewed by describing their general characteristics, approaches, and fundamental properties. A necessity of careful structuring of decision problems is discussed regarding planning, staging and control aspects within broader agricultural context, and in water management in particular. A special emphasis is given to the importance of manipulating decision elements by means ofhierarchingand clustering. The review goes beyond traditionalMCDAtechniques; it describes new modelling approaches. The second purpose is to describe newMCDAparadigms aimed at addressing the inherent complexity of managing water ecosystems, particularly with respect to multiple criteria integrated with biophysical models,multistakeholders, and lack of information. Comments about, and critical analysis of, the limitations of traditional models are made to point out the need for, and propose a call to, a new way of thinking aboutMCDAas they are applied to water and natural resources management planning. These new perspectives do not undermine the value of traditional methods; rather they point to a shift in emphasis from methods for problem solving to methods for problem structuring. Literature review show successfully integrations of watershed management optimization models to efficiently screen a broad range of technical, economic, and policy management options within a watershed system framework and select the optimal combination of management strategies and associated water allocations for designing a sustainable watershed management plan at least cost. Papers show applications in watershed management model that integrates both natural and human elements of a watershed system including the management of ground and surface water sources, water treatment and distribution systems, human demands,wastewatertreatment and collection systems, water reuse facilities,nonpotablewater distribution infrastructure, aquifer storage and recharge facilities, storm water, and land use

    Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria

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    [EN] Bridges, as an important component of infrastructure, are expected to meet all the requirements for a modern society. Traditionally, the primary aim in bridge design has been to achieve the lowest cost while guaranteeing the structural efficiency. However, concerns regarding building a more sustainable future have change the priorities of society. Ecological and durable structures are increasingly demanded. Under these premises, heuristic optimization methods provide an effective alternative to structural designs based on experience. The emergence of new materials, structural designs and sustainable criteria motivate the need to create a methodology for the automatic and accurate design of a real post-tensioned concrete bridge that considers all these aspects. For the first time, this thesis studies the efficient design of post-tensioned concrete box-girder road bridges from a sustainable point of view. This research integrates environmental, safety and durability criteria into the optimum design of the bridge. The methodology proposed provides multiple trade-off solutions that hardly increase the cost and achieve improved safety and durability. Likewise, this approach quantifies the sustainable criteria in economic terms, and evaluates the effect of these criteria on the best values of the variables. In this context, a multi-objective optimization is formulated to provide multiple trade-off and high-performing solutions that balance economic, ecologic and societal goals. An optimization design program selects the best geometry, concrete type, reinforcement and post-tensioning steel that meet the objectives selected. A three-span continuous box-girder road bridge located in a coastal region is selected for a case study. This approach provides vital knowledge about this type of bridge in the sustainable context. The life-cycle perspective has been included through a lifetime performance evaluation that models the bridge deterioration process due to chloride-induced corrosion. The economic, environmental and societal impacts of maintenance actions required to extend the service life are examined. Therefore, the proposed goals for an efficient design have been switch from initial stage to life-cycle consideration. Faced with the large computational time of multi-objective optimization and finite-element analysis, artificial neural networks (ANNs) are integrated in the proposed methodology. ANNs are trained to predict the structural response based on the design variables, without the need to analyze the bridge response. The multi-objective optimization problem results in a set of trade-off solutions characterized by the presence of conflicting objectives. The final selection of preferred solutions is simplified by a decision-making technique. A rational technique converts a verbal pairwise comparison between criteria with a degree of uncertainty into numerical values that guarantee the consistency of judgments. This thesis gives a guide for the sustainable design of concrete structures. The use of the proposed approach leads to designs with lower life-cycle cost and emissions compared to general design approaches. Both bridge safety and durability can be improved with a little cost increment by choosing the correct design variables. In addition, this methodology is applicable to any type of structure and material.[ES] Los puentes, como parte importante de una infraestructura, se espera que reúnan todos los requisitos de una sociedad moderna. Tradicionalmente, el objetivo principal en el diseño de puentes ha sido lograr el menor coste mientras se garantiza la eficiencia estructural. Sin embargo, la preocupación por construir un futuro más sostenible ha provocado un cambio en las prioridades de la sociedad. Estructuras más ecológicas y duraderas son cada vez más demandadas. Bajo estas premisas, los métodos de optimización heurística proporcionan una alternativa eficaz a los diseños estructurales basados en la experiencia. La aparición de nuevos materiales, diseños estructurales y criterios sostenibles motivan la necesidad de crear una metodología para el diseño automático y preciso de un puente real de hormigón postesado que considere todos estos aspectos. Por primera vez, esta tesis estudia el diseño eficiente de puentes de hormigón postesado con sección en cajón desde un punto de vista sostenible. Esta investigación integra criterios ambientales, de seguridad estructural y durabilidad en el diseño óptimo del puente. La metodología propuesta proporciona múltiples soluciones que apenas encarecen el coste y mejoran la seguridad y durabilidad. Al mismo tiempo, se cuantifica el enfoque sostenible en términos económicos, y se evalúa el efecto que tienen dichos criterios en el valor óptimo de las variables. En este contexto, se formula una optimización multiobjetivo que proporciona soluciones eficientes y de compromiso entre los criterios económicos, ecológicos y sociales. Un programa de optimización del diseño selecciona la mejor combinación de geometría, tipo de hormigón, armadura y postesado que cumpla con los objetivos seleccionados. Se ha escogido como caso de estudio un puente continuo en cajón de tres vanos situado en la costa. Este método proporciona un mayor conocimiento sobre esta tipología de puentes desde un punto de vista sostenible. Se ha estudiado el ciclo de vida a través de la evaluación del deterioro estructural del puente debido al ataque por cloruros. Se examina el impacto económico, ambiental y social que produce el mantenimiento necesario para extender la vida útil del puente. Por lo tanto, los objetivos propuestos para un diseño eficiente han sido trasladados desde la etapa inicial hasta la consideración del ciclo de vida. Para solucionar el problema del elevado tiempo de cálculo debido a la optimización multiobjetivo y el análisis por elementos finitos, se han integrado redes neuronales en la metodología propuesta. Las redes neuronales son entrenadas para predecir la respuesta estructural a partir de las variables de diseño, sin la necesidad de analizar el puente. El problema de optimización multiobjetivo se traduce en un conjunto de soluciones de compromiso que representan objetivos contrapuestos. La selección final de las soluciones preferidas se simplifica mediante una técnica de toma de decisiones. Una técnica estructurada convierte los juicios basados en comparaciones por pares de elementos con un grado de incertidumbre en valores numéricos que garantizan la consistencia de dichos juicios. Esta tesis proporciona una guía que extiende y mejora las recomendaciones sobre el diseño de estructuras de hormigón dentro del contexto de desarrollo sostenible. El uso de la metodología propuesta lleva a diseños con menor coste y emisiones del ciclo de vida, comparado con diseños que siguen metodologías generales. Los resultados demuestran que mediante una correcta elección del valor de las variables se puede mejorar la seguridad y durabilidad del puente con un pequeño incremento del coste. Además, esta metodología es aplicable a cualquier tipo de estructura y material.[CA] Els ponts, com a part important d'una infraestructura, s'espera que reunisquen tots els requisits d'una societat moderna. Tradicionalment, l'objectiu principal en el disseny de ponts ha sigut aconseguir el menor cost mentres es garantix l'eficiència estructural. No obstant això, la preocupació per construir un futur més sostenible ha provocat un canvi en les prioritats de la societat. Estructures més ecològiques i durables són cada vegada més demandades. Davall estes premisses, els mètodes d'optimització heurística proporcionen una alternativa eficaç als dissenys estructurals basats en l'experiència. L'aparició de nous materials, dissenys estructurals i criteris sostenibles motiven la necessitat de crear una metodologia per al disseny automàtic i precís d'un pont real de formigó posttesat que considere tots estos aspectos. Per primera vegada, esta tesi estudia el disseny eficient de ponts de formigó posttesat amb secció en calaix des d'un punt de vista sostenible. Esta investigació integra criteris ambientals, de seguretat estructural i durabilitat en el disseny òptim del pont. La metodologia proposada proporciona múltiples solucions que a penes encarixen el cost i milloren la seguretat i durabilitat. Al mateix temps, es quantifica l'enfocament sostenible en termes econòmics, i s'avalua l'efecte que tenen els dits criteris en el valor òptim de les variables. En este context, es formula una optimització multiobjetivo que proporciona solucions eficients i de compromís entre els criteris econòmics, ecològics i socials. Un programa d'optimització del disseny selecciona la millor geometria, tipus de formigó, armadura i posttesat que complisquen amb els objectius seleccionats. S'ha triat com a cas d'estudi un pont continu en calaix de tres vans situat en la costa. Este mètode proporciona un major coneixement sobre esta tipologia de ponts des d'un punt de vista sostenible. S'ha estudiat el cicle de vida a través de l'avaluació del deteriorament estructural del pont a causa de l'atac per clorurs. S'examina l'impacte econòmic, ambiental i social que produïx el manteniment necessari per a estendre la vida útil del pont. Per tant, els objectius proposats per a un disseny eficient han sigut traslladats des de l'etapa inicial fins a la consideració del cicle de vida. Per a solucionar el problema de l'elevat temps de càlcul degut a l'optimització multiobjetivo i l'anàlisi per elements finits, s'han integrat xarxes neuronals en la metodologia proposada. Les xarxes neuronals són entrenades per a predir la resposta estructural a partir de les variables de disseny, sense la necessitat d'analitzar el pont. El problema d'optimització multiobjetivo es traduïx en un conjunt de solucions de compromís que representen objectius contraposats. La selecció final de les solucions preferides se simplifica per mitjà d'una tècnica de presa de decisions. Una tècnica estructurada convertix els juís basats en comparacions per parells d'elements amb un grau d'incertesa en valors numèrics que garantixen la consistència dels dits juís. Esta tesi proporciona una guia que estén i millora les recomanacions sobre el disseny d'estructures de formigó dins del context de desenrotllament sostenible. L'ús de la metodologia proposada porta a dissenys amb menor cost i emissions del cicle de vida, comparat amb dissenys que seguixen metodologies generals. Els resultats demostren que per mitjà d'una correcta elecció del valor de les variables es pot millorar la seguretat i durabilitat del pont amb un xicotet increment del cost. A més, esta metodologia és aplicable a qualsevol tipus d'estructura i material.García Segura, T. (2016). Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/73147TESI

    Optimization for Decision Making II

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    In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

    Minimization of distance between group and individualdecisions using intelligent stochastic algorithms for waterand agricultural management

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    Donošenje odluka u poljoprivredi i vodoprivredi podrazumeva uvažavanje ekonomskih, društvenih i kriterijuma zaštite životne sredine. Proces je složen jer se odluke zbog nemogućnosti kvantifikacije često donose na osnovu kvalitativnih podataka, ili još češće, u kombinaciji sa postojećim kvantitativnim podacima. Analitički hijerarhijski proces (AHP) je teorijsko-metodološki koncept višekriterijumske analize i optimizacije za podršku složenih procesa individualnog i grupnog odlučivanja, koji se pokazao kao jedan od najpogodnijih da podrži takve procese i zato je u svetu široko rasprostranjen. Kod odlučivanja u poljoprivredi i vodoprivredi, zbog složenosti procesa, podrazumeva se interdisciplinarni pristup sa učešćem više interesnih strana (donosilaca odluka). Kod grupnih primena AHP, odluka se najčešće dobija objedinjavanjem individualnih ocena ili objedinjavanjem individualnih prioriteta. U novije vreme AHP se sve više kombinuje sa modelima za postizanje konsenzusa. U disertaciji je predložen mogući novi način objedinjavanja individualnih odluka u grupnu zasnovan na minimizaciji odstupanja grupne od individualnih odluka. Ideja je da se na osnovu individualnih vrednovanja elemenata odlučivanja po metodologiji AHP generiše grupni vektor pomoću algoritma simuliranog kaljenja (SA - simulated annealing) iz klase inteligentnih stohastičkih optimizacionih algoritama, posebno pogodnog kada rešenje treba tražiti u beskonačnim diskretnim prostorima. Pošto se u AHP mogu koristiti različiti metodi za određivanje vektora prioriteta, koji se uobičajeno nazivaju "prioritizacioni metodi", da bi se postupak objedinjavanja učinio nezavisnim od metoda prioritizacije, u disertaciji je definisan univerzalni pokazatelj grupne konzistentnosti nazvan grupno euklidsko rastojanje (GED - group Euclidean distance). Inteligentnim približavanjem grupnog vektora prioriteta individualnim odlukama, odnosno minimizacijom GED, identifikuje se grupni vektor koji dovoljno dobro predstavlja individualne odluke. Predloženi postupak nazvan je metod SAAP (SA aggregation procedure). Za testiranje ispravnosti metoda SAAP korišćena su tri primera i rezultati predloženog metoda su poređeni sa rezultatima najčešće korišćenih kombinacija metoda grupnog objedinjavanja, konsenzus modela i metoda prioritizacije koje su nazvane šeme objedinjavanja. Dobijeni rezultati su pokazali da je SAAP konkurentan sa ostalim šemama objedinjavanja. U disertaciji je predložena i transparentna metodologija za grupno višekriterijumsko ocenjivanje pogodnosti lokaliteta za navodnjavanje na datoj teritoriji. U FAO dokumentima je sugerisano da treba vršiti ocenu pogodnosti lokaliteta za navodnjavanje a ne isključivo zemljišta i da treba uzeti u obzir sve faktore (kriterijume) koji utiču na uspešnost uvođenja navodnjavanja. Višekriterijumsko određivanje pogodnosti lokaliteta za navodnjavanje je zasnovano na kombinaciji AHP i geografskog informacionog sistema (GIS) u grupnom kontekstu. Metodologija se sastoji iz četiri faze. U prvoj fazi se identifikuju podkriterijumi za određivanje pogodnosti lokaliteta za navodnjavanje od interesa za dato područje. Podkriterijumi se zatim grupišu u kriterijume (kao što su osobine zemljišta, klima, socio-ekonomski kriterijum, tehničko-pravni kriterijum i zaštita životne sredine) i na taj način se formira hijerarhija problema odlučivanja. Identifikovani donosioci odluka vrednuju elemente hijerarhije, takođe po metodu AHP, a zatim se vrednovanja koriste za izračunavanje individualnih težina podkriterijuma. Sastavni deo druge faze metodologije je predloženi višekriterijumski metod za određivanje težina donosilaca odluka. Koristeći individualne težine podkriterijuma izračunate u prvoj i težine donosilaca odluka izračunate u ovoj fazi, "otežanim" aritmetičkim osrednjavanjem određuju se grupne (konačne težine) podkriterijuma (GIS slojeva). Da bi rastersko preklapanje slojeva bilo moguće, u trećoj fazi se standardizuju GIS slojevi. Množenjem vrednosti piksela u svakom sloju sa pripadajućim grupnim težinama slojeva i njihovim sabiranjem dobija se konačna mapa pogodnosti lokaliteta za navodnjavanje i ona predstavlja osnovu za definisanje prostornih prioriteta izgradnje novih sistema za navodnjavanje na datom području. U četvrtoj fazi (analiza osetljivosti) se prvo isključuju slojevi koji predstavljaju antropogene podkriterijume, a zatim i slojevi zasnovani na prirodnim  karakteristikama. Na ovaj način se dobijaju dve nove mape pogodnosti lokaliteta za navodnjavanje koje pružaju dodatne informacije za definisanje prostornih prioriteta izgradnje novih sistema za navodnjavanje.Agricultural and water management decision problems are usually complex because many criteria (such as economical, social and environmental) need to be considered. For this kind of problems, decision making process is often based only on qualitative data or sometimes on combination of quantitative and qualitative data. The Analytic Hierarchy Process (AHP) is a multi criteria decision-making method that has been used in many applications related with decision-making based on qualitative data, and is applicable to both individual and group decision making situations. Because of the increasing complexity of decision making problems in agriculture and water management and the necessity to include all interested participants in problem solving, nowadays many AHP decision making processes take place in group settings. There are various aggregation procedures for obtaining a group priority vector within AHP-supported decision making, the most common of which are the aggregation of individual judgments (AIJ), aggregation of individual priorities (AIP) and aggregations based on consensus models. A heuristic stochastic approach to group decision making is proposed in this dissertation as an aggregation procedure which searches for the best group priority vector for a given node in an AHP– generated hierarchy. The group Euclidean distance (GED) is used as a group consistency measure for deriving the group priority vector for a given node in the AHP hierarchy where all participating individuals already set their judgments. The simulated annealing (SA) algorithm tries to minimize the GED, of the process of which can be considered an objective search for maximum consensus between individuals within the group. The group priority vector obtained in this way is invariant to any prioritization method; that is, there is no need to have individual priority vectors as is required by some other aggregation procedures. This approach is named simulated annealing aggregation procedure (SAAP). In order to check validity of this approach, three examples are used to compare it's results with results obtained by various combinations of aggregations (AIJ and AIP), consensus models and prioritization methods. In this dissertation, SAAP and other known combinations of aggregation procedures and prioritization methods are labeled as aggregation schemes. Results shows that the SAAP performs better or at least equally to several other well known combinations of prioritization and aggregation in AHP group decision making frameworks. The second objective of this dissertation was to establish a transferable and transparent procedure for multi criteria group evaluations of land suitability for irrigation. The multi criteria approach is recommended because according to FAO documents all aspects of the problem (environment, social aspect, economy) need to be considered in the evaluation, not just soil. To make a decision on where to build new, sustainable irrigation systems, here we propose multi criteria group decision making approach which combines AHP and Geographic Information System (GIS). This approach is presented as four-phase decision making framework. In the first phase, subcriteria relevant in validating land suitability were grouped into five major criteria: soil, climate, economy, infrastructure and environment. Considered as spatially determined decision making elements, criteria and subcriteria were evaluated within the AHP framework by identified experts in the subject area. In the second phase new multi criteria method is developed for deriving decision makers' weights. Using this weights and individual priority weights of subcriteria from first phase final group weights of subcriteria (GIS layers) are computed. In third phase each subcriterion (GIS layer) is standardized. Then, the cell values in each of the subcriterion layers are multiplied by the corresponding final weights of the subcriteria and aggregated into the final land suitability maps for irrigation in GIS environment. Finally, in the fourth phase, a sensitivity analysis is applied to check the influence of different criteria on the result. By changing the weights of criteria, two more maps were generated showing land suitability for irrigation regarding natural conditions and economy-water infrastructure

    The triangle assessment method: a new procedure for eliciting expert judgement

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    The Analytic Hierarchy Process (AHP) is one of the most widely used Multi-Criteria Decision-Making methods worldwide. As such, it is subject to criticisms that highlight some potential weaknesses. In this study, we present a new Multi-Criteria Decision-Making method denominated the “Triangular Assessment Method” (referred to by its Spanish abbreviation, MTC©). The MTC© aims to make use of the potential of AHP while avoiding some of its drawbacks. The main characteristics and advantages of the MTC© can be summarised as follows: (i) evaluation of criteria, and of the alternative options for each criterion, in trios instead of pairs; (ii) elimination of discrete scales and values involved in judgements; (iii) a substantial reduction in the number of evaluations (trios) relative to the corresponding number of pairs which would have to be considered when applying the AHP method; (iv) consistent decision-making; (v) introduction of closed cyclical series for comparing criteria and alternatives; and (vi) the introduction of opinion vectors and opinion surfaces. This new method is recommended for supporting decision-making with large numbers of subjective criteria and/or alternatives and also for group decisions where the consensus must be evaluated. The MTC© provides a different promising perspective in decision-making and could lead to new research lines in the field of information systems.This work was supported by the Galician Regional Government [“Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas, modalidade de Grupos de Referencia Competitiva” for the period 2006–2017] and by the European Union [ERDF program]. Likewise, the authors thank Daniele de Rigo, Dora Henriques and Cesar Pérez-Cruzado, because his comments improved notably this manuscript.info:eu-repo/semantics/publishedVersio

    Explainable clinical decision support system: opening black-box meta-learner algorithm expert's based

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    Mathematical optimization methods are the basic mathematical tools of all artificial intelligence theory. In the field of machine learning and deep learning the examples with which algorithms learn (training data) are used by sophisticated cost functions which can have solutions in closed form or through approximations. The interpretability of the models used and the relative transparency, opposed to the opacity of the black-boxes, is related to how the algorithm learns and this occurs through the optimization and minimization of the errors that the machine makes in the learning process. In particular in the present work is introduced a new method for the determination of the weights in an ensemble model, supervised and unsupervised, based on the well known Analytic Hierarchy Process method (AHP). This method is based on the concept that behind the choice of different and possible algorithms to be used in a machine learning problem, there is an expert who controls the decisionmaking process. The expert assigns a complexity score to each algorithm (based on the concept of complexity-interpretability trade-off) through which the weight with which each model contributes to the training and prediction phase is determined. In addition, different methods are presented to evaluate the performance of these algorithms and explain how each feature in the model contributes to the prediction of the outputs. The interpretability techniques used in machine learning are also combined with the method introduced based on AHP in the context of clinical decision support systems in order to make the algorithms (black-box) and the results interpretable and explainable, so that clinical-decision-makers can take controlled decisions together with the concept of "right to explanation" introduced by the legislator, because the decision-makers have a civil and legal responsibility of their choices in the clinical field based on systems that make use of artificial intelligence. No less, the central point is the interaction between the expert who controls the algorithm construction process and the domain expert, in this case the clinical one. Three applications on real data are implemented with the methods known in the literature and with those proposed in this work: one application concerns cervical cancer, another the problem related to diabetes and the last one focuses on a specific pathology developed by HIV-infected individuals. All applications are supported by plots, tables and explanations of the results, implemented through Python libraries. The main case study of this thesis regarding HIV-infected individuals concerns an unsupervised ensemble-type problem, in which a series of clustering algorithms are used on a set of features and which in turn produce an output used again as a set of meta-features to provide a set of labels for each given cluster. The meta-features and labels obtained by choosing the best algorithm are used to train a Logistic regression meta-learner, which in turn is used through some explainability methods to provide the value of the contribution that each algorithm has had in the training phase. The use of Logistic regression as a meta-learner classifier is motivated by the fact that it provides appreciable results and also because of the easy explainability of the estimated coefficients

    A Pairwise Comparison Matrix Framework for Large-Scale Decision Making

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    abstract: A Pairwise Comparison Matrix (PCM) is used to compute for relative priorities of criteria or alternatives and are integral components of widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, a PCM suffers from several issues limiting its application to large-scale decision problems, specifically: (1) to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker (DM), (2) inconsistent and (3) imprecise preferences maybe obtained due to the limited cognitive power of DMs. This dissertation proposes a PCM Framework for Large-Scale Decisions to address these limitations in three phases as follows. The first phase proposes a binary integer program (BIP) to intelligently decompose a PCM into several mutually exclusive subsets using interdependence scores. As a result, the number of pairwise comparisons is reduced and the consistency of the PCM is improved. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets. This is done to derive the global weights of the elements from the original PCM. The proposed BIP is applied to both AHP and ANP methodologies. However, it is noted that the optimal number of subsets is provided subjectively by the DM and hence is subject to biases and judgement errors. The second phase proposes a trade-off PCM decomposition methodology to decompose a PCM into a number of optimally identified subsets. A BIP is proposed to balance the: (1) time savings by reducing pairwise comparisons, the level of PCM inconsistency, and (2) the accuracy of the weights. The proposed methodology is applied to the AHP to demonstrate its advantages and is compared to established methodologies. In the third phase, a beta distribution is proposed to generalize a wide variety of imprecise pairwise comparison distributions via a method of moments methodology. A Non-Linear Programming model is then developed that calculates PCM element weights which maximizes the preferences of the DM as well as minimizes the inconsistency simultaneously. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.Dissertation/ThesisPh.D. Industrial Engineering 201
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