Selection of subcontractors using ordinal ranking methods based on Condorcet approach

A choice of a subcontractor may have critical impact on realization of the project, it has influence on the cost, duration, and quality. Selection of the best sucontractor can be defined as multiple criteria decision making problem (MCDM) of choosing a proper offer from set of alternatives evaluated by using set of criteria. Decision maker should determine the criteria as objective and measurable. Significance of decision making problem is presented by large amount of theories and methods developed for solving MCDM problems and number of criteria considered in these problems. A Condorcet method (formulated over two centuries ago) is commonly accepted for democratic (majority of criteria determines the winner) and fair election – a Condorcet winner is the alternative which is preferred in all pair-wise comparisons. According to social choice theory where a Condorcet winner cannot be obtained from a set of alternatives, the best solution is close to being a Condorcet winner. The paper presents four selection methods of the best alternative that is as close as possible to being a Condorcet winner and contains examples of a subcontractor selection using only ordinal scales of evaluation of alternatives.A choice of a subcontractor may have critical impact on realization of the project, it has influence on the cost, duration, and quality. Selection of the best sucontractor can be defined as multiple criteria decision making problem (MCDM) of choosing a proper offer from set of alternatives evaluated by using set of criteria. Decision maker should determine the criteria as objective and measurable. Significance of decision making problem is presented by large amount of theories and methods developed for solving MCDM problems and number of criteria considered in these problems. A Condorcet method (formulated over two centuries ago) is commonly accepted for democratic (majority of criteria determines the winner) and fair election – a Condorcet winner is the alternative which is preferred in all pair-wise comparisons. According to social choice theory where a Condorcet winner cannot be obtained from a set of alternatives, the best solution is close to being a Condorcet winner. The paper presents four selection methods of the best alternative that is as close as possible to being a Condorcet winner and contains examples of a subcontractor selection using only ordinal scales of evaluation of alternatives

Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

Consensus theories: an oriented survey

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2010.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.57 - ISSN : 1955-611XThis article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Cet article présente une vue d'ensemble de sept directions de recherche en théorie du consensus : résultats arrowiens, règles d'agrégation définies au moyen de fédérations, règles définies au moyen de distances, solutions de tournoi, domaines restreints, théories abstraites du consensus, questions de complexité et d'algorithmique. Ce panorama est orienté dans la mesure où il présente principalement – mais non exclusivement – les travaux les plus significatifs obtenus – quelquefois avec d'autres chercheurs – par une équipe de chercheurs français qui sont – ou ont été – membres pléniers ou associés du Centre d'Analyse et de Mathématique Sociale (CAMS)

Analyse d'heuristiques de recherche locale pour l'ordonnancement linéaire

RÉSUMÉ Ce mémoire porte sur le problème d'ordonnancement linéaire (LOP -- Linear Ordering Problem) et le problème équivalent de Feedback Arc Set (FASP). Ces deux problèmes NP-difficiles se distinguent surtout par le type d'exemplaires traités et ont chacun plusieurs applications pratiques dans divers domaines. Alors que le LOP est bien étudié dans la littérature, très peu d'heuristiques sont proposées pour le FASP. Les heuristiques les plus efficaces pour traiter ces problèmes, comme l'algorithme mémétique et la recherche locale itérée, sont des heuristiques hybrides et utilisent à répétition la recherche locale sous forme de descentes. L'implémentation d'un opérateur de recherche est donc critique à la performance de ces heuristiques. L'objectif de ce travail est donc d'implémenter des heuristiques de recherche locale de façon efficace pour le LOP et pour le FASP. Dans ce travail, nous décrivons les heuristiques appliquées au LOP dans la littérature et particulièrement les techniques existantes pour effectuer la recherche locale. Les méthodes les plus efficaces sont alors implémentées et plusieurs améliorations sont proposées pour accélérer le traitement des exemplaires de grande taille ou de faible densité. Par la suite, nous présentons une étude expérimentale des divers opérateurs de recherche en comparant leurs temps d'exécutions pour effectuer une descente sur des exemplaires générés aléatoirement de taille et densité variables. De plus, un modèle simple est utilisé pour décomposer le temps d'exécution en plusieurs facteurs afin d'analyser en détail l'impact de l'implémentation d'un opérateur et de la politique de recherche appliquée. Nous observons que les opérateurs de recherche développés sont très efficaces dans différentes situations et permettent d'améliorer les méthodes existantes. Nous proposons alors des recommandations pour sélectionner l'opérateur approprié selon le type d'exemplaire du problème à traiter en plus de donner des conseils pour son implémentation. En particulier, nous présentons le meilleur opérateur à utiliser pour des exemplaires FASP alors que ce sujet n'a pas été abordé auparavant. Les divers opérateurs de recherche décrits pourront alors être incorporés dans une heuristique hybride afin d'accélérer son exécution. ----------ABSTRACT This thesis focuses on the Linear Ordering Problem (LOP) and the equivalent Feedback Arc Set Problem (FASP). Both NP-hard problems differ mainly by the type of instances they handle and they each have several practical applications in various fields. While the LOP is much studied in the literature, very few heuristics are proposed for the FASP. The most efficient heuristics proposed to tackle these problems, such as memetic algorithm and iterated local search, are hybrid heuristics and use local search repeatedly in a hill climbing (HC) operator. The implementation of a HC operator is critical to the performance of these heuristics. The objective of this work is to implement local search heuristics efficiently for the LOP and the FASP. In this work we describe the heuristics applied to the LOP in the literature and focus on existing techniques to perform local search. The most efficient methods are then implemented and several improvements are proposed to speed up the execution for large or sparse instances. Thereafter, we present an extensive experimental study of the different variants of the HC operator by comparing their running times to reach a local optimum on a large set of randomly generated problem instances which have various sizes and densities. In addition, a simple model is used to decompose the running time into several factors to analyze in detail the impact of the implementation of an operator and the search policy. We observe that the proposed variants of the HC operator are very efficient in different situations and can improve existing methods. We then present recommendations to select an appropriate HC operator according to the type of problem instances to tackle. We also provide some advice for its implementation. Notably, we present the best HC operator to solve FASP instances. This issue has not been addressed before. The various HC operators described can then be incorporated into an hybrid heuristic to speed up its execution

Interruptional Activity and Simulation of Transposable Elements

Transposable elements (TEs) are interspersed DNA sequences that can move or copy to new positions within a genome. The active TEs along with the remnants of many transposition events over millions of years constitute 46.69% of the human genome. TEs are believed to promote speciation and their activities play a significant role in human disease. The 22 AluY and 6 AluS TE subfamilies have been the most active TEs in recent human history, whose transposition has been implicated in several inherited human diseases and in various forms of cancer by integrating into genes. Therefore, understanding the transposition activities is very important. Recently, there has been some work done to quantify the activity levels of active Alu transposable elements based on variation in the sequence. Here, given this activity data, an analysis of TE activity based on the position of mutations is conducted. Two different methods/simulations are created to computationally predict so-called harmful mutation regions in the consensus sequence of a TE; that is, mutations that occur in these regions decrease the transposition activities dramatically. The methods are applied to AluY, the youngest and most active Alu subfamily, to identify the harmful regions laying in its consensus, and verifications are presented using the activity of AluY elements and the secondary structure of the AluYa5 RNA, providing evidence that the method is successfully identifying harmful mutation regions. A supplementary simulation also shows that the identified harmful regions covering the AluYa5 RNA functional regions are not occurring by chance. Therefore, mutations within the harmful regions alter the mobile activity levels of active AluY elements. One of the methods is then applied to two additional TE families: the Alu family and L1 family, in detecting the harmful regions in these elements computationally. Understanding and predicting the evolution of these TEs is of interest in understanding their powerful evolutionary force in shaping their host genomes. In this thesis, a formal model of TE fragments and their interruptions is devised that provides definitions that are compatible with biological nomenclature, while still providing a suitable formal foundation for computational analysis. Essentially, this model is used for fixing terminology that was misleading in the literature, and it helps to describe further TE problems in a precise way. Indeed, later chapters include two other models built on top of this model: the sequential interruption model and the recursive interruption model, both used to analyze their activity throughout evolution. The sequential interruption model is defined between TEs that occur in a genomic sequence to estimate how often TEs interrupt other TEs, which has been shown to be useful in predicting their ages and their activity throughout evolution. Here, this prediction from the sequential interruptions is shown to be closely related to a classic matrix optimization problem: the Linear Ordering Problem (LOP). By applying a well-studied method of solving the LOP, Tabu search, to the sequential interruption model, a relative age order of all TEs in the human genome is predicted from a single genome. A comparison of the TE ordering between Tabu search and the method used in [47] shows that Tabu search solves the TE problem exceedingly more efficiently, while it still achieves a more accurate result. As a result of the improved efficiency, a prediction on all human TEs is constructed, whereas it was previously only predicted for a minority fraction of the set of the human TEs. When many insertions occurred throughout the evolution of a genomic sequence, the interruptions nest in a recursive pattern. The nested TEs are very helpful in revealing the age of the TEs, but cannot be fully represented by the sequential interruption model. In the recursive interruption model, a specific context- free grammar is defined, describing a general and simple way to capture the recursive nature in which TEs nest themselves into other TEs. Then, each production of the context-free grammar is associated with a probability to convert the context-free grammar into a stochastic context-free grammar that maximizes the applications of the productions corresponding to TE interruptions. A modified version of an algorithm to parse context-free grammars, the CYK algorithm, that takes into account these probabilities is then used to find the most likely parse tree(s) predicting the TE nesting in an efficient fashion. The recursive interruption model produces small parse trees representing local TE interruptions in a genome. These parse trees are a natural way of grouping TE fragments in a genomic sequence together to form interruptions. Next, some tree adjustment operations are given to simplify these parse trees and obtain more standard evolutionary trees. Then an overall TE-interaction network is created by merging these standard evolutionary trees into a weighted directed graph. This TE-interaction network is a rich representation of the predicted interactions between all TEs throughout evolution and is a powerful tool to predict the insertion evolution of these TEs. It is applied to the human genome, but can be easily applied to other genomes. Furthermore, it can also be applied to multiple related genomes where common TEs exist in order to study the interactions between TEs and the genomes. Lastly, a simulation of TE transpositions throughout evolution is developed. This is especially helpful in understanding the dynamics of how TEs evolve and impact their host genomes. Also, it is used as a verification technique for the previous theoretical models in the thesis. By feeding the simulated TE remnants and activity data into the theoretical models, a relative age order is predicted using the sequential interruption model, and a quantified correlation between this predicted order and the input age order in the simulation can be calculated. Then, a TE-interaction network is constructed using the recursive interruption model on the simulated data, which can also be converted into a linear age order by feeding the adjacency matrix of the network to Tabu search. Another correlation is calculated between the predicted age order from the recursive interruption model and the input age order. An average correlation of ten simulations is calculated for each model, which suggests that in general, the recursive interruption model performs better than the sequential interruption model in predicting a correct relative age order of TEs. Indeed, the recursive interruption model achieves an average correlation value of ρ = 0.939 with the correct simulated answer