Thesis (PhD (Logistics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Computerised sugarcane harvest scheduling decision support is an active fi eld of research which ties in closely with the broader problem of automating and streamlining the various activities in the sugar supply chain. In this dissertation, the problem of providing decision support with respect to sugarcane harvesting decisions is defined within a number of contexts, each representing a typical kind of organisation of sugarcane farmers into a cohesive decision making unit with its speci fic requirements and limitations that exist in practice. A number of variations relevant to these contexts of an overarching tactical sugarcane harvest scheduling problem (THSP) are considered and solved in this dissertation. The THSP is the problem of providing objective, responsible decision support to persons charged with the task of determining optimal harvesting dates for a set of sugarcane fields across an entire season. Sugarcane fields typically diff er in terms of the age, variety, life-cycle stage and in many other properties of the cane grown on them. The growth of sugarcane crops may also be a ffected by environmental conditions such as accidental fires, frosts or storms which have a detrimental e ffect on crop-value. Since sugarcane is a living organism, its properties change over time, an so does the potential pro t associated with it. The practicalities of farming cause further complication of the problem (for example, seasonal changes alter the conditions under which the crop is harvested and transported). The rainy season carries with it the added cost of disallowing long-range vehicles to drive into the fields, forcing the unloading and reloading of cane at so-called loading zones. Other considerations, such as the early ploughing out of fields to allow them to fallow before being replanted, compounds the THSP into a multi-faceted difficult problem requiring efficient data management, mathematical modelling expertise and efficient computational work. In the literature the THSP has been viewed from many different standpoints and within many contexts, and a variety of operations research methodologies have been employed in solving the problem in part. There is, however, no description in the literature of a solution to the THSP that takes the negative e ffects of extreme environmental conditions on the quality of a harvesting schedule into account in a scienti fically justifi able manner; most models in the literature are based on optimising sucrose yield alone under normal conditions, rendering weak schedules in practice. The scope of the modelling and solution methodologies employed in this dissertation towards solving the THSP is restricted to integer programming formulations and approximate solution methods. The parameters associated with these models were determined empirically using historical data, as well as previous work on deterioration of sugarcane following environmental and other events. The THSP is solved in this dissertation by designing a generic architecture for a conceptual decision support system (DSS) for the THSP in the various contexts referred to above, which is capable of accommodating the e ects of extra-ordinary environmental conditions, as well as the introduction of a computer-implemented version of a real DSS for the THSP conforming to the framework of this generic architecture. The DSS building blocks include prediction models for sugarcane yield, sugarcane recoverable value under normal circumstances, the costs associated with a harvesting schedule and the negative e ects on sugarcane recoverable value of extraordinary environmental conditions. The working of the DSS is based on a combinatorial optimisation model resembling the well-known asymmetric traveling salesman problem with time-dependent costs which is solved approximately by means of an attribute-based tabu search in which both local and global moves have been incorporated. The DSS is also validated by experienced sugarcane industry experts in terms of the practicality and quality of the schedules that it produces. / AFRIKAANSE OPSOMMING: Gerekenariseerde besluitsteun vir die skedulering van suikerriet-oeste is 'n aktiewe navorsingsveld wat nou verwant is aan die bre ër probleem van die outomatisering en vaartbelyning van 'n verskeidenheid aktiwiteite in die suikervoorsieningsketting. Die probleem van die daarstelling van steun rakende suikkerriet oestingsbesluite word in hierdie proefskrif in 'n aantal kontekste oorweeg, elk met betrekking tot 'n tipiese soort organisasie van suikerrietboere in 'n samehorige besluitnemingseenheid met sy spesi eke vereistes en beperkings in die praktyk. Verskeie variasies van 'n oorkoepelende taktiese suikerriet-oesskeduleringsprobleem (TSOSP) wat in hierde kontekste relevant is, naamlik die probleem om objektiewe, verantwoordbare steun aan besluitnemers te bied wat verantwoordelik is vir die bepaling van optimale oesdatums vir 'n versameling suikerrietplantasies oor die bestek van 'n hele seisoen, word in hierdie proefskrif bestudeer en opgelos. Suikerrietplantasies verskil tipies in terme van ouderdom, gewastipe, posisie in die lewensiklus, en vele ander eienskappe van die suikerriet wat daar groei. Omgewingstoestande, soos onbeplande brande, ryp of storms, het verder ook 'n negatiewe impak op die waarde van suikerriet op sulke plantasies. Omdat suikerriet 'n lewende organisme is, verander die eienskappe daarvan oor tyd, en so ook die potensi ele wins wat daarmee geassosieer word. Boerderypraktyke bemoeilik verder die skeduleringsprobleem onder beskouing (seisoenale veranderings beïnvloed byvoorbeeld die wyse waarop suikerriet ge-oes en vervoer word). Addisionele koste gaan voorts met die re ënseisoen gepaard, omdat die plantasies dan nie toeganklik is vir langafstand transportvoertuie nie en suikerriet gevolglik na spesiale laaisones gekarwei moet word voordat dit op hierdie voertuie gelaai kan word. Ander oorwegings, soos die vroe ë uitploeg van plantasies sodat die grond kan rus voordat nuwe suikerriet aangeplant word, veroorsaak dat die TSOSP 'n moeilike multi-faset probleem is, wat goeie databestuur, wiskundige modelleringsvernuf en doeltreff ende rekenaarwerk vereis. Die TSOSP word in die literatuur vanuit verskillende standpunte en in verskeie kontekste oorweeg, en 'n aantal uiteenlopende operasionele navorsingsmetodologie ë is al ingespan om hierdie probleem ten dele op te los. Daar is egter geen poging in die literatuur om 'n oplossing vir die TSOSP daar te stel waarin daar op 'n wetenskaplik-verantwoordbare wyse voorsiening gemaak word vir die negatiewe e ffekte wat uitsonderlike omgewingstoestande op die kwaliteit van oesskedules het nie; die meeste modelle in die literatuure is op slegs sukrose-opbrengs onder normale omstandighede gebaseer, wat lei na swak skedules in die praktyk. Die bestek van die wiskundige modellerings- en gepaardgaande oplossings-metodologie ë word in hierdie proefskrif vir die TSOSP beperk tot onderskeidelik heeltallige programmeringsformulerings en die bepaling van benaderde oplossings deur lokale soekprosedures. Die parameters wat met hierdie modelle en soekmetodes geassosieer word, word empiries bepaal deur gebruikmaking van historiese data asook bestaande werk oor die degradering van suikerriet as gevolg van omgewings- en ander eksterne faktore. Die TSOSP word in hierdie proefskrif opgelos deur die ontwerp van 'n generiese argitektuur vir 'n konseptuele besluitsteunstelsel (BSS) vir die TSOSP in die onderskeie kontekste waarna hierbo verwys word en wat die e ekte van uitsonderlike omgewingsfaktore in ag neem, asook die daarstelling van 'n rekenaar-ge ïmplementeerde weergawe van 'n daadwerklike BSS vir die TSOSP wat in die raamwerk van hierdie generiese argitektuur pas. Die boustene van hierdie BSS sluit modelle in vir die voorspelling van suikerrietopbrengs, die herwinbare waarde van suikerriet onder normale omstandighede, die verwagte koste geassosieer met 'n oesskedule en die negatiewe e ekte van omgewingsfaktore op die herwinbare waarde van suikerriet. Die werking van die BSS is gebaseer op 'n kombinatoriese optimeringsprobleem wat aan die welbekende asimmetriese handelreisigersprobleem met tyd-afhanklike kostes herinner, en hierdie model word benaderd opgelos deur middel van 'n eienskap-gebaseerde tabu-soektog waarin beide lokale en globale skuiwe ge ïnkorporeer is. Die BSS word ook gevalideer in terme van die haalbaarheid en kwaliteit van die skedules wat dit oplewer, soos geassesseer deur ervare kundiges in die suikerrietbedryf.

The implementation of a low carbon electricity system within the GB requires a significant change to the generation mix with an increasing role for renewable generation. Much of this generation will be intermittent. To date system balancing has largely relied on predicting demand and ensuring provision. With substantial intermittency, continuation of this paradigm necessitates significant investment in peaking plant and/or storage. However, some of this investment can be avoided by harnessing the flexibility inherent in many electrical loads. Despite the attractiveness of such services, we do not see their large-scale implementation. The aim of this thesis is to consider why. A historical analysis reveals that both nationalisation and subsequent privatisation provide precedents for significant structural change as the integration of large-scale flexible demand might require. The need for political will is identified as a crucial enabling factor. Without an ideological driver, however, a perception of economic and/or technological risk can preclude the implementation of supportive policy. This perception is addressed through demonstration. An effective demonstration must show the ability to aggregate many small loads in a coordinated manner. A genetic algorithm that provides this core dispatch and optimisation capability is presented. This algorithm is shown to be effective in aggregating many small loads to provide a net effect that can be used as a balancing service and to do so in an optimal way considering both cost and reliability. Having demonstrated feasibility appropriate incentives must be created. An initial outline for a framework based on SysML is presented that can be used to identify where structural barriers to implementation are present to aid the design of appropriate policy incentives.

La validation des charges utiles des satellites de télécommunication nécessite des opérations coûteuses en temps et en personnel. Ce coût augmente régulièrement du fait de la complexité croissante des charges utiles. Il est donc crucial pour Astrium d'optimiser la réalisation des opérations de test. L'objectif de cette thèse CIFRE menée en collaboration entre Astrium et l'Onera est de développer une suite logicielle d'aide à la génération de plans de test. Le problème de génération de plan de test a été modélisé sous forme de graphe orienté à états. La NP-complétude de ce problème a été établie. Des modèles mathématiques ont été construits en programmation linéaire en nombres entiers et en programmation par contraintes en vue d'une résolution par des solveurs génériques. Cependant, ces solveurs génériques se sont heurtés à des problèmes d'insuffisance de mémoire liés à la très grande taille des instances à traiter. Ceci nous a conduits à développer un solveur spécialisé à base de recherche arborescente faisant appel à des mécanismes spécifiques de choix de variables et de valeurs, de propagation de contraintes, de calcul de borne, de retour-arrière, d'apprentissage et de redémarrage. Un solveur spécialisé à base de recherche locale a été développé en parallèle. Les résultats obtenus par ces différents solveurs avec différents paramétrages ont pu être comparés. / Telecommunication satellite payload validation requires operations which are expensive in terms of time and manpower. This cost is constantly increasing as the payloads become more and more complex. It is crucial for Astrium to optimise the testing phase to keep these costs under control. The objective of this CIFRE thesis, conducted in collaboration with Astrium and Onera, is to develop a software suite to help generate test plans for the payloads.The problem of generating test plans was modeled using the form of a directed graph with states. The NP-completeness of this problem was proven. Mathematical models were built using integer linear programming and constraint programming with a view to solving the problems using generic solvers. However, these generic solvers had problems due to insufficient memory on account of the large size of instances to be handled. These problems led us to develop a specialised solver using a tree search, with special mechanisms for choosing variables and values, propagating constraints, computing bounds, backjumping,learning, and restarting. A specialised solver based on local search was developed in parallel.The results obtained by these different solvers with different settings were compared.

La théorie de la rigidité étudie l'unicité des réalisations des graphes, i.e., des charpentes. Initialement motivée par l'ingénierie des structures, la théorie de la rigidité trouve aujourd'hui des applications dans plusieurs domaines importants comme la prédiction de la flexibilité des protéines, la conception assistée par ordinateur, la localisation dans les réseaux des capteurs, etc. Cette thèse traite une grande variété de problèmes concernant différents types de rigidité, qui correspondent à différents niveaux d'unicité (locale/infinitésimale, globale et universelle) dans des modèles variés de charpentes. D'abord, nous développons des résultats sur la construction récursive et la décomposition des graphes avec des conditions mixtes de sparsité ainsi que des résultats sur le packing des arborescences avec des contraintes de matroïde. Ces résultats sont alors utilisés pour obtenir des caractérisations de la rigidité infinitésimale des charpentes avec des contraintes mixtes. Nous étudions aussi l'effet des opérations d'extension sur des charpentes et étendons un résultat connu sur la préservation de la rigidité globale d'$1$-extension dans les charpentes à direction et à longueur de la dimension deux aux dimensions supérieures. Pour la rigidité universelle, un sujet que l'on connait très peu, nous obtenons une caractérisation complète pour la classe des charpentes biparties complètes sur la ligne. Nous généralisons aussi une condition suffisante pour la rigidité universelle des charpentes en permettant des positions non générales. / The theory of rigidity studies the uniqueness of realizations of graphs, i.e., frameworks. Originally motivated by structural engineering, rigidity theory nowadays finds applications in many important problems such as predicting protein flexibility, Computer-Aided Design, sensor network localization, etc. The present thesis treats a wide range of problems concerning different kinds of rigidity, corresponding to different scopes of uniqueness (local/infinitesimal, global and universal), in various types of frameworks. First, we develop results in inductive construction and decomposition of graphs with mixed sparsity conditions as well as results on the packing of arborescences with matroidal constraints. These results are then used to obtain characterizations of infinitesimal rigidity in frameworks with mixed constraints. We also investigate the effect of extension operations on frameworks and extend a known result on the global rigidity preservation of $1$-extension on direction-length frameworks in dimension two to all dimensions. For universal rigidity, where little is known, we obtain a complete characterization for the class of complete bipartite frameworks on the line. We also generalize a sufficient condition for the universal rigidity of frameworks by allowing non-general positions.

Notre objectif est d’évaluer et de rendre opérationnelle la décomposition de problèmes d’optimisation sous contraintes. Nous nous sommes intéressés à deux problèmes en particulier : le problème de la recherche d’un plus grand sous-graphe commun (MCIS), et le problème de somme coloration minimale (MSCP). Il s’agit de problèmes NP-difficiles pour lesquels les approches de résolution complètes passent difficilement à l’échelle, et nous proposons de les améliorer à cet égard en décomposant ces problèmes en sous-problèmes indépendants. Les décompositions que nous proposons s’appuient sur la structure du problème initial pour créer des sous-problèmes de tailles équilibrées. Pour le MCIS, nous introduisons une décomposition basée sur la structure du graphe de compatibilité, et nous montrons que cette décomposition permet d’obtenir des sous-problèmes plus équilibrés que la méthode EPS classiquement utilisée pour paralléliser la résolution de problèmes en programmation par contraintes. Pour le MSCP, nous introduisons une nouvelle décomposition arborescente de hauteur bornée, et nous montrons comment tirer partie de la complémentarité de la programmation par contraintes et de la programmation linéaire en nombres entiers pour obtenir et résoudre les sous-problèmes indépendants qui en découlent. Nous proposons également une approche portfolio qui utilise des techniques d’apprentissage automatique pour choisir dynamiquement l’approche la plus performante en fonction du problème à résoudre. / The objective of this thesis is, from a general standpoint, to design and evaluate decomposition methods for solving constrained optimisation problems. Two optimisation problems in particular are considered: the maximum common induced subgraph problem, in which the largest common part between two graphs is to be found, and the sum colouring problem, where a graph must be coloured in a way that minimises a sum of weights induced by the employed colours. The maximum common subgraph (MCIS) problem is notably difficult, with a strong applicability in domains such as biology, chemistry and image processing, where the need to measure the similarity between structured objects represented by graphs may arise. The outstanding difficulty of this problem makes it strongly advisable to employ a decomposition method, possibly coupled with a parallelisation of the solution process. However, existing decomposition methods are not well suited to solve the MCIS problem: some lead to a poor balance between subproblems, while others, like tree decomposition, are downright inapplicable. To enable the structural decomposition of such problems, Chmeiss et al. proposed an approach, TR-decomposition, acting at a low level: the microstructure of the problem. This approach had yet to be applied to the MCIS problem. We evaluate it in this context, aiming at reducing the size of the search space while also enabling parallelisation. The second problem that caught our interest is the sum colouring problem. It is an NP-hard variant of the widely known classical graph colouring problem. As in most colouring problems, it basically consists in assigning colours to the vertices of a given graph while making sure no neighbour vertices use the same colour. In the sum colouring problem, however, each colour is associated with a weight. The objective is to minimise the sum of the weights of the colours used by every vertex. This leads to generally harder instances than the classical colouring problem, which simply requires to use as few colours as possible. Only a few exact methods have been proposed for this problem. Among them stand notably a constraint programming (CP) model, a branch and bound approach, as well as an integer linear programming (ILP) model. We led an in-depth investigation of CP's capabilities to solve the sum colouring problem, while also looking into ways to make it more efficient. Additionally, we evaluated a combination of integer linear programming and constraint programming, with the intention of conciliating the strong points of these highly complementary approaches. We took inspiration from the classical backtracking bounded by tree decomposition (BTD) approach. We employ a tree decomposition with a strictly bounded height. We then derive profit from the complementarity of our approaches by developing a portfolio approach, able to choose one of the considered approaches automatically by relying on a number of features extracted from each instance.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: An order picking operation in a distribution centre (DC) owned by Pep Stores Ltd, located in Durban, South Africa was considered. The order picking operation utilises picking lines and the concept of wave picking. A picking line is a central area with storage locations for pallet loads of stock keeping units (SKUs) around a conveyor belt. The system shows many similarities to unidirectional carousel systems found in literature, however, the unidirectional carousel system is not common. Sets of SKUs must be assigned to pick waves. The SKUs associated with a single wave are then arranged on a picking line after which pickers move in a clockwise direction around the conveyor belt to pick the orders. The entire order picking operation was broken into three tiers of decision making and three corresponding subproblems were identi ed. The rst two subproblems were investigated which focused on a single picking line. The rst subproblem called the order sequencing problem (OSP) considered the sequencing of orders for pickers and the second called the SKU location problem (SLP) the assignment of SKUs to locations in the picking line for a given wave. A tight lower bound was established for the OSP using the concept of a maximal cut. This lower bound was transformed into a feasible solution within 1 pick cycle of the lower bound. The solution was also shown to be robust and dynamic for use in practice. Faster solution times, however, were required for use in solution techniques for the SLP. Four variations of a greedy heuristic as well as two metaheuristic methods were therefore developed to solve the problem in shorter times. An ant colony approach was developed to solve the SLP. Furthermore, four variations of a hierarchical clustering algorithm were developed to cluster SKUs together on a picking line and three metaheuristic methods were developed to sequence these clusters. All the proposed approaches outperformed known methods for assigning locations to SKUs on a carousel. To test the validity of assumptions and assess the practicality of the proposed solutions an agent based simulation model was built. All proposed solutions were shown to be applicable in practice and the proposed solutions to both subporblems outperformed the current approaches by Pep. Furthermore, it was established that the OSP is a more important problem, in comparison to the SLP, for Pep to solve as limited savings can be achieved when solving the SLP. / AFRIKAANSE OPSOMMING: 'n Stelsel vir die opmaak van bestellings in 'n distribusiesentrum van Pep Stores Bpk. in Durban, Suid-Afrika word beskou. Hierdie stelsel gebruik uitsoeklyne waarop bestellings in golwe opgemaak word. 'n Uitsoeklyn is 'n area met vakkies waarop pallette met voorraadeenhede gestoor kan word. Hierdie vakkies is rondom 'n voerband gerangskik. Die stelsel het ooreenkomste met die eenrigting carrousselstelsels wat in die literatuur voorkom, maar hierdie eenrigtingstelsels is nie algemeen nie. Voorraadeenhede moet aan 'n golf toegewys word wat in 'n uitsoeklyn gerangskik word, waarna werkers dan die bestellings in die betrokke golf opmaak. Die hele operasie van bestellings opmaak kan opgebreek word in drie vlakke van besluite met gepaardgaande subprobleme. Die eerste twee subprobleme wat 'n enkele uitsoeklyn beskou, word aangespreek. Die eerste subprobleem, naamlik die volgorde-van-bestellings-probleem (VBP) beskou die volgorde waarin bestellings opgemaak word. Die tweede probeem is die voorraadeenheidaan- vakkie-toewysingsprobleem (VVTP) en beskou die toewysings van voorraadeenhede aan vakkies in 'n uitsoeklyn vir 'n gegewe golf. 'n Sterk ondergrens vir die VBP is bepaal met behulp van die konsep van 'n maksimum snit. Hierdie ondergrens kan gebruik word om 'n toelaatbare oplossing te bepaal wat hoogstens 1 carrousselsiklus meer as die ondergrens het. Hierdie oplossings kan dinamies gebruik word en kan dus net so in die praktyk aangewend word. Vinniger oplossingstegnieke is egter nodig indien die VVTP opgelos moet word. Twee metaheuristiese metodes word dus voorgestel waarmee oplossings vir die VBP vinniger bepaal kan word. 'n Mierkolonie benadering is ontwikkel om die VVTP op te los. Verder is vier variasies van 'n hi erargiese groeperingsalgoritme ontwikkel om voorraadeenhede saam te groepeer op 'n uitsoeklyn. Drie metaheuristieke is aangewend om hierdie groepe in volgorde te rangskik. Al hierdie benaderings vaar beter as bekende metodes om voorraadeenhede op 'n carroussel te rankskik. Om die geldigheid van die aannames en die praktiese uitvoerbaarheid van die oplossings te toets, is 'n agent gebaseerde simulasie model gebou. Daar is bevind dat al die voorgestelde oplossings prakties implementeerbaar is en dat al die metodes verbeter op die huidige werkswyse in Pep. Verder kon vasgestel word die VBP belangriker as die VVTP vir Pep is omdat veel kleiner potensiele besparings met die VVTP moontlik is as met die VBP.

Nous nous intéressons dans cette thèse aux possibilités d’hybridation entre les méthodes exactes et les méthodes heuristiques afin de pouvoir tirer avantage de chacune des deux approches : optimalité de la résolution exacte, caractère moins déterministe et rapidité de la composante heuristique. Dans l’objectif de résoudre des problèmes NPdifficiles de taille relativement importante tels que les problèmes de transports, nous nous intéressons dans les deux dernières parties de ce mémoire à la conception de méthodes incomplètes basées sur ces hybridations. Dans la première partie, nous allons nous intéresser aux méthodes de résolution par recherche arborescente. Nous introduisons une nouvelle approche pour la gestion des décisions de branchement, que nous appelons Dynamic Learning Search (DLS). Cette méthode définit de manière dynamique des règles de priorité pour la sélection des variables à chaque noeud et l’ordre des valeurs sur lesquelles brancher. Ces règles sont conçues dans une optique de généricité, de manière à pouvoir utiliser la méthode indépendamment du problème traité. Le principe général est de tenir compte par une technique d’apprentissage de l’impact qu’ont eu les décisions de branchement dans les parties déjà explorées de l’arbre. Nous évaluons l’efficacité de la méthode proposée sur deux problèmes classiques : un problème d’optimisation combinatoire et un problème à satisfaction de contraintes. La deuxième partie de ce mémoire traite des recherches à grand voisinage. Nous présentons un nouvel opérateur de voisinage, qui détermine par un algorithme de programmation dynamique la sous-séquence optimale d’un chemin dans un graphe. Nous montrons que cet opérateur est tout particulièrement destiné à des problèmes de tournées pour lesquels tous les noeuds ne nécessitent pas d’être visités. Nous appelons cette classe de problème les Problèmes de Tournées avec Couverture Partielle et présentons quelques problèmes faisant partie de cette classe. Les chapitres 3 et 4 montrent, à travers des tests expérimentaux conséquents, l’efficacité de l’opérateur que nous proposons en appliquant cette recherche à voisinage large sur deux problèmes, respectivement le Problème de l’Acheteur Itinérant (TPP) et le Problème de Voyageur de Commerce Généralisé (GTSP). Nous montrons alors que cet opérateur peut être combiné de manière efficace avec des métaheuristiques classiques, telles que des algorithmes génétiques ou des algorithmes d’Optimisation par Colonies de Fourmis. Enfin, la troisième partie présente des méthodes heuristiques basées sur un algorithme de Génération de Colonnes. Ces méthodes sont appliquées sur un problème complexe : le problème de Tournées de Véhicules avec Contraintes de Chargement à Deux Dimensions (2L-VRP). Nous montrons une partie des possibilités qu’il existe afin de modifier une méthode a priori exacte en une méthode heuristique et nous évaluons ces possibilités à l’aide de tests expérimentaux / We are interested in this thesis in the possibilities of hybridization between the exact methods and the methods heuristics to be able to take advantage of each of both approaches: optimality of the exact resolution, the less determinist character and the speed of the constituent heuristics. In the objective to resolve problems NP-hard of relatively important size such as the transportation problems, we are interested in the last two parts of this report in the conception of incomplete methods based on these hybridizations. In the first part, we are going to be interested in the methods of resolution by tree search. We introduce a new approach for the management of the decisions of connection, which we call Dynamic Learning Search ( DLS). This method defines in a dynamic way rules of priority for the selection of variables in every knot and the order of the values on which to connect. These rules are conceived in an optics of genericity, so as to be able to use the method independently of the treated problem. The general principle is to take into account by a technique of learning of the impact which had the decisions of connection in the parts already investigated in the tree. We estimate the efficiency of the method proposed on two classic problems: a combinatorial optimization problem and a constraints satisfaction problem. The second part of this report handles large neighborhood search. We present a new operator of neighborhood, who determines by an algorithm of dynamic programming the optimal sub-sequence of a road in a graph. We show that this operator is quite particularly intended for problems of tours for which all the vertices do not require to be visited. We call this class of problem the Problems of Tours with Partial Cover and present some problems being a part of this class. Chapters 3 and 4 show, through consequent experimental tests, the efficiency of the operator which we propose by applying this search to wide neighborhood on two problems, respectively the Traveling Purchaser Problem (TPP) and Generalized Traveling Salesman Problem ( GTSP). We show while this operator can be combined in a effective way with classic metaheuristics, such as genetic algorithms or algorithms of Ant Colony Optimization

There are many real cases where a company needs to determine the price of its products so as to maximise its revenue or profit.<p>To do so, the company must consider customers' reactions to these prices, as they may refuse to buy a given product or service if its price is too high. This is commonly known in literature as a pricing problem.<p>This class of problems, which is typically bilevel, was first studied in the 1990s and is NP-hard, although polynomial algorithms do exist for some particular cases. Many questions are still open on this subject.<p><p>The aim of this thesis is to investigate mathematical properties of pricing problems, in order to find structural properties, formulations and solution methods that are as efficient as possible. In particular, we focus our attention on pricing problems over a network. In this framework, an authority owns a subset of arcs and imposes tolls on them, in an attempt to maximise his/her revenue, while users travel on the network, seeking for their minimum cost path.<p><p>First, we provide a detailed review of the state of the art on bilevel pricing problems. <p>Then, we consider a particular case where the authority is using an unit toll scheme on his/her subset of arcs, imposing either the same toll on all of them, or a toll proportional to a given parameter particular to each arc (for instance a per kilometre toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial.<p>We then address a robust approach taking into account uncertainty on parameters. We solve some polynomial cases of the pricing problem where uncertainty is considered using an interval representation.<p><p>Finally, we focus on another particular case where toll arcs are connected such that they constitute a path, as occurs on highways. We develop a Dantzig-Wolfe reformulation and present a Branch-and-Cut-and-Price algorithm to solve it. Several improvements are proposed, both for the column generation algorithm used to solve the linear relaxation and for the branching part used to find integer solutions. Numerical results are also presented to highlight the efficiency of the proposed strategies. This problem is proved to be APX-hard and a theoretical comparison between our model and another one from the literature is carried out. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

In the building automation domain, there are gaps among various tasks related to design engineering. As a result created system designs must be adapted to the given requirements on system functionality, which is related to increased costs and engineering effort than planned. For this reason standards are prepared to enable a coordination among these tasks by providing guidelines and unified artifacts for the design. Moreover, a huge variety of prefabricated devices offered from different manufacturers on the market for building automation that realize building automation functions by preprogrammed software components. Current methods for design creation do not consider this variety and design solution is limited to product lines of a few manufacturers and expertise of system integrators. Correspondingly, this results in design solutions of a limited quality. Thus, a great optimization potential of the quality of design solutions and coordination of tasks related to design engineering arises. For given design requirements, the existence of a high number of devices that realize required functions leads to a combinatorial explosion of design alternatives at different price and quality levels. Finding optimal design alternatives is a hard problem to which a new solution method is proposed based on heuristical approaches. By integrating problem specific knowledge into algorithms based on heuristics, a promisingly high optimization performance is achieved. Further, optimization algorithms are conceived to consider a set of flexibly defined quality criteria specified by users and achieve system design solutions of high quality. In order to realize this idea, optimization algorithms are proposed in this thesis based on goal-oriented operations that achieve a balanced convergence and exploration behavior for a search in the design space applied in different strategies. Further, a component model is proposed that enables a seamless integration of design engineering tasks according to the related standards and application of optimization algorithms.

In the building automation domain, there are gaps among various tasks related to design engineering. As a result created system designs must be adapted to the given requirements on system functionality, which is related to increased costs and engineering effort than planned. For this reason standards are prepared to enable a coordination among these tasks by providing guidelines and unified artifacts for the design. Moreover, a huge variety of prefabricated devices offered from different manufacturers on the market for building automation that realize building automation functions by preprogrammed software components. Current methods for design creation do not consider this variety and design solution is limited to product lines of a few manufacturers and expertise of system integrators. Correspondingly, this results in design solutions of a limited quality. Thus, a great optimization potential of the quality of design solutions and coordination of tasks related to design engineering arises. For given design requirements, the existence of a high number of devices that realize required functions leads to a combinatorial explosion of design alternatives at different price and quality levels. Finding optimal design alternatives is a hard problem to which a new solution method is proposed based on heuristical approaches. By integrating problem specific knowledge into algorithms based on heuristics, a promisingly high optimization performance is achieved. Further, optimization algorithms are conceived to consider a set of flexibly defined quality criteria specified by users and achieve system design solutions of high quality. In order to realize this idea, optimization algorithms are proposed in this thesis based on goal-oriented operations that achieve a balanced convergence and exploration behavior for a search in the design space applied in different strategies. Further, a component model is proposed that enables a seamless integration of design engineering tasks according to the related standards and application of optimization algorithms.:1 Introduction 17 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3 Goals and Use of the Thesis . . . . . . . . . . . . . . . . . . . . . 21 1.4 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . 24 2 Design Creation for Building Automation Systems 25 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Engineering of Building Automation Systems . . . . . . . . . . . 29 2.3 Network Protocols of Building Automation Systems . . . . . . . 33 2.4 Existing Solutions for Design Creation . . . . . . . . . . . . . . . 34 2.5 The Device Interoperability Problem . . . . . . . . . . . . . . . . 37 2.6 Guidelines for Planning of Room Automation Systems . . . . . . 38 2.7 Quality Requirements on BAS . . . . . . . . . . . . . . . . . . . 41 2.8 Quality Requirements on Design . . . . . . . . . . . . . . . . . . 42 2.8.1 Quality Requirements Related to Project Planning . . . . 42 2.8.2 Quality Requirements Related to Project Implementation 43 2.9 Quality Requirements on Methods . . . . . . . . . . . . . . . . . 44 2.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3 The Design Creation Task 47 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 System Design Composition Model . . . . . . . . . . . . . . . . . 49 3.2.1 Abstract and Detailed Design Model . . . . . . . . . . . . 49 3.2.2 Mapping Model . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . 53 3.3.1 Problem properties . . . . . . . . . . . . . . . . . . . . . . 54 3.3.2 Requirements on Algorithms . . . . . . . . . . . . . . . . 56 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4 Solution Methods for Design Generation and Optimization 59 4.1 Combinatorial Optimization . . . . . . . . . . . . . . . . . . . . . 59 4.2 Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Examples for Metaheuristics . . . . . . . . . . . . . . . . . . . . . 62 4.3.1 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . 62 4.3.2 Tabu Search . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.3 Ant Colony Optimization . . . . . . . . . . . . . . . . . . 65 4.3.4 Evolutionary Computation . . . . . . . . . . . . . . . . . 66 4.4 Choice of the Solver Algorithm . . . . . . . . . . . . . . . . . . . 69 4.5 Specialized Methods for Diversity Preservation . . . . . . . . . . 70 4.6 Approaches for Real World Problems . . . . . . . . . . . . . . . . 71 4.6.1 Component-Based Mapping Problems . . . . . . . . . . . 71 4.6.2 Network Design Problems . . . . . . . . . . . . . . . . . . 73 4.6.3 Comparison of Solution Methods . . . . . . . . . . . . . . 74 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 Automated Creation of Optimized Designs 79 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.2 Design Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3 Component Model . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.3.1 Presumptions . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.3.2 Integration of Component Model . . . . . . . . . . . . . . 87 5.4 Design Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.4.1 Component Search . . . . . . . . . . . . . . . . . . . . . . 88 5.4.2 Generation Approaches . . . . . . . . . . . . . . . . . . . 100 5.5 Design Improvement . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.5.1 Problems and Requirements . . . . . . . . . . . . . . . . . 107 5.5.2 Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.5.3 Application Strategies . . . . . . . . . . . . . . . . . . . . 121 5.6 Realization of the Approach . . . . . . . . . . . . . . . . . . . . . 122 5.6.1 Objective Functions . . . . . . . . . . . . . . . . . . . . . 122 5.6.2 Individual Representation . . . . . . . . . . . . . . . . . . 123 5.7 Automated Design Creation For A Building . . . . . . . . . . . . 124 5.7.1 Room Spanning Control . . . . . . . . . . . . . . . . . . . 124 5.7.2 Flexible Rooms . . . . . . . . . . . . . . . . . . . . . . . . 125 5.7.3 Technology Spanning Designs . . . . . . . . . . . . . . . . 129 5.7.4 Preferences for Mapping of Function Blocks to Devices . . 132 5.8 Further Uses and Applicability of the Approach . . . . . . . . . . 133 5.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6 Validation and Performance Analysis 137 6.1 Validation Method . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.2 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.3 Example Abstract Designs and Performance Tests . . . . . . . . 139 6.3.1 Criteria for Choosing Example Abstract Designs . . . . . 139 6.3.2 Example Abstract Designs . . . . . . . . . . . . . . . . . . 140 6.3.3 Performance Tests . . . . . . . . . . . . . . . . . . . . . . 142 6.3.4 Population Size P - Analysis . . . . . . . . . . . . . . . . 151 6.3.5 Cross-Over Probability pC - Analysis . . . . . . . . . . . 157 6.3.6 Mutation Probability pM - Analysis . . . . . . . . . . . . 162 6.3.7 Discussion for Optimization Results and Example Designs 168 6.3.8 Resource Consumption . . . . . . . . . . . . . . . . . . . . 171 6.3.9 Parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . 172 6.4 Optimization Framework . . . . . . . . . . . . . . . . . . . . . . . 172 6.5 Framework Design . . . . . . . . . . . . . . . . . . . . . . . . . . 174 6.5.1 Components and Interfaces . . . . . . . . . . . . . . . . . 174 6.5.2 Workflow Model . . . . . . . . . . . . . . . . . . . . . . . 177 6.5.3 Optimization Control By Graphical User Interface . . . . 180 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 7 Conclusions 185 A Appendix of Designs 189 Bibliography 201 Index 211