Context: Most of the problem of generating timetable for a school belongs to the class of NP-hard problems. Complexity and practical value makes this kind of problem interesting for parallel computing. Objectives: This paper focuses on Class-Teacher problem with weighted time slots and proofs that it is NP-complete problem. Branch and bound scheme and two approaches to distribute the simulated annealing are proposed. Empirical evaluation of described methods is conducted in an elementary school computer laboratory. Methods: Simulated annealing implementation described in literature are adapted for the problem, and prepared for execution in distributed systems. Empirical evaluation is conducted with the real data from Polish elementary school. Results: Proposed branch and bound scheme scales nearly logarithmically with the number of nodes in computing cluster. Proposed parallel simulated annealing models tends to increase solution quality. Conclusions: Despite a significant increase in computing power, computer laboratories are still unprepared for heavy computation. Proposed branch and bound method is infeasible with the real instances. Parallel Moves approach tends to provide better solution at the beginning of execution, but the Multiple Independent Runs approach outruns it after some time. / Sammanhang: De flesta problem med att generera scheman för en skola tillhör klassen av NP-svårt problemen. Komplexitet och praktiskt värde gör att den här typen av problemen forskas med särskild uppmärksamhet på en parallell bearbetning.   Syfte: Detta dokument fokusarar på Klass-Lärare problem med vikter för enskilda tidsluckor och på att visa var ett NP-svårt problem är fullständigt. Branch and bound scheman och två metoder för att distribuera en simulerad glödgning algoritm presenterades. En empirisk analys av beskrivna metoder gjordes i datorlaboratorium i en grundskola. Metod: Implementering av en simulerad glödgning algoritm som beskrivs i litteraturen blev anpassad till ett utvalt problem och distribuerade system. Empirisk utvärdering genomförs med verkliga data från polska grundskolan Resultat: Föreslagit Branch and bound system graderar nästan logaritmiskt antal noder i ett datorkluster. Den simulerade glödgning algoritmen som föreslagits förbättrar lösningarnas kvalitet. Slutsatser: Trots att en betydande ökning med beräkningskraft är inte datasalar i skolor anpassad till avancerade beräkningar. Användning av den Branch and Bound föreslagna metoden till praktiska problem är omöjlig i praktiken. En annan föreslagen metod Parallel Moves ger bättre resultat i början av utförandet men Multiple Independent Runs hittar bättre lösningar efter en viss tid.

[pt] A Programação Quadrática Binária Irrestrita (UBQP) é amplamente estudada. Trata-se de uma ferramenta de modelagem poderosa, mas otimizar de um problema NP-difícil. Neste trabalho uma nova abordagem é apresentada, que pode ser usada para construir um algoritmo exato. Além disso, a ideia básica que fundamenta o trabalho pode ser usado em um espectro ainda mais amplo de problemas. O algoritmo exato derivado do novo método é altamente paralelizável, o que é uma característica desejável nos dias de hoje em que cloud computing já é uma realidade. Para instâncias razoavelmente grandes do UBQP, o novo método pode paralelizar a centenas, ou até milhares, de núcleos com facilidade, com um aumento de desempenho quase linear. / [en] Unconstrained Binary Quadratic Programming (UBQP) is widely studied. It is a powerful modeling tool and its associate problem is NP-hard. In this work a new approach is introduced, which can be used to build an exact algorithm. Also, the fundamental idea behind it can be used in an even wider family of problems. This exact algorithm derived from the new method is highly parallelizable, which is a desired feature nowadays, when the cloud computing is a reality. For reasonably large instances of UBQP, the new method can parallelize to hundreds, or even thousands, of cores easily, with a near-linear speedup.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23322号 / 情博第758号 / 新制||情||129(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 永持 仁, 教授 太田 快人, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第23546号 / 情博第776号 / 新制||情||132(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 太田 快人, 教授 永持 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

This work deals with the way of balancing production-assembly line, which would minimalize set up costs. The production-assembly line shall allow assembling more mutually similar variants of the same product. The time of duration of each operation is constant, but can differs between individual variants of the product. Cycle time is related to the variant of the product.

Étant donné G = (V, E) un graphe non orienté connexe et un entier positif β (n), où n est le nombrede sommets de G, le problème du séparateur (VSP) consiste à trouver une partition de V en troisclasses A, B et C de sorte qu'il n'y a pas d'arêtes entre A et B, max {| A |, | B |} est inférieur ou égal àβ (n) et | C | est minimum. Dans cette thèse, nous considérons une modélisation du problème sous laforme d'un programme linéaire en nombres entiers. Nous décrivons certaines inégalités valides et etdéveloppons des algorithmes basés sur un schéma de voisinage.Nous étudions également le problème du st-séparateur connexe. Soient s et t deux sommets de Vnon adjacents. Un st-séparateur connexe dans le graphe G est un sous-ensemble S de V \ {s, t} quiinduit un sous-graphe connexe et dont la suppression déconnecte s de t. Il s'agit de déterminer un stséparateur de cardinalité minimum. Nous proposons trois formulations pour ce problème et donnonsdes inégalités valides du polyèdre associé à ce problème. Nous présentons aussi une heuristiqueefficace pour résoudre ce problème. / Given G=(V,E) a connected undirected graph and a positive integer β(n), where n is number ofvertices, the vertex separator problem (VSP) is to find a partition of V into three classes A,B and Csuch that there is no edge between A and B, max{|A|,|B|}less than or equal β(n), and |C| isminimum. In this thesis, we consider aninteger programming formulation for this problem. Wedescribe some valid inequalties and using these results to develop algorithms based onneighborhood scheme.We also study st-connected vertex separator problem. Let s and tbe two disjoint vertices of V, notadjacent. A st-connected separator in the graph G is a subset S of V\{s,t} such that there are no morepaths between sand tin G[G\S] and the graph G[S] is connected . The st-connected vertex speratorproblem consists in finding such subset with minimum cardinality. We propose three formulationsfor this problem and give some valid inequalities for the polyhedron associated with this problem.We develop also an efficient heuristic to solve this problem.

In this dissertation, we show two significant applications of combinatorial branch-and-bound as an exact solution methodology in combinatorial optimization problems. In the first problem, we propose a set of new group centrality metrics and show their performance in estimating protein importance in protein-protein interaction networks. The centrality metrics introduced here are extensions of well-known nodal metrics (degree, betweenness, and closeness) for a set of nodes which is required to induce a specific pattern. The structures investigated range from the ``stricter'' induced stars and cliques, to a ``looser'' definition of a representative structure. We derive the computational complexity for each of the newly proposed metrics. Then, we provide mixed integer programming formulations to solve the problems exactly; due to the computational complexity of the problem and the sheer size of protein-protein interaction networks, using a commercial solver with the formulations is not always a viable option. Hence, we also propose a combinatorial branch-and-bound approach to solve the problems introduced. Finally, we conclude this work with a presentation of the performance of the proposed centrality metrics in identifying essential proteins in helicobacter pylori. In the second problem, we introduce the asymmetric probabilistic minimum-cost Hamiltonian cycle problem (APMCHCP) where arcs and vertices in the graph are possible to fail. APMCHCP has applications in many emerging areas, such as post-disaster recovery, electronic circuit design, and security maintenance of wireless sensor networks. For each vertex, we define a chance-constraint to guarantee that the probability of arriving at the vertex must be greater than or equal to a given threshold. Four mixed-integer programming (MIP) formulations are proposed for modeling the problem, including two direct formulations and two recursive formulations. A combinatorial branch-and-bound (CBB) algorithm is proposed for solving the APMCHCP, where data preprocessing steps, feasibility rules, and approaches of finding upper and lower bounds are developed. In the numerical experiments, the CBB algorithm is compared with formulations on a test-bed of two popular benchmark instance sets. The results show that the proposed CBB algorithm significantly outperforms Gurobi solver in terms of both the size of optimally solved instances and the computing time.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

CPU cache hierarchies are the central solution in bridging the memory wall. A proper understanding of how to trade-off their high cost against performance can lead to cost-savings without sacrificing performance.Due to the combinatorial nature of the problem, there exist a large number of configurations to investigate, making design space exploration slow and cumbersome. To improve this process, this Thesis develops and evaluates a model for optimally trading-off cost and performance of CPU cache hierarchies, named the Optimal Cache Problem (OCP), in the form of a Non-linear Integer Problem. A second goal of this work is the development of an efficient solver for the OCP, which was found to be a branch & bound algorithm and proven to function correctly. Experiments were conducted to empirically analyse and validate the model and to showcase possible use-cases. There, it was possible to ascribe the model outputs on measurable performance metrics. The model succeeded in formalising the inherent trade-off between cost and performance in a way that allows for an efficient and complete search of the configuration space of possible cache hierarchies. In future work, the model needs to be refined and extended to allow for the simultaneous analysis of multiple programs.

<p> A solution to an industrial problem of designing a hydrostatic drive system for logging vehicles is presented. A computer program using Land and Doig's method of Branch and Bound Mixed Integer Programming is used to obtain an optimal solution to the problem. A comprehensive users guide to allow the use of the program by unsophisticated users is provided. </p> <p> An attempted alternate method of solution using the Gomory method of Integer Programming is presented and reasons for its failure discussed. </p> / Thesis / Master of Engineering (MEngr)