The problem of finding a schedule with the lowest makespan in the class of all flowtime-optimal schedules for parallel identical machines is an NP-hard problem. Several approximation algorithms have been suggested for this problem. We focus on algorithms that are fast and easy to implement, rather than on more involved algorithms that might provide tighter approximation bounds. A set of approaches for proving conjectured bounds on performance ratios for such algorithms is outlined. These approaches are used to examine Coffman and Sethi's conjecture for a worst-case bound on the ratio of the makespan of the schedule generated by the LD algorithm to the makespan of the optimal schedule. A significant reduction is achieved in the size of a hypothesised minimal counterexample to this conjecture.

The classic flow shop problem assumes that jobs make only single passes through the processing machines and that the processing times are not affected by the length of the delay before jobs are processed. These assumptions are being relaxed in recent papers that consider reentrance problems and those with schedule deterioration. In this study, these two assumptions are both relaxed, and a model of a reentrant flowshop with a deteriorating schedule is considered. A linear programming formulation of the problem is first presented. Three solution heuristics are considered under different deterioration scenarios. It was observed that both Nawaz Enscor and Ham (NEH) algorithm and Genetic Algorithm (GA) performed much better than the Campbell Dudek and Smith (CDS) algorithm. Overall, when considering both the quality of solution and computational time together, the NEH algorithm seems to have performed much better than the others as the size of problems increases. This model would find useful applications in some metallurgical and manufacturing processes where such problems are usually encountered. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2021. / Industrial and Systems Engineering / MEng (Industrial Engineering) / Unrestricted

Large scale systems provide a powerful computing platform for solving large and complex scientific applications. However, the inherent complexity, heterogeneity, wide distribution, and dynamism of the computing environments can lead to performance degradation of the scientific applications executing on these computing systems. Load imbalance arising from a variety of sources such as application, algorithmic, and systemic variations is one of the major contributors to their performance degradation. In general, load balancing is achieved via scheduling. Moreover, frequently occurring resource failures drastically affect the execution of applications running on high performance computing systems. Therefore, the study of deploying support for integrated scheduling and fault-tolerance mechanisms for guaranteeing that applications deployed on computing systems are resilient to failures becomes of paramount importance. Recently, several research initiatives have started to address the issue of resilience. However, the major focus of these efforts was geared more toward achieving system level resilience with less emphasis on achieving resilience at the application level. Therefore, it is increasingly important to extend the concept of resilience to the scheduling techniques at the application level for establishing a holistic approach that addresses the performability of these applications on high performance computing systems. This can be achieved by developing a comprehensive modeling framework that can be used to evaluate the resiliency of such techniques on heterogeneous computing systems for assessing the impact of failures as well as workloads in an integrated way. This dissertation presents an experimental methodology based on discrete event simulation for the analysis and the evaluation of the resilience of scheduling scientific applications on high performance computing systems. With the aid of the methodology a wide class of dependencies existing between application and computing system are captured within a deterministic model for quantifying the performance impact expected from changes in application and system characteristics. Ideally, the results obtained by employing the proposed simulation-based performance prediction framework enabled an introspective design and investigation of scheduling heuristics to reason about how to best fully optimize various often antagonistic objectives, such as minimizing application makespan and maximizing reliability.

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In dieser Arbeit untersuchen wir Algorithmen für Scheduling-Probleme. Wir betrachten semi-online Makespan-Scheduling und generalisiertes Bin Covering. Im online Makespan- Scheduling-Problem sind m Maschinen und n Jobs gegeben, wobei letztere jeweils eine individuelle Bearbeitungszeit haben. Es wird zu jedem Zeitpunkt ein Job offengelegt und muss sofort und unwiderruflich einer Maschine zugewiesen werden, ohne Wissen über zukünftige Jobs. Die Last einer Maschine wird als die Summe der Bearbeitungszeiten der ihr zugewiesenen Jobs definiert. Das Ziel ist es, eine Zuweisung von Jobs zu Maschinen zu finden, sodass die höchste Last einer Maschine minimiert wird. Im semi-online Scheduling-Modell wird dieses strikte Szenario relaxiert. Wir untersuchen drei verschied- ene Modelle. Im ersten ist uns die kumulierte Bearbeitungszeit der Jobs vor Ankunft der einzelnen Jobs bekannt. Im zweiten Modell dürfen wir bis zu einem gewissen Grade bereits zugewiesene Jobs anderen Maschinen neu zuordnen.Im dritten semi-online Scheduling-Modell darf ein Algorithmus mehrere Lösungen parallel konstruieren, von denen die beste ausgegeben wird. Beim generalisierten Bin Covering sind uns m Bintypen und n Objekte gegeben. Ein Bintyp Mj hat einen Bedarf dj und einen Profit rj. Jedes Objekt Jt hat eine Größe pt. Ein Bin vom Typ Mj heißt abgedeckt, wenn die Summe der Größen der ihm zugewiesenen Objekte mindestens dj ist. Wenn ein Bin vom Typ Mj abgedeckt ist, erzielen wir einen Profit von rj. Ziel ist es, die Objekte Bins zuzuweisen, sodass der erzielte Gesamtprofit maximiert wird. Wir untersuchen zwei Modelle, die sich in der Verfügbarkeit von Bintypen unterscheiden. Im Unit-Supply-Modell steht uns von jedem Bintyp genau ein Bin zur Verfügung. Im Gegensatz dazu stehen uns im Infinite-Supply-Modell von jedem Bintyp beliebig viele Bins zur Verfügung. Das Unit-Supply-Modell ist daher eine Verallgemeinerung des Infinite-Supply-Modells. Für alle Modelle zeigen wir beinahe scharfe obere und untere Schranken. / In this thesis we study algorithms for scheduling problems. We investigate semi-online minimum makespan scheduling and generalized bin covering. In online minimum makespan scheduling we are given a set of m machines and n jobs, where each job Jt is specified by a processing time. The jobs arrive one by one and we have to assign them to the machines without any knowledge about future incoming jobs. The load of a machine is defined to be total processing time of the assigned jobs. The goal is to place the jobs on the machines such that the maximum load of a machine is minimized. In semi-online minimum makespan scheduling this strict setting is softened. We investigate three different models. In the first setting an algorithm is given an advice on the total processing time of the jobs. In the second setting we may reassign jobs upto a limited amount. The third semi-online setting we study is minimum makespan scheduling with parallel schedules. In this problem an algorithm may maintain several schedules, the best of which is output after the arrival of the entire job sequence. In generalized bin covering we are given m bin types and n items. Each bin type Mj is specified by a demand dj and a revenue rj. Each item Jt has a size pj. A bin of type Mj is said to be covered if the total size of the assigned items is at least the demand dj. Then the revenue rj is earned. The goal is to find an assignment of items to bins maximizing the total obtained revenue. We study two models of bin supply. In the unit supply model there is only one bin of each type available. By contrast in the infinite supply model each bin type is available arbitrarily often, and hence the former is a generalization of the latter. We provide nearly tight upper and lower bounds for all models.

Le domaine de l'embarqué connaît depuis quelques années un essor important avec le développement d'applications de plus en plus exigeantes en calcul auxquels les architectures traditionnelles à base de processeurs (mono/multi cœur) ne peuvent pas toujours répondre en termes de performances. Si les architectures multiprocesseurs ou multi cœurs sont aujourd'hui généralisées, il est souvent nécessaire de leur adjoindre des circuits de traitement dédiés, reposant notamment sur des circuits reconfigurables, permettant de répondre à des besoins spécifiques et à des contraintes fortes particulièrement lorsqu'un traitement temps-réel est requis. Ce travail présente l'étude des problèmes d'ordonnancement dans les architectures hétérogènes reconfigurables basées sur des processeurs généraux (CPUs) et des circuits programmables (FPGAs). L'objectif principal est d'exécuter une application présentée sous la forme d'un graphe de précédence sur une architecture hétérogène CPU/FPGA, afin de minimiser le critère de temps d'exécution total ou makespan (Cmax). Dans cette thèse, nous avons considéré deux cas d'étude : un cas d'ordonnancement qui tient compte des délais d'intercommunication entre les unités de calcul CPU et FPGA, pouvant exécuter une seule tâche à la fois, et un autre cas prenant en compte le parallélisme dans le FPGA, qui peut exécuter plusieurs tâches en parallèle tout en respectant la contrainte surfacique. Dans un premier temps, pour le premier cas d'étude, nous proposons deux nouvelles approches d'optimisation, GAA (Genetic Algorithm Approach) et MGAA (Modified Genetic Algorithm Approach), basées sur des algorithmes génétiques. Nous proposons également de tester un algorithme par séparation et évaluation (méthode Branch & Bound). Les approches GAA et MGAA proposées offrent un très bon compromis entre la qualité des solutions obtenues (critère d'optimisation de makespan) et le temps de calcul nécessaire à leur obtention pour résoudre des problèmes à grande échelle, en comparant à la méthode par séparation et évaluation (Branch & Bound) proposée et l'autre méthode exacte proposée dans la littérature. Dans un second temps, pour le second cas d'étude, nous avons proposé et implémenté une méthode basée sur les algorithmes génétiques pour résoudre le problème du partitionnement temporel dans un circuit FPGA en utilisant la reconfiguration dynamique. Cette méthode fournit de bonnes solutions avec des temps de calcul raisonnables. Nous avons ensuite amélioré notre précédente approche MGAA afin d'obtenir une nouvelle approche intitulée MGA (Multithreaded Genetic Algorithm), permettent d'apporter des solutions au problème de partitionnement. De plus, nous avons également proposé un algorithme basé sur le recuit simulé, appelé MSA (Multithreaded Simulated Annealing). Ces deux approches proposées, basées sur les méthodes métaheuristiques, permettent de fournir des solutions approchées dans un intervalle de temps très raisonnable aux problèmes d'ordonnancement et de partitionnement sur système de calcul hétérogène / The domain of the embedded systems becomes more and more attractive in recent years with the development of increasing computationally demanding applications to which the traditional processor-based architectures (either single or multi-core) cannot always respond in terms of performance. While multiprocessor or multicore architectures have now become generalized, it is often necessary to add to them dedicated processing circuits, based in particular on reconfigurable circuits, to meet specific needs and strong constraints, especially when real-time processing is required. This work presents the study of scheduling problems into the reconfigurable heterogeneous architectures based on general processors (CPUs) and programmable circuits (FPGAs). The main objective is to run an application presented in the form of a Data Flow Graph (DFG) on a heterogeneous CPU/FPGA architecture in order to minimize the total running time or makespan criterion (Cmax). In this thesis, we have considered two case studies: a scheduling case taking into account the intercommunication delays and where the FPGA device can perform a single task at a time, and another case taking into account parallelism in the FPGA, which can perform several tasks in parallel while respecting the constraint surface. First, in the first case, we propose two new optimization approaches GAA (Genetic Algorithm Approach) and MGAA (Modified Genetic Algorithm Approach) based on genetic algorithms. We also propose to compare these algorithms to a Branch & Bound method. The proposed approaches (GAA and MGAA) offer a very good compromise between the quality of the solutions obtained (optimization makespan criterion) and the computational time required to perform large-scale problems, unlike to the proposed Branch & Bound and the other exact methods found in the literature. Second, we first implemented an updated method based on genetic algorithms to solve the temporal partitioning problem in an FPGA circuit using dynamic reconfiguration. This method provides good solutions in a reasonable running time. Then, we improved our previous MGAA approach to obtain a new approach called MGA (Multithreaded Genetic Algorithm), which allows us to provide solutions to the partitioning problem. In addition, we have also proposed an algorithm based on simulated annealing, called MSA (Multithreaded Simulated Annealing). These two proposed approaches which are based on metaheuristic methods provide approximate solutions within a reasonable time period to the scheduling and partitioning problems on a heterogeneous computing system

Balancing trade-offs between production cost and holding cost is critical for production and operations management. Utilization of an operating room affects production cost, which relates to makespan, and patient flowtime affects holding cost. There are trade-offs between two objectives, to minimize makespan and to minimize flowtime. However, most existing constructive heuristics focus only on single-objective optimization. In the current literature, NEH is the best constructive heuristic to minimize makespan, and LR heuristic is the best to minimize flowtime. In this thesis, we propose a current and future deviation (CFD) heuristic to balance trade-offs between makespan and flowtime minimizations. Based on 5400 randomly generated instances and 120 instances in Taillard’s benchmarks, our CFD heuristic outperforms NEH and LR heuristics on trade-off balancing, and achieves the most stable performances from the perspective of statistical process control.

Los problemas de scheduling aparecen con profusión en la vida real en numerosos entornos productivos y de servicios. Se trata de problemas que requieren organizar en el tiempo la ejecución de tareas que compiten por el uso de un conjunto finito de recursos y que están sujetas a un conjunto de restricciones impuestas por factores como las características físicas del entorno, relaciones temporales o la normativa laboral. Además se trata de optimizar uno o varios criterios que se representan mediante funciones objetivo y que están relacionados normalmente con el coste, el beneficio o el tiempo de ejecución.Algunos ejemplos de problemas de esta naturaleza son los siguientes:· Fabricación de obleas para circuitos semiconductores, donde cada oblea precisa de una serie de tareas como limpieza, oxidación, metalización, etc. El objetivo puede maximizar la utilización de algunas máquinas que son cuello de botella o minimizar el tiempo de ejecución.· Planificar el aterrizaje de un conjunto de aviones sujetos a restricciones temporales que dependen de las características de los aviones. Los objetivos pueden ser minimizar la penalización por desvío con respecto al tiempo preferente de los aviones o maximizar las condiciones de seguridad.· Planificar las rutas de flotas de autobuses, donde se trata de optimizar la ocupación de los vehículos y de ajustar los turnos de los conductores de acuerdo con la normativa laboral.· Enrutamiento de paquetes de datos a través líneas de comunicación, donde se trata de maximizar el uso de la red y de minimizar los tiempos de llegada de los mensajes.Dado que estos problemas son de naturaleza combinatoria, es decir que hay que elegir una entre un conjunto exponencialmente grande de combinaciones posibles, los problemas de scheduling precisan de algoritmos de búsqueda inteligentes para encontrar soluciones aceptables en un tiempo razonable. Así, en la literatura se pueden encontrar aproximaciones a los problemas de scheduling basadas en prácticamente todas las metaheurísticas conocidas y en particular en los algoritmos de búsqueda heurística propios de áreas como la Investigación Operativa y la Inteligencia Artificial.En esta tesis nos centramos en el problema Job Shop Scheduling y en la técnica de búsqueda heurística en espacios de estados. Nuestro objetivo es diseñar estrategias que resulten eficaces y eficientes para diferentes funciones objetivo, tanto para encontrar soluciones exactas, cuando el tamaño del problema lo permita, como para obtener soluciones aproximadas para instancias mayores. La función objetivo a la que los investigadores han prestado mayor atención es sin duda el makespan, o tiempo de finalización de la última tarea. Las propiedades de esta versión del problema son muy bien conocidas y han permitido desarrollar métodos exactos y aproximados muy eficientes que se basan en el concepto de camino crítico. El inconveniente de estos métodos es que no se generalizan de forma eficiente para otras funciones objetivo como el tiempo de flujo total o el tardiness.La aportación principal de esta tesis es la formalización de un método de poda basado en relaciones de dominancia entre los estados del espacio de búsqueda que se puede aplicar en principio a todas las funciones objetivo convencionales. Aunque el método no resulta competitivo con los métodos basados en el camino crítico cuando se trata de minimizar el makespan, sí lo es con los métodos que no están basados en el camino crítico y que son generalizables a otras funciones objetivo. Para funciones objetivo como el tiempo de flujo total, los resultados experimentales que hemos realizado sobre bancos de ejemplos estándar demuestran que el método es competitivo con otros métodos del estado del arte tanto para obtener soluciones óptimas como sub-óptimas.

In cellular manufacturing systems, minimization of the completion time has a great impact on the production time, material flow, and productivity. An effective scheduling is crucial to attaining the advantages of cellular manufacturing systems. This dissertation attempts to solve the Flowshop Manufacturing Cell (cellular flowshop) Scheduling Problem with Sequence Dependent Setup Times (FMCSP with SDSTs) considering two performance measures: the total flow time as a mono objective, and the makespan and total flow time combined as a bi-criteria scheduling problem. The proposed problem is known to be the NP-hard problem because of its complexity. Several metaheuristic algorithms based on Genetic Algorithm (GA), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) are developed for scheduling part families as well as jobs within each part family for FMCSP with SDSTs to minimize the total flow time. A local search method based on SA combined with PSO (named as PSO-SA) is proposed to enhance the intensification and improve the quality of the solution obtained by pure PSO. The effectiveness and efficiency of the proposed metaheuristics are evaluated based on the Relative Percentage Deviation (RPD) from its lower bound, and the robustness. Results indicate PSO-SA is performed similar to best available algorithms for small and medium size test problems. Yet, there is a very small deviation from best results for large problems. A Multi-objective Particle Swarm Optimization (MPSO) and a Multi-objective Simulated Annealing (MOSA) Algorithm are further proposed to solve the bi-criteria optimization problem to minimize the total flow time and makespan simultaneously. An improved PSO is combined with Threshold Acceptance (TA) algorithm to improve effectiveness of the proposed MPSO (named as IMPSO-TA) for the convergence of the obtained Pareto Front. The proposed algorithms are evaluated using several Quality Indicators (QI) measures for multiobjective optimization problems. The proposed algorithms can generate approximated Pareto Fronts in a reasonable CPU time. The proposed IMPSO-SA outperforms MOSA algorithm in terms of CPU time and minimizing the objective functions. / October 2015

Let there be m parallel machines and n jobs to be scheduled non-preemptively. A job j scheduled on machine i takes p_{i,j} time units to complete, where 1 ≤ i ≤ m and 1 ≤ j ≤ n. For a given schedule, the makespan is the completion time of a machine that finishes last. The goal is to produce a schedule of all n jobs with minimum makespan. This is known as the makespan problem on unrelated parallel machines (UPMs), denoted as R||C_{max}. In this thesis, we focus on subclasses of R||C_{max}. Our research consists of two components. First, a survey of theoretic results for R||C_{max} with a focus on approximation algorithms is presented. Second, we present exact polynomial-time algorithms and approximation algorithms for some subclasses of R||C_{max}. For instance, we present k-approximation algorithms on par with or better than the best known for certain subclasses of R||C_{max}.