712 research outputs found

    Very Large-Scale Neighborhoods with Performance Guarantees for Minimizing Makespan on Parallel Machines

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    We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima

    Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines

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    We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima.operations research and management science;

    Local search performance guarantees for restricted related parallel machine scheduling

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    We consider the problem of minimizing the makespan on restricted related parallel machines. In restricted machine scheduling each job is only allowed to be scheduled on a subset of machines. We study the worst-case behavior of local search algorithms. In particular, we analyze the quality of local optima with respect to the jump, swap, push and lexicographical jump neighborhood.operations research and management science;

    Efficient heuristics for the parallel blocking flow shop scheduling problem

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    We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.Peer ReviewedPostprint (author's final draft

    Design and evaluation of a tabu search method for job scheduling in distributed enviorments

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    The efficient allocation of jobs to grid resources is indispensable for high performance grid-based applications. The scheduling problem is computationally hard even when there are no dependencies among jobs. Thus, we present in this paper a new tabu search (TS) algorithm for the problem of batch job scheduling on computational grids. We consider the job scheduling as a bi-objective optimization problem consisting of the minimization of the makespan and flowtime. The bi-objectivity is tackled through a hierarchic approach in which makespan is considered a primary objective and flowtime a secondary one. An extensive experimental study has been first conducted in order to fine-tune the parameters of our TS algorithm. Then, our tuned TS is compared versus two well known TS algorithms in the literature (one of them is hybridized with an ant colony optimization algorithm) for the problem. The computational results show that our TS implementation clearly outperforms the compared algorithms. Finally, we evaluated the performance of our TS algorithm on a new set of instances that better fits with the concept of computational grid. These instances are composed of a higher number of -heterogeneous- machines (up to 256) and emulate the dynamic behavior of these systems.Peer ReviewedPostprint (published version

    Energy-aware scheduling in heterogeneous computing systems

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    In the last decade, the grid computing systems emerged as useful provider of the computing power required for solving complex problems. The classic formulation of the scheduling problem in heterogeneous computing systems is NP-hard, thus approximation techniques are required for solving real-world scenarios of this problem. This thesis tackles the problem of scheduling tasks in a heterogeneous computing environment in reduced execution times, considering the schedule length and the total energy consumption as the optimization objectives. An efficient multithreading local search algorithm for solving the multi-objective scheduling problem in heterogeneous computing systems, named MEMLS, is presented. The proposed method follows a fully multi-objective approach, applying a Pareto-based dominance search that is executed in parallel by using several threads. The experimental analysis demonstrates that the new multithreading algorithm outperforms a set of fast and accurate two-phase deterministic heuristics based on the traditional MinMin. The new ME-MLS method is able to achieve significant improvements in both makespan and energy consumption objectives in reduced execution times for a large set of testbed instances, while exhibiting very good scalability. The ME-MLS was evaluated solving instances comprised of up to 2048 tasks and 64 machines. In order to scale the dimension of the problem instances even further and tackle large-sized problem instances, the Graphical Processing Unit (GPU) architecture is considered. This line of future work has been initially tackled with the gPALS: a hybrid CPU/GPU local search algorithm for efficiently tackling a single-objective heterogeneous computing scheduling problem. The gPALS shows very promising results, being able to tackle instances of up to 32768 tasks and 1024 machines in reasonable execution times.En la última década, los sistemas de computación grid se han convertido en útiles proveedores de la capacidad de cálculo necesaria para la resolución de problemas complejos. En su formulación clásica, el problema de la planificación de tareas en sistemas heterogéneos es un problema NP difícil, por lo que se requieren técnicas de resolución aproximadas para atacar instancias de tamaño realista de este problema. Esta tesis aborda el problema de la planificación de tareas en sistemas heterogéneos, considerando el largo de la planificación y el consumo energético como objetivos a optimizar. Para la resolución de este problema se propone un algoritmo de búsqueda local eficiente y multihilo. El método propuesto se trata de un enfoque plenamente multiobjetivo que consiste en la aplicación de una búsqueda basada en dominancia de Pareto que se ejecuta en paralelo mediante el uso de varios hilos de ejecución. El análisis experimental demuestra que el algoritmo multithilado propuesto supera a un conjunto de heurísticas deterministas rápidas y e caces basadas en el algoritmo MinMin tradicional. El nuevo método, ME-MLS, es capaz de lograr mejoras significativas tanto en el largo de la planificación y como en consumo energético, en tiempos de ejecución reducidos para un gran número de casos de prueba, mientras que exhibe una escalabilidad muy promisoria. El ME-MLS fue evaluado abordando instancias de hasta 2048 tareas y 64 máquinas. Con el n de aumentar la dimensión de las instancias abordadas y hacer frente a instancias de gran tamaño, se consideró la utilización de la arquitectura provista por las unidades de procesamiento gráfico (GPU). Esta línea de trabajo futuro ha sido abordada inicialmente con el algoritmo gPALS: un algoritmo híbrido CPU/GPU de búsqueda local para la planificación de tareas en en sistemas heterogéneos considerando el largo de la planificación como único objetivo. La evaluación del algoritmo gPALS ha mostrado resultados muy prometedores, siendo capaz de abordar instancias de hasta 32768 tareas y 1024 máquinas en tiempos de ejecución razonables

    An Iterated Greedy Algorithm for a Parallel Machine Scheduling Problem with Re-entrant and Group Processing Features

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    This research paper addresses a novel parallel machine scheduling problem with re-entrant and group processing features, specifically motivated by the hot milling process in the modern steel manufacturing industry. The objective is to minimize the makespan. As no existing literature exists on this problem, the paper begins by analyzing the key characteristics of the problem. Subsequently, a mixed integer linear programming model is formulated. To tackle the problem, an improved iterated greedy algorithm (IGA) is proposed. The IGA incorporates a problem-specific heuristic to construct the initial solution. Additionally, it incorporates an effective destruction and reconstruction procedure. Furthermore, an acceptance rule is developed to prevent the IGA from getting stuck in local optima. The proposed approach is evaluated through computational experiments. The results demonstrate that the proposed IGA outperforms three state-of-the-art meta-heuristics, highlighting its high effectiveness. Overall, this research contributes to the understanding and solution of the parallel machine scheduling problem with re-entrant and group processing features in the context of the hot milling process. The proposed algorithm provides insights for practical applications in the steel manufacturing industry

    A DECOMPOSITION-BASED HEURISTIC ALGORITHM FOR PARALLEL BATCH PROCESSING PROBLEM WITH TIME WINDOW CONSTRAINT

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    This study considers a parallel batch processing problem to minimize the makespan under constraints of arbitrary lot sizes, start time window and incompatible families. We first formulate the problem with a mixed-integer programming model. Due to the NP-hardness of the problem, we develop a decomposition-based heuristic to obtain a near-optimal solution for large-scale problems when computational time is a concern. A two-dimensional saving function is introduced to quantify the value of time and capacity space wasted. Computational experiments show that the proposed heuristic performs well and can deal with large-scale problems efficiently within a reasonable computational time. For the small-size problems, the percentage of achieving optimal solutions by the DH is 94.17%, which indicates that the proposed heuristic is very good in solving small-size problems. For large-scale problems, our proposed heuristic outperforms an existing heuristic from the literature in terms of solution quality
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