The identical parallel processors scheduling problem with no-idle time, release date, and delivery time is addressed in this paper. The problem considers a family of tasks that has to be processed by identical paralle...
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The identical parallel processors scheduling problem with no-idle time, release date, and delivery time is addressed in this paper. The problem considers a family of tasks that has to be processed by identical parallel processors without idle time. Each task is ready for processing from a release date (arrival time) in an available processor. After completing the processing, a task is delivered during a delivery time. There is no-idle time in each processor from the first treated task until the last one. This is the no-idle processor time constraint, which is faced in real life problems. In these problems, minimizing the consumed energy during the processing of tasks is a crucial issue. Building a feasible schedule satisfying all the already mentioned constraints and minimizing the makespan (maximum completion time) is the objective. The studied scheduling problem is proofed to be NP-Hard in the strong sense. Therefore, a family of efficient heuristics solving the addressed problem are proposed. These heuristics are composed of two phases: Phase 1 and Phase 2. The building of a feasible schedule is performed during phase 1, while in the second phase (phase 2) an improvement procedure is proposed. In order to evaluate the quality of the proposed heuristics, a tight lower bound is developed. The optimal solution of the parallelprocessors scheduling problem with release date and delivery time is the basic used algorithm while developing the proposed procedures (heuristics and lower bound). In order to assess the performance and the efficiency of the proposed procedures, an extensive experimental study is carried out. During this experimental study the relative mean gap is not exceeding 0.7%, which provides strong evidence of the performance of the developed procedures.
For real-time systems, time optimizing without increasing the complexity of the system and the applications it relies on is a very challenging problem. Using revised algorithms, the authors propose an improved approac...
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ISBN:
(纸本)9781728105215
For real-time systems, time optimizing without increasing the complexity of the system and the applications it relies on is a very challenging problem. Using revised algorithms, the authors propose an improved approach that utilizes the read frequency rate of the data sent by railway track sensors. The track sensors send frequently the captured data to a database in the control unit of the railway monitoring system. The received data will be saved in the database in a table called the DC table. The main question is: How the system can read a maximum number of saved data from the DC table within a predefined time limit? This is an NP-hard problem, and the best solution is to read all DC saved data, while the worst case is to read minimal or no data. For this based problem a new approach was proposed. This approach is based on the separated periods and the jobs algorithm (SPJ) and is demonstrated by six heuristics (LPT, SPT, MF, SS, MSS, and MSK). Experimental results showed that there is no dominance among the implemented six heuristics, heuristic with best results is that based on knapsack problem.
This article considers the problem of scheduling n jobs on m identical parallel processors where an optimal schedule is defined as one that produces minimum makespan (the completion time of the last job) and total tar...
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This article considers the problem of scheduling n jobs on m identical parallel processors where an optimal schedule is defined as one that produces minimum makespan (the completion time of the last job) and total tardiness among the set of schedules. Such a problem is known as identicalparallel processor makespan and total tardiness problem. In order to minimize makespan and total tardiness of identical parallel processors, improved versions of particle swarm optimization and harmony search algorithm are proposed to enhance scheduling performance with less computational burden. The major drawback of particle swarm optimization in terms of premature convergence at initial stage of iterations is avoided through the use of mutation, a commonly used operator in genetic algorithm, by introducing diversity in the solution. The proposed algorithm is termed as particle swarm optimization with mutation. The convergence rate of harmony search algorithm is improved by fine tuning of parameters such as pitch adjusting rate and bandwidth for improving the solution. The performance of the schedules is evaluated in terms of makespan and total tardiness. The results are analyzed in terms of percentage deviation of the solution from the lower bound on makespan. The results indicate that particle swarm optimization with mutation produces better solutions when compared with genetic algorithm and particle swarm optimization in terms of average percentage deviation. However, harmony search algorithm outperforms genetic algorithm, particle swarm optimization, and particle swarm optimization with mutation in terms of average percentage deviation. In certain instances, the solution obtained by harmony search algorithm outperforms existing clonal selection particle swarm optimization.
The problem of scheduling a set of n unit execution time (UET) tasks subject to precedence constraints on m identical parallel processors is known to be N P-hard in the strong sense, However, polynomial time algorithm...
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The problem of scheduling a set of n unit execution time (UET) tasks subject to precedence constraints on m identical parallel processors is known to be N P-hard in the strong sense, However, polynomial time algorithms exist for some classes of precedence graphs. In this paper, we consider a class of divide-and-conquer graphs that naturally models the execution of the recursive control abstraction of divide-and-conquer algorithms. We prove that the Highest Level First (HLF) strategy minimizes the schedule length for this class, thus settling a conjecture of Rayward-Smith and Clark. (C) 2008 Elsevier B.V. All rights reserved.
Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one pro...
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Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family.
A set of unit-time tasks has to be processed on identical parallel processors subject to precedence constraints and unit-time communication delays;does there exist a schedule of length at most d? The problem has two v...
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A set of unit-time tasks has to be processed on identical parallel processors subject to precedence constraints and unit-time communication delays;does there exist a schedule of length at most d? The problem has two variants, depending on whether the number of processors is restrictively small or not. For the first variant the question can be answered in polynomial time for d = 3 and is NP-complete for d = 4. The second variant is solvable in polynomial time for d = 5 and NP-complete for d = 6. As a consequence, neither of the corresponding optimization problems has a polynomial approximation scheme, unless P = NP.
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