Complexity and heuristic algorithms for speed scaling scheduling of parallel jobs with energy constraint

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-09-06 DOI:10.1016/j.cam.2024.116254

Yulia Zakharova, Maria Sakhno

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引用次数: 0

Abstract

Developing modern computer technologies makes it possible not only to solve complex computing problems, but also gives rise to new problems of optimal usage of computing resources. Modern computers can use multiple processors simultaneously and dynamically change the speed of calculations due to additional energy consumption for performing intensive calculations. We consider the speed scaling scheduling problem with energy constraint and parallel jobs. The total sum of completion times is minimized. The NP-hardness of the problem is proved and a mixed integer convex program with continuous time representation is proposed. For searching near-optimal solutions in quick time we develop a genetic algorithm with the generational replacement scheme. The genetic algorithm is experimentally tested and compared with the known greedy algorithm and local improvements technique on meaningful instances. The numerical results highlight the effectiveness and the efficiency of the proposed algorithm. The lower bounds on the objective function and convex program are also experimentally evaluated.

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具有能量约束的并行作业速度扩展调度的复杂性和启发式算法

现代计算机技术的发展不仅使解决复杂的计算问题成为可能，而且还带来了优化使用计算资源的新问题。现代计算机可以同时使用多个处理器，并且由于执行密集型计算需要消耗额外的能量，因此可以动态地改变计算速度。我们考虑的是具有能量约束和并行作业的速度扩展调度问题。完成时间总和最小。我们证明了该问题的 NP 难度，并提出了一个具有连续时间表示的混合整数凸程序。为了在短时间内搜索近似最优解，我们开发了一种采用世代替换方案的遗传算法。我们对遗传算法进行了实验测试，并在有意义的实例上将其与已知的贪婪算法和局部改进技术进行了比较。数值结果凸显了所提算法的有效性和效率。实验还评估了目标函数和凸程序的下限。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.