Task scheduling with precedence constraints to minimize the total completion time

The authors study the problem of scheduling a set of tasks with known execution times and arbitrary precedence constraints to computing systems. The objective function used to measure the performance of a schedule in this paper is the sum of completion times of all tasks, which is called total completion time. Finding the minimum total completion time of tasks with precedence constraints on the uniprocessor system is known to be NP-complete, let alone on the multiprocessor system (Garey and Johnson 1979) Based on the well-known A? algorithm proposed in the field of artificial intelligence (Nilson 1980) two algorithms are developed to solve efficiently the scheduling problems on the uniprocessor system and multiprocessor system. Some evaluation functions are proposed to accelerate the search of an optimal schedule. A table named the backwards range-limited table is used to assist the computation of the evaluation function. Experimental results show that the proposed approaches can achieve the optimal schedule with greatly reduced search tree size, especially when bounding rules are applied.     

A comparison of multiprocessor task scheduling algorithms with communication costs

Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. Of primary concern when analyzing these systems is multiprocessor task scheduling. Therefore, this paper addresses the challenge of multiprocessor task scheduling parallel programs, represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. Moreover, we investigate an alternative paradigm, where genetic algorithms (GAs) have recently received much attention, which is a class of robust stochastic search algorithms for various combinatorial optimization problems. We design the new encoding mechanism with a multi-functional chromosome that uses the priority representation—the so-called priority-based multi-chromosome (PMC). PMC can efficiently represent a task schedule and assign tasks to processors. The proposed priority-based GA has show effective performance in various parallel environments for scheduling methods.     

Task graph pre-scheduling, using Nash equilibrium in game theory

Prescheduling algorithms are targeted at restructuring of task graphs for optimal scheduling. Task graph scheduling is a NP-complete problem. This article offers a prescheduling algorithm for tasks to be executed on the networks of homogeneous processors. The proposed algorithm merges tasks to minimize their earliest start time while reducing the overall completion time. To this end, considering each task as a player attempting to reduce its earliest time as much as possible, we have applied the idea of Nash equilibrium in game theory to determine the most appropriate merging. Also, considering each level of a task graph as a player, seeking for distinct parallel processors to execute each of its independent tasks in parallel with the others, the idea of Nash equilibrium in game theory can be applied to determine the appropriate number of processors in a way that the overall idle time of the processors is minimized and the throughput is maximized. The communication delay will be explicitly considered in the comparisons. Our experiments with a number of known benchmarks task graphs and also two well-known problems of linear algebra, LU decomposition and Gauss–Jordan elimination, demonstrate the distinguished scheduling results provided by applying our algorithm. In our study, we consider ten scheduling algorithms: min–min, chaining, A ^?, genetic algorithms, simulated annealing, tabu search, HLFET, ISH, DSH with task duplication, and our proposed algorithm (PSGT).     

基于动态关键任务的多处理器任务分配算法

多处理器调度问题是影响系统性能的关键问题,基于任务复制的调度算法是解决多处理器调度问题较为有效的方法.文中分析了几个典型的基于任务复制算法,提出了基于动态关键任务(DCT)的多处理器任务分配算法.DCT算法以克服贪心算法不足为要点,调度过程中动态计算任务时间参数,准确确定处理器的关键任务,以关键任务为核心优化调度,逐步改善调度结果,最终取得最优的调度结果.分析和实验证明,DCT算法优于现有其它同类算法.     

Scheduling precedence constrained task graphs with non-negligibleintertask communication onto multiprocessors

The multiprocessor scheduling problem is the problem of scheduling the tasks of a precedence constrained task graph (representing a parallel program) onto the processors of a multiprocessor in a way that minimizes the completion time. Since this problem is known to be NP-hard in the strong sense in all but a few very restricted eases, heuristic algorithms are being developed which obtain near optimal schedules in a reasonable amount of computation time. We present an efficient heuristic algorithm for scheduling precedence constrained task graphs with nonnegligible intertask communication onto multiprocessors taking contention in the communication channels into consideration. Our algorithm for obtaining satisfactory suboptimal schedules is based on the classical list scheduling strategy. It simultaneously exploits the schedule-holes generated in the processors and in the communication channels during the scheduling process in order to produce better schedules. We demonstrate the effectiveness of our algorithm by comparing with two competing heuristic algorithms available in the literature     

基于分批优化的实时多处理器系统的集成动态调度算法

提出了一种基于分批优化的实时多处理器系统的集成动态调度算法，该算法采用在每次扩充当前局部调度时，通过对所选取的一批任务进行优化分配的策略以及软实时任务的服务质量QoS（quality of service）降级策略，以统一方式实现了对实时多处理器糸统中硬、软实时任务的集成动态调度．进行了大量的模拟研究，结果表明．在多种任务参数取值下，新算法的调度成功率均高于近视算法（Myopic Algorithm）．     

Communication-aware task scheduling and voltage selection for total energy minimization in a multiprocessor system using Ant Colony Optimization

Energy consumption is a key parameter when highly computational tasks should be performed in a multiprocessor system. In this case, in order to reduce total energy consumption, task scheduling and low-power methodology should be combined in an efficient way. This paper proposes an algorithm for off-line communication-aware task scheduling and voltage selection using Ant Colony Optimization. The proposed algorithm minimizes total energy consumption of an application executing on a homogeneous multiprocessor system. The artificial agents explore the search space based on stochastic decision-making using global heuristic information with total energy consumption and local heuristic information with interprocessor communication volume. In search space exploration, both voltage selection and the dependencies between tasks are considered. The pheromone trails are updated by normalizing the total energy consumption. The pheromone trails represent the global heuristic information in order to utilize all entire energy consumption information from previous evaluated solutions. Experimental results show that the proposed algorithm outperforms traditional communication-aware task scheduling and task scheduling using genetic algorithms in terms of total energy consumption.     

Real-time task scheduling by multiobjective genetic algorithm

Real-time tasks are characterized by computational activities with timing constraints and classified into two categories: a hard real-time task and a soft real-time task. In hard real-time tasks, tardiness can be catastrophic. The goal of hard real-time tasks scheduling algorithms is to meet all tasks’ deadlines, in other words, to keep the feasibility of scheduling through admission control. However, in the case of soft real-time tasks, slight violation of deadlines is not so critical.In this paper, we propose a new scheduling algorithm for soft real-time tasks using multiobjective genetic algorithm (moGA) on multiprocessors system. It is assumed that tasks have precedence relations among them and are executed on homogeneous multiprocessor environment.The objective of the proposed scheduling algorithm is to minimize the total tardiness and total number of processors used. For these objectives, this paper combines adaptive weight approach (AWA) that utilizes some useful information from the current population to readjust weights for obtaining a search pressure toward a positive ideal point. The effectiveness of the proposed algorithm is shown through simulation studies.     

Data‐aware task scheduling on heterogeneous hybrid memory multiprocessor systems

In this paper, we propose a method about task scheduling and data assignment on heterogeneous hybrid memory multiprocessor systems for real‐time applications. In a heterogeneous hybrid memory multiprocessor system, an important problem is how to schedule real‐time application tasks to processors and assign data to hybrid memories. The hybrid memory consists of dynamic random access memory and solid state drives when considering the performance of solid state drives into the scheduling policy. To solve this problem, we propose two heuristic algorithms called improvement greedy algorithm and the data assignment according to the task scheduling algorithm, which generate a near‐optimal solution for real‐time applications in polynomial time. We evaluate the performance of our algorithms by comparing them with a greedy algorithm, which is commonly used to solve heterogeneous task scheduling problem. Based on our extensive simulation study, we observe that our algorithms exhibit excellent performance and demonstrate that considering data allocation in task scheduling is significant for saving energy. We conduct experiments on two heterogeneous multiprocessor systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Efficient scheduling algorithms for real-time multiprocessorsystems

Efficient scheduling algorithms based on heuristic functions are developed for scheduling a set of tasks on a multiprocessor system. The tasks are characterized by worst-case computation times, deadlines, and resources requirements. Starting with an empty partial schedule, each step of the search extends the current partial schedule by including one of the tasks yet to be scheduled. The heuristic functions used in the algorithm actively direct the search for a feasible schedule, i.e. they help choose the task that extends the current partial schedule. Two scheduling algorithms are evaluated by simulation. To extend the current partial schedule, one of the algorithms considers, at each step of the search, all the tasks that are yet to be scheduled as candidates. The second focuses its attention on a small subset of tasks with the shortest deadlines. The second algorithm is shown to be very effective when the maximum allowable scheduling overhead is fixed. This algorithm is hence appropriate for dynamic scheduling in real-time systems     

A hybrid evolutionary approach for heterogeneous multiprocessor scheduling

This article investigates the assignment of tasks with interdependencies in a heterogeneous multiprocessor environment; specific to this problem, task execution time varies depending on the nature of the tasks as well as with the processing element assigned. The solution to this heterogeneous multiprocessor scheduling problem involves the optimization of complete task assignments and processing order between the assigned processors to arrive at a minimum makespan, subject to a precedence constraint. To solve an NP-hard combinatorial optimization problem, as is typified by this problem, this paper presents a hybrid evolutionary algorithm that incorporates two local search heuristics, which exploit the intrinsic structure of the solution, as well as through the use of specialized genetic operators to promote exploration of the search space. The effectiveness and contribution of the proposed features are subsequently validated on a set of benchmark problems characterized by different degrees of communication times, task, and processor heterogeneities. Preliminary results from simulations demonstrate the effectiveness of the proposed algorithm in finding useful schedule sets based on the set of new benchmark problems.     

实时多处理器系统的动态分批优化调度算法

提出了一种实时多处理器系统的新的高效动态调度算法--动态分批优化调度算法,该算法突破了以往算法中一次只安排一项任务的做法,采用在每次扩充当前局部调度时,按一定规则在待调度的任务集中选取一批任务,对该批任务中的每项任务在每个处理器上运行构造目标函数,将问题转化为非平衡分配问题,一次性为这些任务都安排一个处理器或为每个处理器安排一项任务,使得这种安排具有最好的"合适性",以增大未安排任务的可行性.这种方法极大地提高了算法的调度成功率.同时,为了研究该算法的有效性,对其进行了大量的模拟,分析了一些任务参数的变化对算法调度成功率的影响,并与节约算法的调度成功率进行了比较.模拟结果显示,在节约算法的调度成功率小于10%的约束条件下,该算法的调度成功率大于90%,说明新算法的优势是非常明显的.     

A Heuristic for the Maximum Processor Requirement for Scheduling Layered Task Graphs with Cloning

Programming models for distributed systems often construct a task graph for the program to be executed on a distributed system of processors. While the topology of the task graph can be constructed from the program structure, often the task execution times and data transfer costs between tasks depend on the input data, or more specifically, on the particular problem instance. Though this indicates that the optimal schedule of a task graph cannot be determined until the input data is available, it is possible to estimate theworst caseprocessor requirement for the optimal schedule of a program solely from the topology of its task graph. In this paper, we study the problem of estimating worst case processor requirements for scheduling (with cloning) layered task graphs based on their topology. We show that computing an accurate processor bound for layered graphs is NP hard (even for two layers) and present a polynomial time algorithm which computes an upper bound on the processor requirement. We show that the algorithm provides tight bounds for several common classes of layered task graphs.     

A two-phase scheduling method with the consideration of task clustering for earth observing satellites

Satellite observation scheduling plays a significant role in improving the efficiency of satellite observation systems. Although extensive scheduling algorithms have been proposed for the satellite observation scheduling problem (SOSP), the task clustering strategy has not been taken into account up to now. This paper presents a novel two-phase based scheduling method with the consideration of task clustering for solving SOSP. This method comprises two phases: a task clustering phase and a task scheduling phase. In the task clustering phase, we construct a task clustering graph model and use an improved minimum clique partition algorithm to obtain cluster-tasks. In the task scheduling phase, based on overall tasks and obtained cluster-tasks, we construct an acyclic directed graph model and utilize a hybrid ant colony optimization coming with a mechanism of local search, called ACO–LS, to produce optimal or near optimal schedules. Extensive experimental simulations demonstrate the efficiency of the proposed scheduling method.     

A heuristic-based hybrid genetic-variable neighborhood search algorithm for task scheduling in heterogeneous multiprocessor system

Effective task scheduling, which is essential for achieving high performance in a heterogeneous multiprocessor system, remains a challenging problem despite extensive studies. In this article, a heuristic-based hybrid genetic-variable neighborhood search algorithm is proposed for the minimization of makespan in the heterogeneous multiprocessor scheduling problem. The proposed algorithm distinguishes itself from many existing genetic algorithm (GA) approaches in three aspects. First, it incorporates GA with the variable neighborhood search (VNS) algorithm, a local search metaheuristic, to exploit the intrinsic structure of the solutions for guiding the exploration process of GA. Second, two novel neighborhood structures are proposed, in which problem-specific knowledge concerned with load balancing and communication reduction is utilized respectively, to improve both the search quality and efficiency of VNS. Third, the proposed algorithm restricts the use of GA to evolve the task-processor mapping solutions, while taking advantage of an upward-ranking heuristic mostly used by traditional list scheduling approaches to determine the task sequence assignment in each processor. Empirical results on benchmark task graphs of several well-known parallel applications, which have been validated by the use of non-parametric statistical tests, show that the proposed algorithm significantly outperforms several related algorithms in terms of the schedule quality. Further experiments are carried out to reveal that the proposed algorithm is able to maintain high performance within a wide range of parameter settings.     

基于布谷鸟搜索的多处理器任务调度算法

多处理器系统在高性能计算中扮演着重要角色.为提高系统的并行性能,基于布谷鸟搜索算法,提出一种新的多处理器任务调度算法.该算法以全部任务的最晚完成时间最小为目标,利用基于任务优先权的编码方式使连续的布谷鸟搜索算法适用于离散的多处理器任务调度问题.实验结果表明,所提算法不仅求解质量高,而且求解速度最快,与目前广泛采用的遗传算法和粒子群算法相比其执行时间缩短超过60％.     

基于任务图的并行调度MEWFM算法

随着多核处理器体系结构在计算机领域的广泛应用,如何合理地对计算任务进行调度成为人们广泛讨论的问题。目前已经有针对多处理器的任务调度算法,但是这些算法在执行时要经过多次迭代,执行效率比较低。提出一种改进的波前调度算法MEWFM,它是一种执行时间短,加速比接近处理器核数的一种算法。这种算法主要包括任务图分层,层内调度和误差下降调度三个子算法。详细分析了这些算法的特点和执行流程。实验评测表明,算法在多处理器环境下的任务调度方面具有执行速度快,性能高等优势。     

基于任务-资源分配图优化选取的网格依赖任务调度

任务调度是网格应用系统获得高性能的关键.网格计算中一个大型的应用程序往往被分解为具有依赖关系的多个任务.在资源个体差异较大、广域互连的网格环境下任务间的依赖关系对传统的调度策略提出了新的挑战.任务调度的主要工作是为任务分配资源以及确定任务的执行次序,将依赖任务的可能的资源分配方案表示为任务-资源分配图（T-RAG）,在该图的基础上提出了基于T-RAG优化选取的依赖任务调度模型,将依赖任务调度问题转化为图的优化选取问题,解析最优任务-资源分配图可以同时确定资源分配方案和任务的执行次序即为最优调度方案.最后,实现了基于该模型的任务调度算法,该算法与ILHA算法的对比分析表明,在资源差异较大及任务间存在大量数据传输的情况下所提出的算法更优.     

同构计算环境中一种快速有效的静态任务调度算法

快速有效的调度任务是多处理器计算环境中的一个关键问题．目前任务调度算法中刻画任务依赖关系最流行的模型是DAG,在以前的文献中,提出了一种新的更实际、更普遍的TTIG模型及其相应的MATE算法(基于同构计算环境)．延伸了TTIG模型,并提出基于同构系统的新的算法及两种启发式方法(GBHA1和GBHA2)．GBHA以组的形式尽量消除图中回路,因而能获得任务图的全局信息,具有更好的调度性能．在模拟实验中,将此算法与MATE和其他同构环境中基于DAG的有效调度算法,在不同测试条件下进行了比较,结果显示GBHA在性能上明显优于MATE,与基于DAG模型的调度算法比较而言,在性能方面各有千秋,但在算法时间复杂度方面具有显著的优势．     

多处理器调度算法实现及其Petri网建模与仿真

多处理器调度算法在嵌入式实时系统领域中起着关键的作用。根据多处理器的特点,提出一种实时多处理器动态分割并行调度算法SPara。该算法解决了此前多处理器算法,如Myopic、EDPF等仅依据截止期对任务调度产生的问题,实现了增加任务紧迫度限制的调度策略,以及针对执行时间长、截止期紧迫任务的有效调度方法。同时算法结合高级颜色时间Petri网理论进行建模并仿真。测试结果表明,SPara算法在处理器利用率以及调度成功率方面较Myopic等算法有较大提高。