Genetic algorithms for task scheduling problem

The scheduling and mapping of the precedence-constrained task graph to processors is considered to be the most crucial NP-complete problem in parallel and distributed computing systems. Several genetic algorithms have been developed to solve this problem. A common feature in most of them has been the use of chromosomal representation for a schedule. However, these algorithms are monolithic, as they attempt to scan the entire solution space without considering how to reduce the complexity of the optimization process. In this paper, two genetic algorithms have been developed and implemented. Our developed algorithms are genetic algorithms with some heuristic principles that have been added to improve the performance. According to the first developed genetic algorithm, two fitness functions have been applied one after the other. The first fitness function is concerned with minimizing the total execution time (schedule length), and the second one is concerned with the load balance satisfaction. The second developed genetic algorithm is based on a task duplication technique to overcome the communication overhead. Our proposed algorithms have been implemented and evaluated using benchmarks. According to the evolved results, it has been found that our algorithms always outperform the traditional algorithms.     

A comparison of two chromosome representation schemes used in solving a family-based scheduling problem

Meta-heuristic algorithms have been widely used in solving scheduling problems; previous studies focused on enhancing existing algorithmic mechanisms. This study advocates a new perspective—developing new chromosome (solution) representation schemes may improve the performance of existing meta-heuristic algorithms. In the context of a scheduling problem, known as permutation manufacturing-cell flow shop (PMFS), we compare the effectiveness of two chromosome representation schemes (S_old and S_new) while they are embedded in a meta-heuristic algorithm to solve the PMFS scheduling problem. Two existing meta-heuristic algorithms, genetic algorithm (GA) and ant colony optimization (ACO), are tested. Denote a tested meta-heuristic algorithm by X_Y, where X represents an algorithmic mechanism and Y represents a chromosome representation. Experiment results indicate that GA_ S_new outperforms GA_S_old, and ACO_S_new also outperforms ACO_S_old. These findings reveal the importance of developing new chromosome representations in the application of meta-heuristic algorithms.     

A Load Balanced Task Scheduling Heuristic for Large-Scale Computing Systems

Optimal task allocation in Large-Scale Computing Systems (LSCSs) that endeavors to balance the load across limited computing resources is considered an NP-hard problem. MinMin algorithm is one of the most widely used heuristic for scheduling tasks on limited computing resources. The MinMin minimizes makespan compared to other algorithms, such as Heterogeneous Earliest Finish Time (HEFT), duplication based algorithms, and clustering algorithms. However, MinMin results in unbalanced utilization of resources especially when majority of tasks have lower computational requirements. In this work we consider a computational model where each machine has certain bounded capacity to execute a predefined number of tasks simultaneously. Based on aforementioned model, a task scheduling heuristic Extended High to Low Load (ExH2LL) is proposed that attempts to balance the workload across the available computing resources while improving the resource utilization and reducing the makespan. ExH2LL dynamically identifies task-to-machine assignment considering the existing load on all machines. We compare ExH2LL with MinMin, H2LL, Improved MinMin Task Scheduling (IMMTS), Load Balanced MaxMin (LBM), and M-Level Suffrage-Based Scheduling Algorithm (MSSA). Simulation results show that ExH2LL outperforms the compared heuristics with respect to makespan and resource utilization. Moreover, we formally model and verify the working of ExH2LL using High Level Petri Nets, Satisfiability Modulo Theories Library, and Z3 Solver.     

求解多处理机调度问题的蚁群算法

蚁群算法是受自然界中的蚂蚁觅食行为启发而设计的智能优化算法，特别适合处理离散型的组合优化问题。提出一种求解多处理机调度的蚁群算法,利用一个蚂蚁代表一个处理机来选择任务，并通过分析关键路径及每个任务的最早、最迟开始时间来确定每个任务的紧迫程度，让蚂蚁以此来选择任务。实验证明，该算法可比传统算法取得有更好运行效率的调度策略。     

An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups

In many real-world production systems, it requires an explicit consideration of sequence-dependent setup times when scheduling jobs. As for the scheduling criterion, the weighted tardiness is always regarded as one of the most important criteria in practical systems. While the importance of the weighted tardiness problem with sequence-dependent setup times has been recognized, the problem has received little attention in the scheduling literature. In this paper, we present an ant colony optimization (ACO) algorithm for such a problem in a single-machine environment. The proposed ACO algorithm has several features, including introducing a new parameter for the initial pheromone trail and adjusting the timing of applying local search, among others. The proposed algorithm is experimented on the benchmark problem instances and shows its advantage over existing algorithms. As a further investigation, the algorithm is applied to the unweighted version of the problem. Experimental results show that it is very competitive with the existing best-performing algorithms.     

Contribution to the scheduling of trajectories in robotics

In this paper, we intend to propose a method for minimizing the cycle time of robotic tasks by using an optimal scheduling of trajectory points: we consider functional points (welding or laser-cutting points on a car-body for example) that a robot has to reach. The problem is to order these points in such a way that the global cycle time is minimum. Originally, this scheduling problem is similar to the well-known travelling salesman problem. Among the algorithms used in combinatorial optimization, we have taken an interest in an original connectionist method called “the elastic net method”, initially presented in an euclidian two-dimension space. The method described in this article is adapted for robotic purpose. It has been tested in industrial cases and compared with a classical method in combinatorial optimization: the Little’s algorithm. The elastic net method is generalized to the specific case of robotics applications. The elastic net method is generalized in the case of non-redundant and redundant robots; we develop a simultaneous research of the optimal scheduling and of the optimal choice of the configurations of the robot for each functional point. The optimal scheduling of the points of a trajectory in the case of redundant robots is presented. We consider it to be the original contribution of this work. In the case of cluttered environments, the above algorithm is adapted by introducing a repulsion potential between the obstacles and the “elastic”. This leads to the simultaneous research of the optimal scheduling and of the free path planning. The method, using a new kind of algorithm, leads to original and reliable results for minimizing cycle time in robotics.     

Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems

Earliness/tardiness scheduling problems with undetermined common due date which have wide application background in textile industry, mechanical industry, electronic industry and so on, are very important in the research fields such as industry engineering and CIMS. In this paper, a kind of genetic algorithm based on sectional code for minimizing the total cost of assignment of due date, earliness and tardiness in this kind of scheduling problem is proposed to determine the optimal common due date and the optimal scheduling policy for determining the job number and their processing order on each machine. Also, simulated annealing mechanism and the iterative heuristic fine-tuning operator are introduced into the genetic algorithm so as to construct three kinds of hybrid genetic algorithms with good performance. Numerical computational results focusing on the identical parallel machine scheduling problem and the general parallel machine scheduling problem shows that these algorithms outperform heuristic procedures, and fit for larger scale parallel machine earliness/tardiness scheduling problem. Moreover, with practical application data from one of the largest cotton colored weaving enterprises in China, numerical computational results show that these genetic algorithms are effective and robust, and that especially the performance of the hybrid genetic algorithm based on simulated annealing and the iterative heuristic fine-tuning operator is the best among them.     

一种基于调度簇树的周期性分布实时任务调度算法

本文针对现有的基于任务复制的静态调度算法在调度周期性分布实时任务时存在的缺点，提出了一种称之为调度簇树（SCT）的新的结构并研究了其特性，在此基础上给出了一种基于SCT树的周期性分布实时任务调度算法（SAS）。通过与OSA算法进行比较的实验结果表明，SAS算法可实现调度长度向上最接近分布实时任务周期，最大程度减少所需顸留处理器数目，大大提高分布实时系统的处理器利用率，同时并不增加调度算法的复杂度。     

离散微粒群优化算法在网格任务调度中的应用

网格任务调度算法是影响网格成功与否的关键技术之一.在研究现有任务调度策略的基础上,指出Min-Min算法的负载不均衡性.借鉴遗传算法中的交叉操作过程,提出了一种新的任务调度算法.该算法对传统的连续型微粒群优化算法进行改进,使其适用于网格任务调度问题的优化处理,实现网格资源的优化分配.仿真研究表明该算法更符合网格调度的复杂环境,能得到较短的任务执行时间和较好的负载均衡性.对比分析表明,离散微粒群优化算法所得结果优于常用的Min-Min调度方案,是一种高效的调度方法.     

基于改进DPSO的网格资源调度算法

基于市场经济模型的网格资源调度问题是一个典型的离散问题及NP-Hard问题,考虑到离散粒子群优化算法在解决离散问题上的有效性,本文在现有算法的研究基础上,提出一种基于改进的离散粒子群优化算法的网格资源分配和任务调度算法,并采用GridSim模拟器对相关算法进行仿真模拟实验和比较。实验结果表明,本文提出的调度算法在作业完成时间、综合性能以及资源的负载平衡方面均具有较大的优势。     

遗传算法解柔性作业车间调度问题应用综述

柔性作业车间调度问题是典型的NP难问题,对实际生产应用具有指导作用。近年来,随着遗传算法的发展,利用遗传算法来解决柔性作业车间调度问题的思想和方法层出不穷。为了促进遗传算法求解柔性作业车间调度问题的进一步发展,阐述了柔性作业车间调度问题的研究理论,对已有改进方法进行了分类,通过对现存问题的分析,探讨了未来的发展方向。     

并行任务调度的近似算法

并行任务调度不论是从理论上还是应用上近年来都倍受关注。但是目前出现的大量算法很难应用于实际,基于此,论文探讨了典型的调度问题P3｜fix｜Cmax,这类问题是强NP-难的。论文在Goemans的研究基础上,给出了一个很简单的线性算法,构造出调度性能为9/8的半规则调度,改进了Goemans的7/6的结果。     

A hierarchical reliability-driven scheduling algorithm in grid systems

In a Grid computing system, many distributed scientific and engineering applications often require multi-institutional collaboration, large-scale resource sharing, wide-area communication, etc. Applications executing in such systems inevitably encounter different types of failures such as hardware failure, program failure, and storage failure. One way of taking failures into account is to employ a reliable scheduling algorithm. However, most existing Grid scheduling algorithms do not adequately consider the reliability requirements of an application. In recognition of this problem, we design a hierarchical reliability-driven scheduling architecture that includes both a local scheduler and a global scheduler. The local scheduler aims to effectively measure task reliability of an application in a Grid virtual node and incorporate the precedence constrained tasks’ reliability overhead into a heuristic scheduling algorithm. In the global scheduler, we propose a hierarchical reliability-driven scheduling algorithm based on quantitative evaluation of independent application reliability. Our experiments, based on both randomly generated graphs and the graphs of some real applications, show that our hierarchical scheduling algorithm performs much better than the existing scheduling algorithms in terms of system reliability, schedule length, and speedup.     

Reliability-aware scheduling strategy for heterogeneous distributed computing systems

Heterogeneous computing systems are promising computing platforms, since single parallel architecture based systems may not be sufficient to exploit the available parallelism with the running applications. In some cases, heterogeneous distributed computing (HDC) systems can achieve higher performance with lower cost than single-machine supersystems. However, in HDC systems, processors and networks are not failure free and any kind of failure may be critical to the running applications. One way of dealing with such failures is to employ a reliable scheduling algorithm. Unfortunately, most existing scheduling algorithms for precedence constrained tasks in HDC systems do not adequately consider reliability requirements of inter-dependent tasks. In this paper, we design a reliability-driven scheduling architecture that can effectively measure system reliability, based on an optimal reliability communication path search algorithm, and then we introduce reliability priority rank (RRank) to estimate the task’s priority by considering reliability overheads. Furthermore, based on directed acyclic graph (DAG) we propose a reliability-aware scheduling algorithm for precedence constrained tasks, which can achieve high quality of reliability for applications. The comparison studies, based on both randomly generated graphs and the graphs of some real applications, show that our scheduling algorithm outperforms the existing scheduling algorithms in terms of makespan, scheduling length ratio, and reliability. At the same time, the improvement gained by our algorithm increases as the data communication among tasks increases.     

On multiprocessor task scheduling using efficient state space search approaches

Obtaining an optimal schedule for a set of precedence-constrained tasks is a well-known NP-complete problem in its general form. In view of the intractability of the problem, most of the previous work relies on heuristics that try to find reasonably high quality solutions in an acceptable amount of time. While optimal polynomial-time algorithms are known only for a few simple cases (and in other cases can only be obtained through an exhaustive search with prohibitively high time complexity), they may be critically important for applications in which performance is the prime objective. Optimal solutions can also serve as a reference to test the performance of various heuristics. Moreover, an optimal schedule for a program at hand needs to be determined only once (and off-line) but the program using that schedule is in general executed several times. In this paper, we propose optimal algorithms for static scheduling of task graphs with arbitrary parameters to multiple homogeneous processors. The first algorithm is based on the A^* search technique and uses a computationally efficient cost function for guiding the search with reduced complexity. Additionally, we propose a number of effective state-pruning techniques to reduce the search space. For further lowering the complexity, we propose an efficient parallelization of the search algorithm. We parallelize the algorithm with reduced interprocessor communication as well as with static and dynamic load-balancing schemes to evenly distribute the search states to the processors. We also propose an approximate algorithm that guarantees a bounded deviation from the optimal solution but executes in a considerably shorter time. Based on an extensive experimental evaluation of the algorithms, we conclude that the parallel algorithm with pruning techniques is an efficient scheme for generating optimal solutions of reasonably large problems while the approximate algorithm is effective if slightly degraded solutions are acceptable.     

Using quadratic programming to solve high multiplicity scheduling problems on parallel machines

We introduce and analyze several models of schedulingn different types (groups) of jobs onm parallel machines, where in each group all jobs are identical. Our main goal is to exhibit the usefulness of quadratic programming approaches to solve these classes of high multiplicity scheduling problems, with the total weighted completion time as the minimization criterion. We develop polynomial algorithms for some models, and strongly polynomial algorithms for certain special cases. In particular, the model in which the weights are job independent, as well as the generally weighted model in which processing requirements are job independent, can be formulated as an integer convex separable quadratic cost flow problem, and therefore solved in polynomial time. When we specialize further, strongly polynomial bounds are achievable. Specifically, for the weighted model with job-independent processing requirements if we restrict the weights to be machine independent (while still assuming different machine speeds), anO(mn+n logn) algorithm is developed. If it is also assumed that all the machines have the same speed, the complexity of the algorithm can be improved toO(m logm+n logn). These results can be extended to related unweighted models with variable processing requirements in which all the machines are available at time zero. The research of Frieda Granot was partially supported by Natural Sciences and Engineering Research Council of Canada Grant 5-83998. The research of Jadranka Skorin-Kapov was partially supported by National Science Foundation Grant DDM-8909206.     

On-line scheduling of parallel machines to minimize total completion times

In this paper, we consider the scheduling problem on identical parallel machines, in which jobs are arriving over time and preemption is not allowed. The goal is to minimize the total completion times. According to the idea of the Delayed-SPT Algorithm proposed by Hoogeven and Vestjens [Optimal on-line algorithms for single-machine scheduling. In: Proceedings 5th international conference on integer programming and combinatorial optimization (IPCO). Lecture notes in computer science, vol. 1084. Berlin: Springer; 1996. p. 404–14], we give an on-line algorithm for the scheduling problem on m$m$ identical parallel machines. We show that this algorithm is 2-competitive and the bound is tight.     

带约束的清洁排班问题模型及其求解

保洁服务公司的清洁任务往往具有不同级别、不同时长和不同周期等特点,缺乏通用清洁排班问题模型,现阶段主要依赖人工排班方案,存在耗时费力且排班质量不稳定等问题。因此提出了属于NP难问题的带约束的清洁排班问题的数学模型,并使用模拟退火算法（SA）、蜂群算法（BCO）、蚁群算法（ACO）和粒子群优化算法（PSO）对该模型进行求解,最后以某清洁服务公司实际排班情况进行了实证分析。实验结果表明,与人工排班方案进行对比,启发式智能优化算法求解带约束的清洁排班问题具有明显优势,获得的清洁排班表的人力需求明显减少。具体来说,在一年排班周期内这些算法比人工排班方案可节省清洁人力218.62~513.30 h。可见基于启发式智能优化算法的数学模型对带约束的清洁排班问题的求解可行且有效,能为保洁服务公司提供科学管理的决策支持。     

GIS空间数据格式并行转换的调度算法

分析了GIS两种常见的空间数据格式（GRID、TIN）并行转换的可行性，并给出了两种基于Cluster结构的并行转换的任务调度算法。其中确定模式的调度算实现比较简单，但在任务的执行有严格的次序；非确定模式的调度算法可以根据任务具体的执行时间确定任务执行的次序。实验表明：在任务分配不均衡时，非确定模式的调度算法效率更高。     

Minimizing Makespan and Preemption Costs on a System of Uniform Machines

It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for non-preemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem. In generalized multiprocessor scheduling (GMS) we have a job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS) the only feasible schedules are preemptive schedules with the smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions. For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. Our scheme for a fixed number of machines has linear running time, and can be applied also for instances where jobs have release dates, and for instances with arbitrary preemption costs. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule. Our results for MPS hold for any instance in which a job, J_j, can be processed simultaneously by ρ_j machines, for some ρ_j ≥ 1.