Aproximating static list schedules in dynamic multithreaded applications

List scheduling algorithms are known to be efficient when the application to be executed can be described statically as a Directed Acyclic Graph (DAG) of tasks. Regardless of knowing the entire DAG beforehand, obtaining an optimal schedule in a parallel machine is a NP-hard problem. Moreover, many programming tools propose the use of scheduling techniques based on list strategies. This paper presents an analysis of scheduling algorithms for multithread programs in a dynamic scenario where threads are created and destroyed during execution. We introduce an algorithm to convert DAGs, describing applications as tasks, into Directed Cyclic Graphs (DCGs) describing the same application designed in a multithread programming interface. Our algorithm covers case studies described in previous works, successfully mapping from the abstract level of graphs to the application environment. These mappings preserve the guarantees offered by the abstract model, providing efficient scheduling of dynamic programs that follow the intended multithread model. We conclude the paper presenting some performance results we obtained by list schedulers in dynamic multithreaded environments. We also compare these results with the best scheduling we could obtain with similar static task schedulers.     

Resource dedication problem in a multi-project environment

There can be different approaches to the management of resources within the context of multi-project scheduling problems. In general, approaches to multi-project scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may not be feasible. In such cases, the resources must be dedicated to individual projects throughout the project durations. This multi-project problem environment is defined here as the resource dedication problem (RDP). RDP is defined as the optimal dedication of resource capacities to different projects within the overall limits of the resources and with the objective of minimizing a predetermined objective function. The projects involved are multi-mode resource constrained project scheduling problems with finish to start zero time lag and non-preemptive activities and limited renewable and nonrenewable resources. Here, the characterization of RDP, its mathematical formulation and two different solution methodologies are presented. The first solution approach is a genetic algorithm employing a new improvement move called combinatorial auction for RDP, which is based on preferences of projects for resources. Two different methods for calculating the projects’ preferences based on linear and Lagrangian relaxation are proposed. The second solution approach is a Lagrangian relaxation based heuristic employing subgradient optimization. Numerical studies demonstrate that the proposed approaches are powerful methods for solving this problem.     

Genetic Algorithm Based Scheduling of Meta-Tasks with Stochastic Execution Times in Heterogeneous Computing Systemst1

In this study, we address the meta-task scheduling problem in heterogeneous computing (HC) systems, which is to find a task assignment that minimizes the schedule length of a meta-task composed of several independent tasks with no data dependencies. The fact that the meta-task scheduling problem in HC systems is NP-hard has motivated the development of many heuristic scheduling algorithms. These heuristic algorithms, however, neglect the stochastic nature of task execution times in an attempt to minimize a deterministic objective function, which is the maximum of the expected values of machine loads. Contrary to existing heuristics, we account for this stochastic nature by modeling task execution times as random variables. We, then, formulate a stochastic scheduling problem where the objective is to minimize the expected value of the maximum of machine loads. We prove that this new objective is underestimated by the deterministic objective function and that an optimal task assignment obtained with respect to the deterministic objective function could be inefficient in a real computing platform. In order to solve the stochastic scheduling problem posed, we develop a genetic algorithm based scheduling heuristic. Our extensive simulation studies show that the proposed genetic algorithm can produce better task assignments as compared to existing heuristics. Specifically, we observe a performance improvement on the relative cost heuristic (M.-Y. Wu and W. Shu, A high-performance mapping algorithm for heterogeneous computing systems, in: Int. Parallel and Distributed Processing Symposium, San Francisco, CA, April 2001) by up to 61%.     

New meta-heuristics for the resource-constrained project scheduling problem

In this paper, we study the resource-constrained project scheduling problem and introduce an annealing-like search heuristic which simulates the cooling process of a gas into a highly-ordered crystal. To achieve this, we develop diversification procedures that simulate the motion of high energy molecules as well as a local refinement procedure that simulates the motion of low energy molecules. We further improve the heuristic by incorporating a genetic algorithm framework. The meta-heuristic algorithms are applied to Kolisch’s PSPLIB J30, J60 and J120 RCPSP instances. Experimental results show that they are effective and are among the best performing algorithms for the RCPSP.     

A New Cyclic Scheduling Algorithm for Flexible Manufacturing Systems

Flexible manufacturing system control is an NP-hard problem. A cyclic approach has been demonstrated to be adequate for an infinite scheduling problem because of maximal throughput reachability. However, it is not the only optimization criterion in general. In this article we consider the minimization of the work in process (WIP) as an economical and productivity factor. We propose a new cyclic scheduling algorithm giving the maximal throughput (a hard constraint) while minimizing WIP. This algorithm is based on progressive operations placing. A controlled beam search approach has been developed to determine at each step the schedule of the next operations. After presenting the main principles of the algorithm, we compare our approach to several most known cyclic scheduling algorithms using a significant existing example from the literature.     

Comparison of mixed integer linear programming models for the resource-constrained project scheduling problem with consumption and production of resources

This paper addresses an extension of the resource-constrained project scheduling problem that takes into account storage resources which may be produced or consumed by activities. To solve this problem, we propose the generalization of two existing mixed integer linear programming models for the classical resource-constrained project scheduling problem, as well as one novel formulation based on the concept of event. Computational results are reported to compare these formulations with each other, as well as with a reference method from the literature. Conclusions are drawn on the merits and drawbacks of each model according to the instance characteristics.     

Project scheduling with resource capacities and requests varying with time: a case study

This paper discusses an extension of the classical resource-constrained project scheduling problem in which the resource availability as well as the resource request of the activities may change from period to period. While the applicability of this extension should be obvious, we provide a case study in order to emphasize the need for the extension. A real-world medical research project is presented which has a structure that is typical for many other medical and pharmacological research projects that consist of experiments. Subsequently, we provide a mathematical model and analyze some properties of the extended problem setting. We also introduce a new priority rule heuristic that is based on a randomized activity selection mechanism which makes use of so-called tournaments. Finally, we report our computational results for the original data of the medical research project as well as for a set of systematically generated test instances.     

A study of nurse scheduling in Japan

Scheduling nurses to staff shifts is a major problem in hospitals. The necessity of maintaining a certain level of service and skill in the makeup of every shift, while balancing the workload among the nurses involved, is incredibly difficult. It is often impossible to develop a schedule which satisfies all the requirements despite the time and resources spent in the effort. This paper summarizes all our published research on nurse scheduling to date. The difficulties realized by our two investigations in Japan are shown first, together with a resulting scheduling problem. The nurse scheduling model based on the results is then described. In this model, all constraints are divided into two essentially different types; that which maintains a certain level of skill for each shift ('shift constraints') and that which concerns the workload for each nurse ('nurse constraints'). By classifying the constraints in this manner, we can determine what is affected by a specific constraint when the constraint is not satisfied. We developed efficient algorithms while taking advantage of the structure of this model. Finally, it is shown that our algorithm can solve this problem for a 2-shift system efficiently.     

HSGA: a hybrid heuristic algorithm for workflow scheduling in cloud systems

In heterogeneous distributed computing systems like cloud computing, the problem of mapping tasks to resources is a major issue which can have much impact on system performance. For some reasons such as heterogeneous and dynamic features and the dependencies among requests, task scheduling is known to be a NP-complete problem. In this paper, we proposed a hybrid heuristic method (HSGA) to find a suitable scheduling for workflow graph, based on genetic algorithm in order to obtain the response quickly moreover optimizes makespan, load balancing on resources and speedup ratio. At first, the HSGA algorithm makes tasks prioritization in complex graph considering their impact on others, based on graph topology. This technique is efficient to reduction of completion time of application. Then, it merges Best-Fit and Round Robin methods to make an optimal initial population to obtain a good solution quickly, and apply some suitable operations such as mutation to control and lead the algorithm to optimized solution. This algorithm evaluates the solutions by considering efficient parameters in cloud environment. Finally, the proposed algorithm presents the better results with increasing number of tasks in application graph in contrast with other studied algorithms.     

A novel task scheduling approach based on dynamic queues and hybrid meta-heuristic algorithms for cloud computing environment

Task scheduling is one of the most challenging aspects to improve the overall performance of cloud computing and optimize cloud utilization and Quality of Service (QoS). This paper focuses on Task Scheduling optimization using a novel approach based on Dynamic dispatch Queues (TSDQ) and hybrid meta-heuristic algorithms. We propose two hybrid meta-heuristic algorithms, the first one using Fuzzy Logic with Particle Swarm Optimization algorithm (TSDQ-FLPSO), the second one using Simulated Annealing with Particle Swarm Optimization algorithm (TSDQ-SAPSO). Several experiments have been carried out based on an open source simulator (CloudSim) using synthetic and real data sets from real systems. The experimental results demonstrate the effectiveness of the proposed approach and the optimal results is provided using TSDQ-FLPSO compared to TSDQ-SAPSO and other existing scheduling algorithms especially in a high dimensional problem. The TSDQ-FLPSO algorithm shows a great advantage in terms of waiting time, queue length, makespan, cost, resource utilization, degree of imbalance, and load balancing.     

Hierarchical genetic-based grid scheduling with energy optimization

An optimization of power and energy consumptions is the important concern for a design of modern-day and future computing and communication systems. Various techniques and high performance technologies have been investigated and developed for an efficient management of such systems. All these technologies should be able to provide good performance and to cope under an increased workload demand in the dynamic environments such as Computational Grids (CGs), clusters and clouds. In this paper we approach the independent batch scheduling in CG as a bi-objective minimization problem with makespan and energy consumption as the scheduling criteria. We use the Dynamic Voltage Scaling (DVS) methodology for scaling and possible reduction of cumulative power energy utilized by the system resources. We develop two implementations of Hierarchical Genetic Strategy-based grid scheduler (Green-HGS-Sched) with elitist and struggle replacement mechanisms. The proposed algorithms were empirically evaluated versus single-population Genetic Algorithms (GAs) and Island GA models for four CG size scenarios in static and dynamic modes. The simulation results show that proposed scheduling methodologies fairly reduce the energy usage and can be easily adapted to the dynamically changing grid states and various scheduling scenarios.     

Managing performance and power consumption tradeoff for multiple heterogeneous servers in cloud computing

There are typically multiple heterogeneous servers providing various services in cloud computing. High power consumption of these servers increases the cost of running a data center. Thus, there is a problem of reducing the power cost with tolerable performance degradation. In this paper, we optimize the performance and power consumption tradeoff for multiple heterogeneous servers. We consider the following problems: (1) optimal job scheduling with fixed service rates; (2) joint optimal service speed scaling and job scheduling. For problem (1), we present the Karush-Kuhn-Tucker (KKT) conditions and provide a closed-form solution. For problem (2), both continuous speed scaling and discrete speed scaling are considered. In discrete speed scaling, the feasible service rates are discrete and bounded. We formulate the problem as an MINLP problem and propose a distributed algorithm by online value iteration, which has lower complexity than a centralized algorithm. Our approach provides an analytical way to manage the tradeoff between performance and power consumption. The simulation results show the gain of using speed scaling, and also prove the effectiveness and efficiency of the proposed algorithms.     

Energy-aware task scheduling in heterogeneous computing environments

Efficient application scheduling is critical for achieving high performance in heterogeneous computing (HC) environments. Because of such importance, there are many researches on this problem and various algorithms have been proposed. Duplication-based algorithms are one kind of well known algorithms to solve scheduling problems, which achieve high performance on minimizing the overall completion time (makespan) of applications. However, they pursuit of the shortest makespan overly by duplicating some tasks redundantly, which leads to a large amount of energy consumption and resource waste. With the growing advocacy for green computing systems, energy conservation has been an important issue and gained a particular interest. An existing technique to reduce energy consumption of an application is dynamic voltage/frequency scaling (DVFS), whose efficiency is affected by the overhead of time and energy caused by voltage scaling. In this paper, we propose a new energy-aware scheduling algorithm with reduced task duplication called Energy-Aware Scheduling by Minimizing Duplication (EAMD), which takes the energy consumption as well as the makespan of an application into consideration. It adopts a subtle energy-aware method to search and delete redundant task copies in the schedules generated by duplication-based algorithms, and it is easier to operate than DVFS, and produces no extra time and energy consumption. This algorithm not only consumes less energy but also maintains good performance in terms of makespan compared with duplication-based algorithms. Two kinds of DAGs, i.e., randomly generated graphs and two real-world application graphs, are tested in our experiments. Experimental results show that EAMD can save up to 15.59 % energy consumption for HLD and HCPFD, two classic duplication-based algorithms. Several factors affecting the performance are also analyzed in the paper.     

Robust optimization for resource-constrained project scheduling with uncertain activity durations

The purpose of this paper is to propose models for project scheduling when there is considerable uncertainty in the activity durations, to the extent that the decision maker cannot with confidence associate probabilities with the possible outcomes of a decision. Our modeling techniques stem from robust discrete optimization, which is a theoretical framework that enables the decision maker to produce solutions that will have a reasonably good objective value under any likely input data scenario. We develop and implement a scenario-relaxation algorithm and a scenario-relaxation-based heuristic. The first algorithm produces optimal solutions but requires excessive running times even for medium-sized instances; the second algorithm produces high-quality solutions for medium-sized instances and outperforms two benchmark heuristics.     

Reconstruction of ancestral genomic sequences using likelihood.

A challenging task in computational biology is the reconstruction of genomic sequences of extinct ancestors, given the phylogenetic tree and the sequences at the leafs. This task is best solved by calculating the most likely estimate of the ancestral sequences, along with the most likely edge lengths. We deal with this problem and also the variant in which the phylogenetic tree in addition to the ancestral sequences need to be estimated. The latter problem is known to be NP-hard, while the computational complexity of the former is unknown. Currently, all algorithms for solving these problems are heuristics without performance guarantees. The biological importance of these problems calls for developing better algorithms with guarantees of finding either optimal or approximate solutions.We develop approximation, fix parameter tractable (FPT), and fast heuristic algorithms for two variants of the problem; when the phylogenetic tree is known and when it is unknown. The approximation algorithm guarantees a solution with a log-likelihood ratio of 2 relative to the optimal solution. The FPT has a running time which is polynomial in the length of the sequences and exponential in the number of taxa. This makes it useful for calculating the optimal solution for small trees. Moreover, we combine the approximation algorithm and the FPT into an algorithm with arbitrary good approximation guarantee (PTAS). We tested our algorithms on both synthetic and biological data. In particular, we used the FPT for computing the most likely ancestral mitochondrial genomes of hominidae (the great apes), thereby answering an interesting biological question. Moreover, we show how the approximation algorithms find good solutions for reconstructing the ancestral genomes for a set of lentiviruses (relatives of HIV). Supplementary material of this work is available at www.nada.kth.se/~isaac/publications/aml/aml.html.     

MIP formulations for an application of project scheduling in human resource management

In the literature, various discrete-time and continuous-time mixed-integer linear programming (MIP) formulations for project scheduling problems have been proposed. The performance of these formulations has been analyzed based on generic test instances. The objective of this study is to analyze the performance of discrete-time and continuous-time MIP formulations for a real-life application of project scheduling in human resource management. We consider the problem of scheduling assessment centers. In an assessment center, candidates for job positions perform different tasks while being observed and evaluated by assessors. Because these assessors are highly qualified and expensive personnel, the duration of the assessment center should be minimized. Complex rules for assigning assessors to candidates distinguish this problem from other scheduling problems discussed in the literature. We develop two discrete-time and three continuous-time MIP formulations, and we present problem-specific lower bounds. In a comparative study, we analyze the performance of the five MIP formulations on four real-life instances and a set of 240 instances derived from real-life data. The results indicate that good or optimal solutions are obtained for all instances within short computational time. In particular, one of the real-life instances is solved to optimality. Surprisingly, the continuous-time formulations outperform the discrete-time formulations in terms of solution quality.     

Block‐cyclic redistribution over heterogeneous networks

Clusters of workstations and networked parallel computing systems are emerging as promising computational platforms for HPC applications. The processors in such systems are typically interconnected by a collection of heterogeneous networks such as Ethernet, ATM, and FDDI, among others. In this paper, we develop techniques to perform block-cyclic redistribution over P processors interconnected by such a collection of heterogeneous networks. We represent the communication scheduling problem using a timing diagram formalism. Here, each interprocessor communication event is represented by a rectangle whose height denotes the time to perform this event over the heterogeneous network. The communication scheduling problem is then one of appropriately positioning the rectangles so as to minimize the completion time of all the communication events. For the important case where the block size changes by a factor of K, we develop a heuristic algorithm whose completion time is at most twice the optimal. The running time of the heuristic is O(PK ²). Our heuristic algorithm is adaptive to variations in network performance, and derives schedules at run-time, based on current information about the available network bandwidth. Our experimental results show that our schedules always have communication times that are very close to optimal. This revised version was published online in July 2006 with corrections to the Cover Date.     

An ant-based coordination mechanism for resource-constrained project scheduling with multiple agents and cash flow objectives

We consider a multi-agent extension of the non-preemptive single-mode resource-constrained project scheduling problem with discounted cash flow objectives. Such a problem setting is related to project scheduling problems which involve different autonomous firms where project activities are uniquely assigned to the project parties (agents). Taking into account opportunistic agents and the resulting information asymmetry we propose a general decentralized negotiation approach which uses ideas from ant colony optimization. In the course of the negotiation the agents iteratively vote on proposed project schedules without disclosing preference information regarding cash flow values. Computational experiments serve to analyze the agent-based coordination mechanism in comparison to other approaches from the literature. The proposed mechanism turns out as an effective method for coordinating self-interested agents with conflicting goals which collaborate in resource-constrained projects.     

Link contention-constrained scheduling and mapping of tasks and messages to a network of heterogeneous processors

In this paper, we consider the problem of scheduling and mapping precedence-constrained tasks to a network of heterogeneous processors. In such systems, processors are usually physically distributed, implying that the communication cost is considerably higher than in tightly coupled multiprocessors. Therefore, scheduling and mapping algorithms for such systems must schedule the tasks as well as the communication traffic by treating both the processors and communication links as equally important resources. We propose an algorithm that achieves these objectives and adapts its task scheduling and mapping decisions according to the given network topology. Just like tasks, messages are also scheduled and mapped to suitable links during the minimization of the finish times of tasks. Heterogeneity of processors is exploited by scheduling critical tasks to the fastest processors. Our experimental study has demonstrated that the proposed algorithm is efficient and robust, and yields consistent performance over a wide range of scheduling parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

A task scheduling algorithm for arbitrarily-connected processors with awareness of link contention

In this paper, we present a new task scheduling algorithm, called Contention-Aware Scheduling (CAS) algorithm, with the objective of delivering good quality of schedules in low running-time by considering contention on links of arbitrarily-connected, heterogeneous processors. The CAS algorithm schedules tasks on processors and messages on links by considering the earliest finish time attribute with the virtual cut-through (VCT) or the store-and-forward (SAF) switching. There are three types of CAS algorithm presented in this paper, which differ in ordering the messages from immediate predecessor tasks. As part of the experimental study, the performance of the CAS algorithm is compared with two well-known APN (arbitrary processor network) scheduling algorithms. Experiments on the results of the synthetic benchmarks and the task graphs of the well-known problems clearly show that our CAS algorithm outperforms the related work with respect to performance (given in normalized schedule length) and cost (given in running time) to generate output schedules. Ali Fuat Alkaya received the B.Sc. degree in mathematics from Koc University, Istanbul, Turkey in 1998, and the M.Sc. degree in computer engineering from Marmara University, Istanbul, Turkey in 2002. He is currently a Ph.D. student in engineering management department at the same university. His research interests include task scheduling and analysis of algorithms. Haluk Rahmi Topcuoglu received the B.Sc. and M.Sc. degrees in computer engineering from Bogazici University, Istanbul, Turkey, in 1991 and 1993, respectively. He received the Ph.D. degree in computer science from Syracuse University in 1999. He has been on the faculty at Marmara University, Istanbul, Turkey since Fall 1999, where he is currently an Associate Professor in computer engineering department. His main research interests are task scheduling and mapping in parallel and distributed systems; parallel processing; evolutionary algorithms and their applicability for stationary and dynamic environments. He is a member of the ACM, the IEEE, and the IEEE Computer Society. e-mail: haluk@eng.marmara.edu.tr e-mail: falkaya@eng.marmara.edu.tr