List Scheduling Approach Research Articles

An Efficient Augmented Lagrange Multiplier Method for Steelmaking and Continuous Casting Production Scheduling

The steelmaking and continuous casting (SCC) process is one of the vital processes in iron and steel plants since it determines chemical compositions of slabs and is often a bottleneck for iron and steel manufacturing. In this paper, we first develop a discrete-time mixed-integer linear programming (MILP) formulation for a new SCC scheduling problem where different processing routes are used to produce diversified and personalized slab products. To solve the proposed MILP formulation efficiently, we then propose a novel efficient solution algorithm using Augmented Lagrange multiplier method (e-ALM) through relaxation of the coupling constraints and incorporation of penalty components. A heuristic-based list scheduling approach as well as adjacent pairwise swap operations is used to construct a high-quality feasible schedule. A fine-adjusting strategy based on the subgradient direction is proposed to update Lagrangian multipliers dynamically to speed up the convergence. It is shown that the proposed e-ALM is able to generate optimal or near-optimal solutions with 5% optimality for 150 industrial-scale instances and outperform the commercial solver GAMS/CPLEX and the existing Lagrangian relaxation algorithms with better feasible solutions and smaller duality gap within the specified computational time.

Decomposition methods for cost and tardiness reduction in aircraft manufacturing flow lines

A manufacturing system consisting of two subsystems is considered in low-volume manufacturing as found in the aerospace industry. The first subsystem consists of parallel mixed-model assembly lines whereas identical parallel stations form the second one. A finite buffer is between the subsystems. A combined objective function is used which accounts for total labor and inventory costs at the first subsystem and for the makespan and total weighted tardiness (TWT) at the second subsystem. The jobs have to be assigned to one of the parallel assembly lines. They then have to be sequenced at each single assembly line. Workers have to be assigned to each job and station. Assignment and sequencing decisions have to be made for the jobs at the second subsystem to calculate the makespan and the TWT value. A random-key genetic algorithm (RKGA) assigns jobs to the assembly lines and sequences them there. The RKGA is hybridized with heuristics and exact approaches to determine start and completion times of the jobs at the stations. A list scheduling approach makes the decisions associated with the second subsystem. Outsourcing is applied to deal with the finite buffer between the two subsystems. Results of computational experiments based on randomly generated problem instances demonstrate that the decomposition approaches perform well.

Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived.

An Efficient Task Priority Measurement for List-Scheduling in Multiprocessor Environments

Optimized task scheduling is one the most important factors to achieve highperformance in multiprocessor environments such as parallel and distributed systems. A large number of proposed approaches to solve this problem use list-scheduling technique in which a list of tasks is created based on the some priority measurements, and then in each step, the most priority task in the list is selected to schedule on the processor that allows the earliest start time. Therefore, the achieved schedule length is highly coherent with how order the tasks are selected to execute. Whereas selected task priority measurement determines which task order would be extracted, in this paper, we survey five traditional task priority measurements named height-level (HL), top-level (TL), bottom-level (BL), static-level (SL) and as-late-as-possible (ALAP) which have been extensively used in the different list-scheduling approaches. In addition, a new efficient task priority measurement based on the number-ofoffspring (NOO) of tasks in task-graph is introduced and evaluated beside the others. The evaluation is made by doing various experiments on random task-graphs with different shape parameters and task-graphs of real-world programs using measures such as normalized schedule length (NSL), pair-wise and global comparison and best solution. Based on the results, it can generally be seen that the proposed NOO is the best, HL, BL, SL and ALAP are temperate (their ranks are slightly changed based on the selected comparison measure), and TL has the worst performance.

Scheduling with an Orthogonal Resource Constraint

We address a scheduling problem that arises in highly parallelized environments like modern multi-core CPU/GPU computer architectures where simultaneously active jobs share a common limited resource, e.g., memory cache. The scheduler must ensure that the demand for the common resource never exceeds the available capacity. This introduces an orthogonal constraint to the classical minimum makespan scheduling problem. Such a constraint also arises in other contexts where a common resource is shared across machines. We study the non-preemptive case of this problem and present a (2+ϵ)-approximation algorithm which relies on the interplay of several classical and modern techniques in scheduling like grouping, job-classification, and the use of configuration-LPs. This improves upon previous bound of 3 that can be obtained by list scheduling approaches, and gets close to the (3/2−ϵ) inapproximability bound. If the number of machines or the number of different resource requirements are bounded by a constant we obtain a polynomial time approximation scheme.

Task scheduling using Bayesian optimization algorithm for heterogeneous computing environments

Abstract Efficient task scheduling, as a crucial step to achieve high performance for multiprocessor platforms, remains one of the challenge problems despite of numerous studies. This paper presents a novel scheduling algorithm based on the Bayesian optimization algorithm (BOA) for heterogeneous computing environments. In the proposed algorithm, scheduling is divided into two phases. First, according to the task graph of multiprocessor scheduling problems, Bayesian networks are initialized and learned to capture the dependencies between different tasks. And the promising solutions assigning tasks to different processors are generated by sampling the Bayesian network. Second, the execution sequence of tasks on the same processor is set by the heuristic-based priority used in the list scheduling approach. The proposed algorithm is evaluated and compared with the related approaches by means of the empirical studies on random task graphs and benchmark applications. The experimental results show that the proposed algorithm is able to deliver more efficient schedules. Further experiments indicate that the proposed algorithm maintains almost the same performance with different parameter settings.

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.

Late work minimization in flow shops by a genetic algorithm

The work concerns the permutation flow shop scheduling problem with release times and the late work criterion. The late work criterion estimates the quality of a solution with regard to the duration of the late parts of jobs, not taking into account the quantity of the delay for the fully late activities. Particular jobs consist of a sequence of tasks, which have to be executed in the same order on a set of dedicated machines. The execution of a job has to start after its release time and it should finish preferably before its due date. Since the problem is known to be NP-hard, we propose a genetic algorithm to solve this scheduling case. We describe the components of the method, which is based on an indirect solution representation as a sequence of priority dispatching rules. A sequence of rules is transformed to a schedule by the list scheduling approach. Then, we report results of computational experiments, which were preceded by the tuning process of the genetic algorithm. Tests were performed for randomly generated instances of different difficulty in terms of the distribution of release times and due dates over time, as well as the number of jobs and machines. We analyze the results of computational experiments disclosing a strong influence of the problem data on the efficiency of the proposed meta-heuristic algorithm.

Greedy Tree Growing Heuristics on Block-Test Scheduling Under Power Constraints

Greedy scheduling algorithms are proposed here to improve the test concurrency under power limits. An extended tree growing technique is used to model the power-constrained test scheduling problem in these algorithms. A constant additive model is employed for power dissipation analysis and estimation. The efficiency of this approach is assessed with test scheduling examples and the experimental results are presented. Known list scheduling approaches are proven to give acceptable power-constrained test scheduling results quickly, but not guaranteed to be optimal.

Iterative schedule optimization for voltage scalable distributed embedded systems

We present an iterative schedule optimization for multirate system specifications, mapped onto heterogeneous distributed architectures containing dynamic voltage scalable processing elements (DVS-PEs). To achieve a high degree of energy reduction, we formulate a generalized DVS problem, taking into account the power variations among the executing tasks. An efficient heuristic is presented that identifies optimized supply voltages by not only "simply" exploiting slack time, but under the additional consideration of the power profiles. Thereby, this algorithm minimizes the energy dissipation of heterogeneous architectures, including power-managed processing elements, effectively. Further, we address the simultaneous schedule optimization toward timing behavior and DVS utilization by integrating the proposed DVS heuristic into a genetic list scheduling approach. We investigate and analyze the possible energy reduction at both steps of the co-synthesis (voltage scaling and scheduling), including the power variations effects. Extensive experiments indicate that the presented work produces solutions with high quality.

Algorithms and analysis of scheduling for low-power high-performance DSP on VLIW processors

Switching activity and schedule length are the two most important factors that influence the energy consumption of an application executed on a VLIW (very long instruction word) processor. Considering these two factors together, we propose an instruction-level energy-minimisation scheduling technique to reduce the energy consumption of applications on VLIW processors. We first formally prove that this problem is NP-complete. Then three heuristic algorithms, MSAS, MLMSA, and EMSA, are proposed. While switching activity and schedule length are given higher priority in MSAS and MLMSA respectively, EMSA gives the best result considering both of them. The experimental results show that EMSA gives a 31.7% reduction in energy compared with the traditional list scheduling approach on average.

List scheduling of general task graphs under LogP

List scheduling is the most frequently used scheduling technique. In this context worst case analysis as well as many experimental studies were performed for various computational models. However, many new models have been proposed during the last decade with the aim to provide a realistic but still simple and general model of parallel computation. LogP is one of the most popular models so far suggested. It takes into account the time a computation processor spends to manage a communication. Many experimental studies on current parallel architectures have shown that such a parameter cannot be neglected. The aim of this paper is to assess the applicability of the list scheduling approach to the LogP model. More precisely, we present two adaptations of the earliest task first (ETF) heuristic. Then, we establish an upper bound on list schedules under LogP. Finally, we present an extensive experimental study for different graph classes and model instances.

Due-date based loading and scheduling methods for a flexible manufacturing system with an automatic tool transporter

We consider the loading and scheduling problems in flexible manufacturing systems (FMSs) in which each part visits only one machine for its entire processing. In this type of FMS, if required tools are not loaded on the tool magazine of a machine, they can be transferred from other machines or a tool crib. For the efficient operation of such systems, loading and scheduling of parts and tools should be done carefully. This paper focuses on the problems of part loading, tool loading, and part sequencing with the objective of minimizing the total tardiness. We suggest three heuristic approaches, called list scheduling, sequential, and iterative approaches. In the list scheduling approach, loading plans of parts and tools and schedules are determined simultaneously according to part priorities. In the sequential approach, a parallel machine scheduling problem is solved to determine the loading plan and the sequence of parts, and then the tool loading problem is solved using the part loading plan. With methods similar to those used in the sequential approach, the part loading and sequencing problem and tool loading problem are solved iteratively in the iterative approach. Results of computational tests on randomly generated problems show that the iterative approach performs better than the others.

Static scheduling for barrier MIMD architectures

In a SIMD or VLIW machine, conceptual synchronizations are accomplished by using a static code schedule that does not require run-time synchronization. The lack of run-time synchronization overhead makes these machines very effective for fine-grain parallelism, but they cannot execute parallel code structures as general as those executed by MIMD architectures, and this limits their utility.In this paper we present a timing analysis that allows a compiler for a MIMD machine to eliminate a large fraction of the run-time synchronization by making efficient use of static code scheduling. Although these techniques can be adapted to be applied to most MIMD machines, this paper centers on the analysis and scheduling for barrier MIMD machines. Barrier MIMDs are asynchronous multiple instruction stream/multiple data stream architectures capable of parallel execution of variable execution-time instructions and arbitrary control flow (e.g., while loops and calls). However, they also incorporate a special hardware barrier synchronization mechanism that facilitates static scheduling by providing a mechanism which the compiler can use to enforce precise timing constraints. In other words, the compiler tracks relative timing between processors and uses static code scheduling until the timing imprecision becomes too large, at which point the compiler simply inserts a barrier to reduce that timing imprecision to zero (or a small constant).This paper describes new scheduling and barrier placement algorithms for barrier MIMDs that are based loosely on the list scheduling approach employed for VLIWs [Ellis 1985]. In addition, the experimental results from scheduling thousands of synthetic benchmark programs for a parameterized barrier MIMD machine are presented.