Multiprocessor Task Research Articles

Chaotic Walk in Simulated Annealing Search Space for Task Allocation in a Multiprocessing System

This paper proposes the application of chaos in large search space problems, and suggests that this represents the next evolutionary step in the development of adaptive and intelligent systems towards cognitive machines and systems. Three different versions of chaotic simulated annealing (XSA) were applied to combinatorial optimization problems in multiprocessor task allocation. Chaotic walks in the solution space were taken to search for the global optimum or “good enough” task-to-processor allocation solutions. Chaotic variables were generated to set the number of perturbations made in each iteration of a XSA algorithm. In addition, parameters of a chaotic variable generator were adjusted to create different chaotic distributions with which to search the solution space. The results show that the convergence rate of the XSA algorithm is faster than simulated annealing when the solutions are far apart in the solution space. In particular, the XSA algorithms found simulated annealing’s best result on average about 4 times faster than simulated annealing.

A multiprocessor-oriented power-conscious scheduling algorithm for periodic tasks

With the rapid development of advanced technology in VLSI circuit designs, many processors could provide dynamic voltage scaling (DVS) to save power consumption when the supply voltage is allowed to be lower. In this paper, we propose a multiprocessor-oriented power-conscious scheduling algorithm for the real-time periodic tasks with task migration constrained scheme. We classify periodic tasks into fixed tasks and migration tasks, and limit the number of migration tasks and the number of destination processors which execute migration tasks. The proposed algorithm is made up of two steps. Firstly, choosing a processor to sort all of the periodic tasks in a non-increasing order according to task utilization, afterwards, allocating them to other processors. Secondly, scheduling the migration tasks with a virtual execution windows policy, and then scheduling the fixed tasks with EDF algorithm. The experiment results show that compared with arbitrary task migration policy and no task migration allowed policy, the power consumption in multiprocessor real-time periodic tasks scheduling is lowered significantly with the proposed algorithm.

Static scheduling of directed acyclic data flow graphs onto multiprocessors using particle swarm optimization

An efficient method based on particle swarm optimization (PSO) is developed to solve the Multiprocessor Task Scheduling Problem (MPTSP). To efficiently execute parallelized programs on a multiprocessor environment, a scheduling problem must be solved to determine the assignment of tasks to the processors, the execution order of the tasks, and the starting time of each task, such that some optimality criteria are met. The scheduling problem is known as an NP-complete problem even when the target processors are fully connected and no communication delay is considered among the tasks in the task graph. The complexity of the scheduling problem depends on the number of tasks (N), the number of processors (M), the task processing time and the precedence constraints. The Directed Acyclic Graph (DAG) was exploited to represent the tasks and their precedence constraints. The proposed algorithm was compared with the Genetic Algorithm (GA) and the Duplication Scheduling Heuristic (DSH). We also provide a systematic investigation on the effect of varying problem settings. The results show that the proposed algorithm could not outperform the DSH while it could outperform the GA in some cases.

An effective shuffled frog-leaping algorithm for hybrid flow-shop scheduling with multiprocessor tasks

As a strongly NP-hard problem, the hybrid flow-shop problem with multiprocessor tasks (HFSPMT) has gained increasing attention due to its academic significance and application value. In this paper, an effective algorithm based on the shuffled frog leaping algorithm (SFLA) is proposed for solving the HFSPMT. First, three decoding methods are used together to decode a solution to a better schedule. Especially, the forward scheduling decoding method is employed, aiming at narrowing the idle time between consecutive operations in the processor as well as increasing the flexibility in selecting processors to schedule the following operations. Second, a bilevel crossover is designed to make each individual share the good “meme” within each memeplex and exchange the good “meme” between different memeplexes. Third, multiple local search operators are used in an effective way by employing the meta-Lamarckian learning strategy to enhance the local exploitation ability. Meanwhile, the use of crossover and local search together in the SFLA can enrich the memetic search behavior and balance the exploration and exploitation abilities. In addition, the effect of parameter setting of the algorithm is investigated based on the Taguchi method of design of experiment, and suitable values are suggested for the parameters. Extensive testing results based on two types of well-known benchmarks are provided. And the effectiveness of the proposed algorithm is demonstrated by the comparisons with some existing algorithms.

An effective immune algorithm based on novel dispatching rules for the flexible flow-shop scheduling problem with multiprocessor tasks

As a strongly NP-hard problem, the flexible flow-shop problem with multiprocessor tasks (FFSPMT) has gained much attention due to its academic significance and wide application background. To solve the FFSPMT, the dispatching rule is crucial to decode job order sequences to schedules, which has a great effect on the quality of the solution. In this paper, several novel dispatching rules are proposed to arrange the job processing order and machine assignment to minimize makespan of the FFSPMT by narrowing the idle time between the consecutive operations in the processor as well as by increasing the flexibility in selecting processors to schedule the following operations. With these rules, an immune algorithm (IA) is proposed to solve the FFSPMT, where special crossover, mutation, and vaccination operators are well designed and utilized. Meanwhile, some theoretical analysis for the local search operators is provided for guiding local search reasonably. The computational results based on 120 well-known benchmark instances and comparisons with some existing algorithms demonstrate the effectiveness of the proposed dispatching rules and the immune algorithm.

Multiprocessor task scheduling in multistage hybrid flowshops: A hybrid artificial bee colony algorithm with bi-directional planning

In this paper, the problem of scheduling multistage hybrid flowshops with multiprocessor tasks is contemplated. This is a strongly NP-hard problem for which a hybrid artificial bee colony (HABC) algorithm with bi-directional planning is developed to minimize makespan. To validate the effectiveness of the proposed algorithm, computational experiments were tested on two well-known benchmark problem sets. The computational evaluations manifestly support the high performance of the proposed HABC against the best-so-far algorithms applied in the literature for the same benchmark problem sets.

A hybrid approach based on the variable neighborhood search and particle swarm optimization for parallel machine scheduling problems—A case study for solar cell industry

Abstract This paper studies a solar cell industry scheduling problem which is similar to the traditional hybrid flow shop scheduling (HFS). In a typical HFS with parallel machines problem, the allocation of machine resources for each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage could be determined. However, the challenge in solar cell manufacturing is the number of machines can be dynamically adjusted to complete the job within the shortest possible time. Therefore, the paper addresses a multi-stage HFS scheduling problem with characteristics of parallel processing, dedicated machines, sequence-independent setup time, and sequence-dependent setup time. The objective is to schedule the job production sequence, number of sublots, and dynamically allocate sublots to parallel machines such that the makespan time is minimized. The problem is formulated as a mixed integer linear programming (MILP) model. A hybrid approach based on the variable neighborhood search and particle swarm optimization (VNPSO) is developed to obtain the near-optimal solution. Preliminary computational study indicates that the developed VNPSO not only provides good quality solutions within a reasonable amount of time but also outperforms the classic branch and bound method and the current industry heuristic practiced by the case company.

Particle swarm optimization with cocktail decoding method for hybrid flow shop scheduling problems with multiprocessor tasks

This paper addresses the problem of multiprocessor task-scheduling in a hybrid flow shop (HFS) problem to minimize the makespan. Due to the complex nature of an HFS problem, it is decomposed into the following two sequential decision problems: determining the job permutation in stage 1, followed by a decoding method to assign jobs into each machine in subsequent stages when designing a heuristic algorithm. The decoding method plays a pivotal role for improving the solution quality of any algorithm for the HFS problem. However, the majority of existing algorithms ignores the problem and is only concerned with the first decision problem. This study emphasizes the importance of the decoding method via a small test, and searches for a number of solid decoding methods that can be incorporated into the cocktail decoding method. Then, this study develops a particle swarm optimization (PSO) algorithm that can be combined with the cocktail decoding method. In the PSO, a variety of job sequences are generated using the PSO procedure in stage 1, and the cocktail decoding method is used to assign the jobs to machines in sequential stages. Moreover, a modified lower bound is introduced. Computational results show that the proposed lower bound is competitive, and with the help of the cocktail decoding method, the proposed PSO, and even the adoption of a standard PSO framework, significantly outperforms the majority of existing algorithms in terms of quality of solutions, especially for large problems.

Performance Assessment of Feasible Scheduling Multiprocessor Tasks Solutions by using DEA FDH method

In this paper, an attempt has been made to investigate how DEA FDH method based on linear programming can select one or more efficient scheduling solutions on multiprocessor tasks obtained by any heuristic algorithms through some feasible solutions for NP-complete problems. This article will consider the problem of scheduling multiprocessor tasks with multi-criteria, namely, minimizing total completion time (makespan) and minimizing the number of tardy tasks and shows that most efficient schedule(s) will be determined.

Minimising makespan for multistage hybrid flowshop scheduling problems with multiprocessor tasks by a hybrid immune algorithm

The scheduling problem of multistage hybrid flowshop with multiprocessor tasks is a core topic for numerous industrial applications but under-represented in the research literature. In this study, a new hybrid immune algorithm based on the features of artificial immune systems and iterated greedy algorithms is presented to minimise the makespan of this problem. To validate the performance of the proposed algorithm, computational experiments are conducted on two well-known benchmark problem sets. The experiment results clearly reveal that the proposed algorithm is highly effective and efficient as compared to three state-of-the-art metaheuristics on the same benchmark instances.

Simulated Annealing‐Based Ant Colony Algorithm for Tugboat Scheduling Optimization

As the “first service station” for ships in the whole port logistics system, the tugboat operation system is one of the most important systems in port logistics. This paper formulated the tugboat scheduling problem as a multiprocessor task scheduling problem (MTSP) after analyzing the characteristics of tugboat operation. The model considers factors of multianchorage bases, different operation modes, and three stages of operations (berthing/shifting‐berth/unberthing). The objective is to minimize the total operation times for all tugboats in a port. A hybrid simulated annealing‐based ant colony algorithm is proposed to solve the addressed problem. By the numerical experiments without the shifting‐berth operation, the effectiveness was verified, and the fact that more effective sailing may be possible if tugboats return to the anchorage base timely was pointed out; by the experiments with the shifting‐berth operation, one can see that the objective is most sensitive to the proportion of the shifting‐berth operation, influenced slightly by the tugboat deployment scheme, and not sensitive to the handling operation times.

A swarm optimization approach for flexible flow shop scheduling with multiprocessor tasks

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (Cmax). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.

Hybrid Flow Shop Scheduling Problems with Multiprocessor Tasks

Hybrid flow shop scheduling problems with multiprocessor tasks to minimize the makespan have been addressed and solved efficiently. Several approaches were used, including greedy methods and metaheuristics. In this paper, we proposed a mixed integer programming (MIP) model that can define explicitly and precisely the nature of a given problem. We also addressed a modified lower bound to obtain tighter bounds. Additionally, we propose different decoding methods and emphasize their importance in hybrid flow shop scheduling problems with multiprocessor tasks. By using existing test problems with n=5 in examining the proposed methods, many optimal solutions can be obtained as benchmarks for reference by the MIP model. Accordingly, the results are indicative of the influence of the decoding methods on the solutions to the hybrid flow shop problems with multiprocessor tasks.

A novel decoding method for the hybrid flow-shop scheduling problem with multiprocessor tasks

As the strongly NP-hard problem, the hybrid flow-shop problem with multiprocessor tasks (HFSPMT) has gained increasing attention due to its academic significance and wide application background. For many heuristics and meta-heuristics to solve the HFSPMT, decoding method is the key element to decode sequences to schedules, which has great effect on the solution quality. To narrow the idle time between the consecutive operations in the processor and to increase the flexibility in selecting processors to schedule the following operations, several rules are proposed to adjust sequences to minimize the makespan of the HFSPMT. Based on the rules, a novel and effective decoding method named forward scheduling (FS) is proposed in this paper for solving the HFSPMT. At each stage, it first decodes the solution according to the non-decreasing order of the jobs’ completion times at the previous stage, and then it adjusts the processing order of the jobs dynamically according to the rules to obtain potentially better schedule. Numerical results based on the well-known benchmarks and comparisons with some existing decoding methods demonstrate the effectiveness of the proposed FS decoding method.

An Immune-based Genetic Algorithm with Reduced Search Space Coding for Multiprocessor Task Scheduling Problem

Multiprocessor task scheduling is an important problem in parallel applications and distributed systems. In this way, solving the multiprocessor task scheduling problem (MTSP) by heuristic, meta-heuristic, and hybrid algorithms have been proposed in literature. Although the problem has been addressed by many researchers, challenges to improve the convergence speed and the reliability of methods for solving the problem are still continued especially in the case that the communication cost is added to the problem frame work. In this paper, an Immune-based Genetic algorithm (IGA), a meta-heuristic approach, with a new coding scheme is proposed to solve MTSP. It is shown that the proposed coding reduces the search space of MTSP in many practical problems, which effectively influences the convergence speed of the optimization process. In addition to the reduced search space offered by the proposed coding that eventuate in exploring better solutions at a shorter time frame, it guarantees the validity of solutions by using any crossover and mutation operators. Furthermore, to overcome the regeneration phenomena in the proposed GA (generating similar chromosomes) which leads to premature convergence, an affinity based approach inspired from Artificial Immune system is employed which results in better exploration in the searching process. Experimental results showed that the proposed IGA surpasses related works in terms of found makespan (20% improvement in average) while it needs less iterations to find the solutions (90% improvement in average) when it is applied to standard test benches.

WORST-CASE PERFORMANCE EVALUATION ON MULTIPROCESSOR TASK SCHEDULING WITH RESOURCE AUGMENTATION

We study the worst-case performance of approximation algorithms for the problem of multiprocessor task scheduling on m identical processors with resource augmentation, whose objective is to minimize the makespan. In this case, the approximation algorithms are given k (k ≥ 0) extra processors than the optimal off-line algorithm. For on-line algorithms, the Greedy algorithm and shelf algorithms are studied. For off-line algorithm, we consider the LPT (longest processing time) algorithm. Particularly, we prove that the schedule produced by the LPT algorithm is no longer than the optimal off-line algorithm if and only if k ≥ m - 2.

A Lagrangian heuristic for satellite range scheduling with resource constraints

The data exchange between ground stations and satellite constellations is becoming a challenging task, as more and more communication requests must be daily scheduled on a few, expensive stations located all around the Earth. Most of the scheduling procedures adopted in practice cannot cope with such complexity, and the development of optimization-based tools is strongly spurred.We show that the problem can be formulated as a multiprocessor task scheduling problem in which each job (communication) requires a time dependent pair of resources (ground station and satellite) to be processed, and the objective consists of maximizing the total revenue of on-time jobs. A time-indexed {0,1}-linear programming formulation is then introduced able to include all the complex technological constraints of current constellations. Unfortunately, relevant real-world scenarios yield integer programs with hundreds of thousands variables and a few million constraints, which cannot be tackled by standard integer programming (either exact or heuristic) techniques.To overcome this difficulty, we developed a Lagrangian version of the Fix-and-Relax MIP heuristic. It is based on a Lagrangian relaxation of the problem which is shown to be equivalent to a sequence of maximum weighted independent set problems on interval graphs. The heuristic has been implemented in a tool used by the Italian reference operator for the GALILEO constellation, providing near optimal solutions to relevant large scale test problems.

An efficient genetic algorithm for hybrid flow shop scheduling with multiprocessor task problems

The hybrid flow shop scheduling with multiprocessor task (HFSMT) problem is a substantial production scheduling problem for minimizing the makespan, and there exist many difficulties in solving large scale HFSMT problems which include many jobs, machines and tasks. The HFSMT problems known as NP-hard and the proposal of an efficient genetic algorithm (GA) were taken into consideration in this study. The numerical results prove that the computational performance of a GA depends on the factors of initial solution, reproduction, crossover, and mutation operators and probabilities. The implementation details, including a new mutation operator, were described and a full factorial experimental design was determined with our GA program by using the best values of the control parameters and the operators. After a comparison was made with the studies of Oğuz [1], Oğuz and Ercan [2] and Kahraman et al. [3] related to the HFSMT problems, the computational results indicated that the proposed genetic algorithm approach is very effective in terms of reduced total completion time or makespan ( C max) for the attempted problems.

Lagrangian Relaxation for Multiprocessor Task Scheduling Problem with Variable Job Profiles

In this paper the multiprocessor task scheduling problem with variable job profile is addressed. Such problem originates from many practical resource assignment contexts. Based on discretized parameters, the problem is formulated as an integer programming model. Due to the complexity of the problem, a Lagrangian relaxation is applied to solve the problem. The numerical experiment demonstrates the effectiveness of our algorithm procedure.

A simulated annealing for hybrid flow shop scheduling with multiprocessor tasks to minimize makespan

This paper studies a hybrid flow shop scheduling problem (hybrid FSSP) with multiprocessor tasks, in which a set of independent jobs with distinct processor requirements and processing times must be processed in a k-stage flow shop to minimize the makespan criterion. This problem is known to be strongly nondeterministic polynomial time (NP)-hard, thus providing a challenging area for meta-heuristic approaches. This paper develops a simulated annealing (SA) algorithm in which three decode methods (list scheduling, permutation scheduling, and first-fit method) are used to obtain the objective function value for the problem. Additionally, a new neighborhood mechanism is combined with the proposed SA for generating neighbor solutions. The proposed SA is tested on two benchmark problems from the literature. The results show that the proposed SA is an efficient approach in solving hybrid FSSP with multiprocessor tasks, especially for large problems.