Search results for: Scheduling algorithm

Authors: Parviz Fattahi

Abstract:

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it quit difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. In this paper, a Pareto approach to solve the multi objective flexible job shop scheduling problems is proposed. The objectives considered are to minimize the overall completion time (makespan) and total weighted tardiness (TWT). An effective simulated annealing algorithm based on the proposed approach is presented to solve multi objective flexible job shop scheduling problem. An external memory of non-dominated solutions is considered to save and update the non-dominated solutions during the solution process. Numerical examples are used to evaluate and study the performance of the proposed algorithm. The proposed algorithm can be applied easily in real factory conditions and for large size problems. It should thus be useful to both practitioners and researchers.

Keywords: Flexible job shop, Scheduling, Hierarchical approach, simulated annealing, tabu search, multi objective.

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Authors: D. Sumathi, P. Poongodi

Abstract:

Cloud Computing refers to applications delivered as services over the internet, and the datacenters that provide those services with hardware and systems software. These were earlier referred to as Software as a Service (SaaS). Scheduling is justified by job components (called tasks), lack of information. In fact, in a large fraction of jobs from machine learning, bio-computing, and image processing domains, it is possible to estimate the maximum time required for a task in the job. This study focuses on Trust based scheduling to improve cloud security by modifying Heterogeneous Earliest Finish Time (HEFT) algorithm. It also proposes TR-HEFT (Trust Reputation HEFT) which is then compared to Dynamic Load Scheduling.

Keywords: Software as a Service (SaaS), Trust, Heterogeneous Earliest Finish Time (HEFT) algorithm, Dynamic Load Scheduling.

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Authors: R.A.Mahdavinejad

Abstract:

In this paper, multi-processors job shop scheduling problems are solved by a heuristic algorithm based on the hybrid of priority dispatching rules according to an ant colony optimization algorithm. The objective function is to minimize the makespan, i.e. total completion time, in which a simultanous presence of various kinds of ferons is allowed. By using the suitable hybrid of priority dispatching rules, the process of finding the best solution will be improved. Ant colony optimization algorithm, not only promote the ability of this proposed algorithm, but also decreases the total working time because of decreasing in setup times and modifying the working production line. Thus, the similar work has the same production lines. Other advantage of this algorithm is that the similar machines (not the same) can be considered. So, these machines are able to process a job with different processing and setup times. According to this capability and from this algorithm evaluation point of view, a number of test problems are solved and the associated results are analyzed. The results show a significant decrease in throughput time. It also shows that, this algorithm is able to recognize the bottleneck machine and to schedule jobs in an efficient way.

Keywords: Job shops scheduling, Priority dispatching rules, Makespan, Hybrid heuristic algorithm.

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Authors: Vishnu Kant Soni, Raksha Sharma, Manoj Kumar Mishra

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Grid computing is a high performance computing environment to solve larger scale computational applications. Grid computing contains resource management, job scheduling, security problems, information management and so on. Job scheduling is a fundamental and important issue in achieving high performance in grid computing systems. However, it is a big challenge to design an efficient scheduler and its implementation. In Grid Computing, there is a need of further improvement in Job Scheduling algorithm to schedule the light-weight or small jobs into a coarse-grained or group of jobs, which will reduce the communication time, processing time and enhance resource utilization. This Grouping strategy considers the processing power, memory-size and bandwidth requirements of each job to realize the real grid system. The experimental results demonstrate that the proposed scheduling algorithm efficiently reduces the processing time of jobs in comparison to others.

Keywords: Grid computing, Job grouping and Jobscheduling.

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Authors: Ahmad Rabanimotlagh

Abstract:

In this paper an ant colony optimization algorithm is developed to solve the permutation flow shop scheduling problem. In the permutation flow shop scheduling problem which has been vastly studied in the literature, there are a set of m machines and a set of n jobs. All the jobs are processed on all the machines and the sequence of jobs being processed is the same on all the machines. Here this problem is optimized considering two criteria, makespan and total flow time. Then the results are compared with the ones obtained by previously developed algorithms. Finally it is visible that our proposed approach performs best among all other algorithms in the literature.

Keywords: Scheduling, Flow shop, Ant colony optimization, Makespan, Flow time

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Authors: J. Kaabi, Y. Harrath

Abstract:

This paper studied the flow shop scheduling problem under machine availability constraints. The machines are subject to flexible preventive maintenance activities. The nonresumable scenario for the jobs was considered. That is, when a job is interrupted by an unavailability period of a machine it should be restarted from the beginning. The objective is to minimize the total tardiness time for the jobs and the advance/tardiness for the maintenance activities. To solve the problem, a genetic algorithm was developed and successfully tested and validated on many problem instances. The computational results showed that the new genetic algorithm outperforms another earlier proposed algorithm. 

Keywords: Flow shop scheduling, maintenance, genetic algorithm, priority rules.

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Authors: Saleem Z. Ramadan, Gürsel A. Süer

Abstract:

In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

Abstract:

As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling. The research proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling. The paper concludes the challenges and improvement directions for Deep Reinforcement Learning-based resource scheduling algorithms.

Keywords: Resource scheduling, deep reinforcement learning, distributed system, artificial intelligence.

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Authors: Danping Lin, C.K.M. Lee

Abstract:

Re-entrant scheduling is an important search problem with many constraints in the flow shop. In the literature, a number of approaches have been investigated from exact methods to meta-heuristics. This paper presents a genetic algorithm that encodes the problem as multi-level chromosomes to reflect the dependent relationship of the re-entrant possibility and resource consumption. The novel encoding way conserves the intact information of the data and fastens the convergence to the near optimal solutions. To test the effectiveness of the method, it has been applied to the resource-constrained re-entrant flow shop scheduling problem. Computational results show that the proposed GA performs better than the simulated annealing algorithm in the measure of the makespan

Keywords: Resource-constrained, re-entrant, genetic algorithm (GA), multi-level encoding

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Authors: Christian Böning, Henrik Prinzhorn, Eric C. Hund, Malte Stonis

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In this article, the flexible job-shop scheduling problem is extended by consideration of energy costs which arise owing to the power peak, and further decision variables such as work in process and throughput time are incorporated into the objective function. This enables a production plan to be simultaneously optimized in respect of the real arising energy and logistics costs. The energy-costs-aware flexible job-shop scheduling problem (EFJSP) which arises is described mathematically, and a memetic algorithm (MA) is presented as a solution. In the MA, the evolutionary process is supplemented with a local search. Furthermore, repair procedures are used in order to rectify any infeasible solutions that have arisen in the evolutionary process. The potential for lowering the real arising costs of a production plan through consideration of energy consumption levels is highlighted.

Keywords: Energy costs, flexible job-shop scheduling, memetic algorithm, power peak.

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Authors: Lu Yanhui, Wang Chunming, Yin Changchuan, Yue Guangxin

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In this paper, we address the problem of adaptive radio resource allocation (RRA) and packet scheduling in the downlink of a cellular OFDMA system, and propose a downlink multi-carrier proportional fair (MPF) scheduler and its joint with adaptive RRA algorithm to distribute radio resources among multiple users according to their individual QoS requirements. The allocation and scheduling objective is to maximize the total throughput, while at the same time maintaining the fairness among users. The simulation results demonstrate that the methods presented provide for user more explicit fairness relative to RRA algorithm, but the joint scheme achieves the higher sum-rate capacity with flexible parameters setting compared with MPF scheduler.

Keywords: OFDMA, adaptive radio resource allocation, scheduling, QoS.

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Authors: Anis Gharbi, Mohamed Haouari, Talel Ladhari, Mohamed Ali Rakrouki

Abstract:

We address a complex scheduling problem arising in the wood panel industry with the objective of minimizing a quadratic function of job tardiness. The proposed solution strategy, which is based on an effective genetic algorithm, has been coded and implemented within a major Tunisian company, leader in the wood panel manufacturing. Preliminary experimental results indicate significant decrease of delivery times.

Keywords: Genetic algorithm, heuristic, hybrid flowshop, total weighted squared tardiness.

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Authors: Sunita Dhingra, Satinder Bal Gupta, Ranjit Biswas

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Multiprocessor task scheduling is a NP-hard problem and Genetic Algorithm (GA) has been revealed as an excellent technique for finding an optimal solution. In the past, several methods have been considered for the solution of this problem based on GAs. But, all these methods consider single criteria and in the present work, minimization of the bi-criteria multiprocessor task scheduling problem has been considered which includes weighted sum of makespan & total completion time. Efficiency and effectiveness of genetic algorithm can be achieved by optimization of its different parameters such as crossover, mutation, crossover probability, selection function etc. The effects of GA parameters on minimization of bi-criteria fitness function and subsequent setting of parameters have been accomplished by central composite design (CCD) approach of response surface methodology (RSM) of Design of Experiments. The experiments have been performed with different levels of GA parameters and analysis of variance has been performed for significant parameters for minimisation of makespan and total completion time simultaneously.

Keywords: Multiprocessor task scheduling, Design of experiments, Genetic Algorithm, Makespan, Total completion time.

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

Abstract:

This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of the resource constraint project scheduling and material ordering problems have received significant attention within the last decades. Hence, the issue has been investigated here with the aim to minimize total project costs. Furthermore, the presented model considers different discount options in order to approach the real world conditions. The incorporated alternatives consist of all-unit and incremental discount strategies. On the other hand, a modified version of the genetic algorithm is applied in order to solve the model for larger sizes, in particular. Finally, the applicability and efficiency of the given model is tested by different numerical instances.

Keywords: Genetic algorithm, material ordering, project management, project scheduling.

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Authors: Sedighe Arabameri, Nasser Salmasi

Abstract:

In this researcha particle swarm optimization (PSO) algorithm is proposedfor no-wait flowshopsequence dependent setuptime scheduling problem with weighted earliness-tardiness penalties as the criterion (
|, |Σ   " ).The smallestposition value (SPV) rule is applied to convert the continuous value of position vector of particles in PSO to job permutations.A timing algorithm is generated to find the optimal schedule and calculate the objective function value of a given sequence in PSO algorithm. Twodifferent neighborhood structures are applied to improve the solution quality of PSO algorithm.The first one is based on variable neighborhood search (VNS) and the second one is a simple one with invariable structure. In order to compare the performance of two neighborhood structures, random test problems are generated and solved by both neighborhood approaches.Computational results show that the VNS algorithmhas better performance than the other one especially for the large sized problems.

Keywords: minimization of summation of weighed earliness and tardiness, no-wait flowshop scheduling, particle swarm optimization, sequence dependent setup times

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Authors: Farhad Kolahan, Vahid Kayvanfar

Abstract:

In this paper we address a multi-objective scheduling problem for unrelated parallel machines. In unrelated parallel systems, the processing cost/time of a given job on different machines may vary. The objective of scheduling is to simultaneously determine the job-machine assignment and job sequencing on each machine. In such a way the total cost of the schedule is minimized. The cost function consists of three components, namely; machining cost, earliness/tardiness penalties and makespan related cost. Such scheduling problem is combinatorial in nature. Therefore, a Simulated Annealing approach is employed to provide good solutions within reasonable computational times. Computational results show that the proposed approach can efficiently solve such complicated problems.

Keywords: Makespan, Parallel machines, Scheduling, Simulated Annealing

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Authors: Miloš Šeda

Abstract:

Resource-constrained project scheduling is an NPhard optimisation problem. There are many different heuristic strategies how to shift activities in time when resource requirements exceed their available amounts. These strategies are frequently based on priorities of activities. In this paper, we assume that a suitable heuristic has been chosen to decide which activities should be performed immediately and which should be postponed and investigate the resource-constrained project scheduling problem (RCPSP) from the implementation point of view. We propose an efficient routine that, instead of shifting the activities, extends their duration. It makes it possible to break down their duration into active and sleeping subintervals. Then we can apply the classical Critical Path Method that needs only polynomial running time. This algorithm can simply be adapted for multiproject scheduling with limited resources.

Keywords: Project management, resource-constrained scheduling, NP-hard problem, CPM, heuristic method.

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Authors: P. Keerthika, P. Suresh

Abstract:

Grid is an environment with millions of resources which are dynamic and heterogeneous in nature. A computational grid is one in which the resources are computing nodes and is meant for applications that involves larger computations. A scheduling algorithm is said to be efficient if and only if it performs better resource allocation even in case of resource failure. Resource allocation is a tedious issue since it has to consider several requirements such as system load, processing cost and time, user’s deadline and resource failure. This work attempts in designing a resource allocation algorithm which is cost-effective and also targets at load balancing, fault tolerance and user satisfaction by considering the above requirements. The proposed Budget Constrained Load Balancing Fault Tolerant algorithm with user satisfaction (BLBFT) reduces the schedule makespan, schedule cost and task failure rate and improves resource utilization. Evaluation of the proposed BLBFT algorithm is done using Gridsim toolkit and the results are compared with the algorithms which separately concentrates on all these factors. The comparison results ensure that the proposed algorithm works better than its counterparts.

Keywords: Grid Scheduling, Load Balancing, fault tolerance, makespan, cost, resource utilization.

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

Abstract:

This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: Distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm.

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Authors: Halil Ibrahim Demir, Alper Goksu, Onur Canpolat, Caner Erden, Melek Nur

Abstract:

Traditionally process planning, scheduling and due date assignment are performed sequentially and separately. High interrelation between these functions makes integration very useful. Although there are numerous works on integrated process planning and scheduling and many works on scheduling with due date assignment, there are only a few works on the integration of these three functions. Here we tested the different integration levels of these three functions and found a fully integrated version as the best. We applied genetic search and random search and genetic search was found better compared to the random search. We penalized all earliness, tardiness and due date related costs. Since all these three terms are all undesired, it is better to penalize all of them.

Keywords: Process planning, scheduling, due-date assignment, genetic algorithm, random search.

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Authors: Mian Tahir Aftab, Muhammad Umer, Riaz Ahmad

Abstract:

This article proposes an Ant Colony Optimization (ACO) metaheuristic to minimize total makespan for scheduling a set of jobs and assign workers for uniformly related parallel machines. An algorithm based on ACO has been developed and coded on a computer program Matlab®, to solve this problem. The paper explains various steps to apply Ant Colony approach to the problem of minimizing makespan for the worker assignment & jobs scheduling problem in a parallel machine model and is aimed at evaluating the strength of ACO as compared to other conventional approaches. One data set containing 100 problems (12 Jobs, 03 machines and 10 workers) which is available on internet, has been taken and solved through this ACO algorithm. The results of our ACO based algorithm has shown drastically improved results, especially, in terms of negligible computational effort of CPU, to reach the optimal solution. In our case, the time taken to solve all 100 problems is even lesser than the average time taken to solve one problem in the data set by other conventional approaches like GA algorithm and SPT-A/LMC heuristics.

Keywords: Ant Colony Optimization (ACO), Genetic algorithms (GA), Makespan, SPT-A/LMC heuristic.

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: Supriya Arya, Sunita Dhingra

Abstract:

Multiprocessor task scheduling problem for dependent and independent tasks is computationally complex problem. Many methods are proposed to achieve optimal running time. As the multiprocessor task scheduling is NP hard in nature, therefore, many heuristics are proposed which have improved the makespan of the problem. But due to problem specific nature, the heuristic method which provide best results for one problem, might not provide good results for another problem. So, Simulated Annealing which is meta heuristic approach is considered. It can be applied on all types of problems. However, due to many runs, meta heuristic approach takes large computation time. Hence, the hybrid approach is proposed by combining the Duplication Scheduling Heuristic and Simulated Annealing (SA) and the makespan results of Simple Simulated Annealing and Hybrid approach are analyzed.

Keywords: Multiprocessor task scheduling Problem, Makespan, Duplication Scheduling Heuristic, Simulated Annealing, Hybrid Approach.

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Authors: Jian Zheng, Yoshiyasu Takahashi, Yuichi Kobayashi, Tatsuhiro Sato

Abstract:

In the study, we present a conceptual framework for developing a scheduling system that can generate self-explanatory and easy-understanding schedules. To this end, a user interface is conceived to help planners record factors that are considered crucial in scheduling, as well as internal and external sources relating to such factors. A hybrid approach combining machine learning and constraint programming is developed to generate schedules and the corresponding factors, and accordingly display them on the user interface. Effects of the proposed system on scheduling are discussed, and it is expected that scheduling efficiency and system understandability will be improved, compared with previous scheduling systems.

Keywords: Constraint programming, Factors considered in scheduling, machine learning, scheduling system.

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Authors: Leehter Yao, Chin-Chin Lin

Abstract:

An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.

Keywords: Gain scheduling, fuzzy PID controller, adaptive control, genetic algorithm.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper is concerned with minimization of mean tardiness and flow time in a real single machine production scheduling problem. Two variants of genetic algorithm as metaheuristic are combined with hyper-heuristic approach are proposed to solve this problem. These methods are used to solve instances generated with real world data from a company. Encouraging results are reported.

Keywords: Hyper-heuristics, evolutionary algorithms, production scheduling.

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Authors: Florin Pop

Abstract:

Simulation is a very powerful method used for highperformance and high-quality design in distributed system, and now maybe the only one, considering the heterogeneity, complexity and cost of distributed systems. In Grid environments, foe example, it is hard and even impossible to perform scheduler performance evaluation in a repeatable and controllable manner as resources and users are distributed across multiple organizations with their own policies. In addition, Grid test-beds are limited and creating an adequately-sized test-bed is expensive and time consuming. Scalability, reliability and fault-tolerance become important requirements for distributed systems in order to support distributed computation. A distributed system with such characteristics is called dependable. Large environments, like Cloud, offer unique advantages, such as low cost, dependability and satisfy QoS for all users. Resource management in large environments address performant scheduling algorithm guided by QoS constrains. This paper presents the performance evaluation of scheduling heuristics guided by different optimization criteria. The algorithms for distributed scheduling are analyzed in order to satisfy users constrains considering in the same time independent capabilities of resources. This analysis acts like a profiling step for algorithm calibration. The performance evaluation is based on simulation. The simulator is MONARC, a powerful tool for large scale distributed systems simulation. The novelty of this paper consists in synthetic analysis results that offer guidelines for scheduler service configuration and sustain the empirical-based decision. The results could be used in decisions regarding optimizations to existing Grid DAG Scheduling and for selecting the proper algorithm for DAG scheduling in various actual situations.

Keywords: Scheduling, Simulation, Performance Evaluation, QoS, Distributed Systems, MONARC

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Authors: Wahyudin P. Syam, Ibrahim M. Al-Harkan

Abstract:

This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.

Keywords: Flow shop, genetic algorithm, simulated annealing, tabu search.

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Authors: Fatemeh Dadkhah, Hossein Ali Akbarpour

Abstract:

This paper considers a scheduling problem in flexible flow shops environment with the aim of minimizing two important criteria including makespan and cumulative tardiness of jobs. Since the proposed problem is known as an Np-hard problem in literature, we have to develop a meta-heuristic to solve it. We considered general structure of Genetic Algorithm (GA) and developed a new version of that based on Data Envelopment Analysis (DEA). Two objective functions assumed as two different inputs for each Decision Making Unit (DMU). In this paper we focused on efficiency score of DMUs and efficient frontier concept in DEA technique. After introducing the method we defined two different scenarios with considering two types of mutation operator. Also we provided an experimental design with some computational results to show the performance of algorithm. The results show that the algorithm implements in a reasonable time.

Keywords: Data envelopment analysis, Efficiency, Flexible flow shops, Genetic algorithm

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