Finding Optimal Schedules Research Articles

DYNAMIC JOB SCHEDULING IN GRID COMPUTING

Grid computing is growing rapidly in the distributed heterogeneous systems for utilizing and sharing large-scale resources to solve complex scientific problems. Scheduling is the most recent topic used to achieve high performance in grid environments. It aims to find a suitable allocation of resources for each job. A typical problem which arises during this task is the decision of scheduling. It is about an effective utilization of processor to minimize tardiness time of a job, when it is being scheduled. Scheduling jobs to resources in grid computing is complicated due to the distributed and heterogeneous nature of the resources. The efficient scheduling of independent jobs in a heterogeneous computing environment is an important problem in domains such as grid computing. In general, finding optimal schedule for such an environment using the traditional sequential method is an NP-hard problem whereas heuristic approaches will provide near optimal solutions for complex problems. The Ant colony algorithm, which is one of the heuristic algorithms, suits well for the grid scheduling environment using stigmeric communication.

Mathematical approach assisted differential evolution for generator maintenance scheduling

Maintenance scheduling of power generating units is very essential for the economical and reliable operation of a power system. The objective of Generator Maintenance Scheduling (GMS) problem is to find the exact time interval for preventive maintenance of power generating units in order to minimize the operating cost, maximize the system reliability and to extend the life time of the generating units. In this paper, the problem of scheduling of generating units for maintenance is formulated as a mixed integer optimization problem by considering minimizing the operating cost. Since generator maintenance scheduling is a mixed integer problem, differential evolution algorithm is suitably modified to handle the integer variables. The control variables in differential evolution algorithm are integers which denote the starting period of each generating unit for carrying out maintenance work. The lambda iteration method is used to determine the optimal generation schedule of committed generating units. This paper presents a mathematical approach assisted differential evolution (MADE) to solve maintenance scheduling problem in a power system. The performance of the proposed algorithm is validated by considering two test systems. The result obtained by the proposed MADE method is compared with mathematical approach assisted particle swarm optimization. The test results reveal the capability of the proposed MADE algorithm in finding optimal maintenance schedule for the GMS problem.

Reliability based Generator Maintenance Scheduling using Integer Coded Differential Evolution Algorithm

In this paper, Generator Maintenance Scheduling (GMS) in a vertically integrated power system is considered. The objective of the GMS problem is to find the particular time interval for maintenance of power generating units with an intention of maximizing the security of the power system. In this paper, scheduling of generating units for planned preventive maintenance is formulated as a mixed integer optimization problem by considering maximizing the average value of reliability index subject to a set of nonlinear constraints. Integer Coded Differential Evolution (ICDE) algorithm is developed to solve the GMS problem. The Lagrange Multiplier method is used to find the overall production cost for the maintenance schedule that is obtained using ICDE algorithm. To demonstrate the effectiveness of the proposed approach, two test systems are considered and are validated by comparing results obtained with that of Integer Coded Particle Swarm Optimization. The test results reveal the capability of the proposed ICDE algorithm in finding optimal maintenance schedule for the generator maintenance scheduling problem.

Multiobjective Departure Runway Scheduling Using Dynamic Programming

At busy airports, air traffic controllers seek to find schedules for aircraft at the runway that aim to minimize delays of the aircraft while maximizing runway throughput. In reality, finding optimal schedules by a human controller is hard to accomplish since the number of feasible schedules available for the scheduling problem is quite large. In this paper, we pose this problem as a multiobjective optimization problem, with respect to total aircraft delay and runway throughput. Using principles of multiobjective dynamic programming, we develop an algorithm to find a set of Pareto-optimal solutions that completely specify the nondominated frontier. In addition to finding these solutions, this paper provides a proof of the algorithm's correctness and gives an analysis of its performance against a baseline algorithm using the operational data for a model of the Dallas/Fort Worth International Airport.

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.

Scheduling with Contingent Resources and Tasks

Finding optimal schedules for the most commonly considered classes of scheduling problems is NP-complete. Best algorithms scale up to very large scheduling problems when optimality is not required and good solution quality suffices. These problems have perfect information in the sense that the resource availability, set of tasks, task duration, and other important facts, are fully known at the time of constructing a schedule. However, the assumption of perfect information is rarely satisfied, and real-world scheduling faces several forms of uncertainty, most notably with respect to durations and availability of resources. The effective handling of uncertainty is a major issue in applying scheduling in new areas. In this work, we investigate the properties of a number of classes of problems of contingent scheduling, in which assignments of resources to tasks depend on resource availability and other facts that are only known fully during execution, and hence the off-line construction of one fixed schedule is insufficient. We show that contingent scheduling in most general cases is most likely outside the complexity class NP, and resides, depending on the assumptions, in PSPACE, Sigma-p-2 or Pi-p-2. The results prove that standard constraint-satisfaction and SAT frameworks are in general not straightforwardly applicable to contingent scheduling.

Computing Near-Optimal Policies in Generalized Joint Replenishment

We provide a practical methodology for solving the generalized joint replenishment (GJR) problem, based on a mathematical programming approach to approximate dynamic programming. We show how to automatically generate a value function approximation basis built upon piecewise-linear ridge functions by developing and exploiting a theoretical connection with the problem of finding optimal cyclic schedules. We provide a variant of the algorithm that is effective in practice, and we exploit the special structure of the GJR problem to provide a coherent, implementable framework.

Metaheuristics for scheduling a no-wait flowshop manufacturing cell with sequence-dependent family setups

This paper examines the no-wait flowshop manufacturing cell scheduling problem (FMCSP) with sequence-dependent family setup times. To the best of our knowledge, the present study is among the first to investigate FMSCPs with no-wait consideration, though it is a necessary production constraint in many real-world applications. In view of the strongly NP-hard nature of this problem, three metaheuristic-based algorithms were proposed and empirically evaluated for effectively finding optimal schedules. The experimental results demonstrate that the proposed algorithms are effective and efficient at finding good quality solutions for the FMCSP with makespan criterion.

Safety‐critical Java with cyclic executives on chip‐multiprocessors

SUMMARYChip‐multiprocessors offer increased processing power at a low cost. However, in order to use them for real‐time systems, tasks have to be scheduled efficiently and predictably. It is well known that finding optimal schedules is a computationally hard problem. In this paper we present a solution that uses model checking to find a static schedule, if one exists at all, which gives an implementation of a table driven multiprocessor scheduler. Mutual exclusion to access shared resources is guaranteed by including access constraints in the schedule generation. To evaluate the proposed cyclic executive for multiprocessors, we have implemented it in the context of safety‐critical Java on a Java processor. Copyright © 2011 John Wiley & Sons, Ltd.

Determination of an Optimal Operating Schedule for Thermal Units with an Energy Storage System

This paper presents a determination methodology for finding optimal operation schedules of thermal units (namely unit commitment) integrated with an energy storage system (ESS) to minimize total operating costs. A generic ESS formulation along with a method for solving unit commitment (UC) of thermal units with ESS is proposed to serve this purpose. The problem of unit commitment with an ESS is solved using the Priority List method. Intelligent Genetic algorithm (GA) is included in the algorithm for generating new and potential solutions. The proposed method consists of two steps. The first step is to determine the schedule of ESS and the schedule of thermal units. The second step is to dispatch the hourly output of thermal units and the ESS which comply a minimized total production cost. The proposed method is applied to a power system with ten thermal units and a large ESS. The presented simulation results show that the schedule of thermal units with an ESS of a particular life cycle, achieved by the proposed method, minimizes the operating cost. The discussion regarding the determination of schedule thermal units (TU) along with the integrated ESS may interest many types of ESS due to their generalized formulations.

Scheduling identical parallel machines to minimize total tardiness

This paper considers the problem of scheduling a given number of jobs on a specified number of identical parallel machines to minimize total tardiness. In view of its NP-hard nature, we propose a new heuristic approach which is general enough for solving several important types of parallel-machine scheduling problems. Consequently, we develop and evaluate an efficient heuristic algorithms for finding optimal or near-optimal schedules for the identical parallel-machine problem to minimize total tardiness. Computational results of empirical experiments involving the proposed and the three best available heuristics are used to identify the most effective heuristic algorithms for minimizing total tardiness.

A genetic algorithm and memetic algorithm to sequencing and scheduling of cellular manufacturing systems

This paper presents a group scheduling problem for manufacturing cells, in which parts may visit different cells. By addressing intra-cell scheduling, the sequence of parts within manufacturing cells is determined. In inter-cell scheduling however, the sequence of cells is obtained. Two evolutionary algorithms, namely a genetic algorithm (GA) and a memetic algorithm (MA), are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The performance of the proposed GA and MA is shown and evaluated on 15 test problems. The computational results reveal that the proposed MA outperforms the proposed GA and Lingo software in these test problems with respect to the average elapsed time to obtain the makespan and objective function value.

Minimizing flow time in a flow-line manufacturing cell with family setup times

This paper considers the problem of scheduling part families and jobs within each part family in a flowline manufacturing cell with independent family setup times where parts (jobs) in each family are processed together. The objective is to minimize total flow time. A branch-and-bound algorithm capable of solving moderate sized problems is developed. Several heuristic algorithms are proposed and empirically evaluated as to their effectiveness and efficiency in finding optimal permutation schedules. These results show that several heuristic algorithms generate solutions that are better than those generated by an existing genetic algorithm.

PGGA: A predictable and grouped genetic algorithm for job scheduling

This paper presents a predictable and grouped genetic algorithm (PGGA) for job scheduling. The novelty of the PGGA is two-fold: (1) a job workload estimation algorithm is designed to estimate a job workload based on its historical execution records and (2) the divisible load theory (DLT) is employed to predict an optimal fitness value by which the PGGA speeds up the convergence process in searching a large scheduling space. Comparison with traditional scheduling methods, such as first-come-first-serve (FCFS) and random scheduling, heuristics, such as a typical genetic algorithm, Min–Min and Max–Min indicates that the PGGA is more effective and efficient in finding optimal scheduling solutions.

Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups

This paper considers the problem of scheduling part families and jobs within each part family in a flowshop manufacturing cell with sequence dependent family setups times where it is desired to minimize the makespan while processing parts (jobs) in each family together. Two evolutionary algorithms-a Genetic Algorithm and a Memetic Algorithm with local search-are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The proposed algorithms use a compact representation for the solution and a hierarchically structured population where the number of possible neighborhoods is limited by dividing the population into clusters. In comparison to a Multi-Start procedure, solutions obtained by the proposed evolutionary algorithms were very close to the lower bounds for all problem instances. Moreover, the comparison against the previous best algorithm, a heuristic named CMD, indicated a considerable performance improvement.

Optimal cyclic scheduling for printed circuit board production lines with multiple hoists and general processing sequence

We introduce a mixed-integer programming formulation for finding optimal cyclic schedules for printed circuit board lines with multiple hoists on a shared track, where the processing sequence may be different than the location sequence of the tanks. Computational results on some benchmark problems indicate that optimal cyclic schedules for problems of realistic size can be found in a reasonable time.

File transmission over wireless fast fading downlink

The third-generation code division multiple access (3G CDMA) mobile communication networks are designed to transmit voice and data over wireless channels. Fundamental problems need to be solved for such mobile communication networks to operate efficiently. One of the problems is finding optimal scheduling algorithms for file transmission over the fading downlink channel from a base station to mobile users. Here, the problem is solved in the case of transmission of a given number of files. Optimal algorithms that minimize the delay and the transmission time are found. Also, specific nonoptimal algorithms are considered and compared numerically with the optimal ones. We consider a slotted downlink with channels to the mobile users that are dependent in the same slot but independent for different slots. Additionally, some generalizations are presented.

On Multicast Algorithms for Heterogeneous Networks of Workstations

Networks of workstations (NOWs) provide an economical platform for high performance parallel computing. Such networks may comprise a variety of different types of workstations and network devices. This paper addresses the problem of efficient multicast in a heterogeneous communication model. Although the problem of finding optimal multicast schedules is known to be NP-complete in this model, a greedy algorithm has been shown experimentally to find good solutions in practice. In this paper we show that the greedy algorithm finds provably near-optimal schedules in polynomial time and that optimal schedules can be found in polynomial time when the number of distinct types of workstations is bounded by a constant. Specifically, this paper presents three results. First, when there are n workstations of some constant k distinct types, the greedy algorithm is shown to find schedules that complete at most a constant additive term later than optimal. Second, an algorithm is given that finds optimal schedules in time O(n2k). Finally, it is shown that for the general problem, the greedy algorithm finds solutions that complete the multicast in at most twice the optimal time.

Minimizing makespan subject to minimum total flow-time on identical parallel machines

This paper considers the identical parallel-machine scheduling problem of minimizing makespan subject to minimum total flow-time. In view of the NP-hard nature of the problem, lower bounds on the optimal makespan value and efficient heuristic algorithms for finding optimal schedules are described and empirically evaluated as to their effectiveness in finding optimal schedules.

Scheduling a flowline manufacturing cell with sequence dependent family setup times

This paper considers the problem of scheduling part families and jobs within each part family in a flowline manufacturing cell where the setup times for each family are sequence dependent and it is desired to minimize the makespan while processing parts (jobs) in each family together. Lower bounds on the optimal makespan value and efficient heuristic algorithms for finding permutation schedules are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules.