Multiprocessor task scheduling in multistage hyrid flowshops: a genetic algorithm approach

This paper considers multiprocessor task scheduling in a multistage hybrid flow-shop environment. The objective is to minimize the make-span, that is, the completion time of all the tasks in the last stage. This problem is of practical interest in the textile and process industries. A genetic algorithm (GA) is developed to solve the problem. The GA is tested against a lower bound from the literature as well as against heuristic rules on a test bed comprising 400 problems with up to 100 jobs, 10 stages, and with up to five processors on each stage. For small problems, solutions found by the GA are compared to optimal solutions, which are obtained by total enumeration. For larger problems, optimum solutions are estimated by a statistical prediction technique. Computational results show that the GA is both effective and efficient for the current problem. Test problems are provided in a web site at www.benchmark.ibu.edu.tr/mpt-h; fsp

Very Large-Scale Neighborhoods with Performance Guarantees for Minimizing Makespan on Parallel Machines

We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima

Automated problem scheduling and reduction of synchronization delay effects

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs

Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines

We study the problem of minimizing the makespan on m parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition the jobs assigned to the same machine into two sets. This partitioning is done for every machine with some chosen rule to receive 2m parts. A new assignment is received by putting to every machine exactly two parts. The neighborhood Nsplit consists of all possible rearrangements of the parts to the machines. The best assignment of Nsplit can be calculated in time O(mlogm) by determining the perfect matching having minimum maximal edge weight in an improvement graph, where the vertices correspond to parts and the weights on the edges correspond to the sum of the processing times of the jobs belonging to the parts. Additionally, we examine local optima in this neighborhood and in combinations with other neighborhoods. We derive performance guarantees for these local optima.operations research and management science;

Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods

We survey results that address the problem of non-preemptive scheduling on parallel machines with fixed jobs or unavailability periods with the purpose of minimizing the maximum completion time. We consider both identical and uniform processors, and also address the special case of scheduling on nonsimultaneous parallel machines, which may start processing at different times. The discussed results include polynomial-time approximation algorithms that achieve the best possible worst-case approximation bound of 1.5 in the class of polynomial algorithms unless P = NP for scheduling on identical processors with at most one fixed job on each machine and on uniform machines with at most one fixed job on each machine. The presented heuristics have similarities with the LPT algorithm or the MULTIFIT algorithm and they are fast and easy to implement. For scheduling on nonsimultaneous machines, experiments suggest that they would perform well in practice. We also include references to the relevant work in this area that contains more complex algorithms. We then discuss the main methods of argument used in the approximation bound proofs for the simple heuristics, and comment upon current challenges in this area by describing aspects of related practical problems from the automotive industry

A QoS-Aware Dynamic Bandwidth Allocation algorithm for passive optical networks with non-zero laser tuning time

The deployment of new 5G services and future demands for 6G make it necessary to increase the performance of access networks. This challenge has prompted the development of new standardization proposals for Passive Optical access Networks (PONs) that offer greater bandwidth, greater reach and a higher rate of aggregation of users per fiber, being Time- and Wavelength-Division Multiplexing (TWDM) a promising technological solution for increasing the capacity by up to 40 Gbps by using several wavelengths. This solution introduces tunable transceivers into the Optical Network Units (ONUs) for switching from one wavelength to the other, thus addressing the ever-increasing bandwidth demands in residential broadband and mobile fronthaul networks based on Fiber to the Home (FTTH) technology. This adds complexity and sources of inefficiency, such as the laser tuning time (LTT) delay, which is often ignored when evaluating the performance of Dynamic Bandwidth Allocation (DBA) mechanisms. We present a novel DBA algorithm that dynamically handles the allocation of bandwidth and switches the ONUs’ lasers from one wavelength to the other while taking LTT into consideration. To optimize the packet delay, we introduce a scheduling mechanism that follows the Longest Processing Time first (LPT) scheduling discipline, which is implemented over the Interleaved Polling with Adaptive Cycle Time (IPACT) DBA. We also provide quality of service (QoS) differentiation by introducing the Max-Min Weighted Fair Share Queuing principle (WFQ) into the algorithm. The performance of our algorithm is evaluated through simulations against the original IPACT algorithm, which we have extended to support multi-wavelengths. With the introduction of LPT, we obtain an improved performance of up to 73% reduction in queue delay over IPACT while achieving QoS differentiation with WFQ.This work has been supported by the Agencia Estatal de Investigación of Spain under project PID2019‐108713RB‐C51/AEI/10.13039/501100011033.Peer ReviewedObjectius de Desenvolupament Sostenible::9 - Indústria, Innovació i InfraestructuraObjectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura::9.1 - Desenvolupar infraestructures fiables, sostenibles, resilients i de qualitat, incloent infraestructures regionals i transfrontereres, per tal de donar suport al desenvolupament econòmic i al benestar humà, amb especial atenció a l’accés assequible i equitatiu per a totes les personesObjectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura::9.4 - Per a 2030, modernitzar les infraestructures i reconvertir les indústries perquè siguin sostenibles, usant els recursos amb més eficàcia i promovent l’adopció de tecnologies i processos industrials nets i racionals ambiental­ment, i aconseguint que tots els països adoptin mesures d’acord amb les capacitats respectivesPostprint (published version