An ordered heuristic for the allocation of resources in unrelated parallel-machines

All rights reserved. Global competition pressures have forced manufactures to adapt their productive capabilities. In order to satisfy the ever-changing market demands many organizations adopted flexible resources capable of executing several products with different performance criteria. The unrelated parallel-machines makespan minimization problem (Rm||Cmax) is known to be NP-hard or too complex to be solved exactly. In the heuristics used for this problem, the MCT (Minimum Completion Time), which is the base for several others, allocates tasks in a random like order to the minimum completion time machine. This paper proposes an ordered approach to the MCT heuristic. MOMCT (Modified Ordered Minimum Completion Time) will order tasks in accordance to the MS index, which represents the mean difference of the completion time on each machine and the one on the minimum completion time machine. The computational study demonstrates the improved performance of MOMCT over the MCT heuristic.This work is supported by FEDER Funds through the “Programa Operacional Factores de Competitividade - COMPETE” program and by National Funds through FCT “Fundação para a Ciência e a Tecnologia” under the project: FCOMP-01-0124-FEDER-PEst-OE/EEI/UI0760/2011 and PEstOE/EEI/UI0760/2014.info:eu-repo/semantics/publishedVersio

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource

[EN] In this paper, we study the unrelated parallel machine scheduling problem with one scarce additional resource to minimise the maximum completion time of the jobs or makespan. Several heuristics are proposed following two strategies: the first one is based on the consideration of the resource constraint during the whole solution construction process. The second one starts from several assignment rules without considering the resource constraint, and repairs the non feasible assignments in order to obtain a feasible solution. Several computation experiments are carried out over an extensive benchmark. A comparative evaluation against previously proposed mathematical models and matheuristics (combination of mathematical models and heuristics) is carried out. From the results, we can conclude that our methods outperform the existing ones, and the second strategy performs better, especially for large instances. (C) 2017 Elsevier Ltd. All rights reserved.The authors are supported by the Spanish Ministry of Economy and Competitiveness, under the projects "SCHEYARD - Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) and "OPTEMAC - Optimizacion de Procesos en Terminales Maritimas de Contenedores" (No. DPI2014-53665-P), all of them partially financed with FEDER funds. The authors are also partially supported by the EU Horizon 2020 research and innovation programme under grant agreement no. 731932 "Transforming Transport: Big Data Value in Mobility and Logistics". Interested readers can download contents from http://soa.iti.es, like the instances used and a software for generating further instances. Source codes are available upon justified request from the authors.Villa Juliá, MF.; Vallada Regalado, E.; Fanjul Peyró, L. (2018). Heuristic algorithms for the unrelated parallel machine scheduling problem with one scarce additional resource. Expert Systems with Applications. 93:28-38. https://doi.org/10.1016/j.eswa.2017.09.054S28389

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio

Spatial-temporal data modelling and processing for personalised decision support

The purpose of this research is to undertake the modelling of dynamic data without losing any of the temporal relationships, and to be able to predict likelihood of outcome as far in advance of actual occurrence as possible. To this end a novel computational architecture for personalised ( individualised) modelling of spatio-temporal data based on spiking neural network methods (PMeSNNr), with a three dimensional visualisation of relationships between variables is proposed. In brief, the architecture is able to transfer spatio-temporal data patterns from a multidimensional input stream into internal patterns in the spiking neural network reservoir. These patterns are then analysed to produce a personalised model for either classification or prediction dependent on the specific needs of the situation. The architecture described above was constructed using MatLab© in several individual modules linked together to form NeuCube (M1). This methodology has been applied to two real world case studies. Firstly, it has been applied to data for the prediction of stroke occurrences on an individual basis. Secondly, it has been applied to ecological data on aphid pest abundance prediction. Two main objectives for this research when judging outcomes of the modelling are accurate prediction and to have this at the earliest possible time point. The implications of these findings are not insignificant in terms of health care management and environmental control. As the case studies utilised here represent vastly different application fields, it reveals more of the potential and usefulness of NeuCube (M1) for modelling data in an integrated manner. This in turn can identify previously unknown (or less understood) interactions thus both increasing the level of reliance that can be placed on the model created, and enhancing our human understanding of the complexities of the world around us without the need for over simplification. Read less Keywords Personalised modelling; Spiking neural network; Spatial-temporal data modelling; Computational intelligence; Predictive modelling; Stroke risk predictio

Unrelated Machines Scheduling With Machine Eligibility Restrictions

In this paper we present a new heuristic algorithm to minimize the makespan for scheduling jobs on unrelated parallel machines with machine eligibility restrictions ( R^ I M .1 C^^). To the best of our knowledge, the problem has not been addressed previously in the literature. The multi-phase heuristic algorithm incorporates new concepts from the multi-depot vehicle routing in the constructive heuristic. A computational study includes problems with two or four machines, up to 105 jobs, and three levels of a machine selection parameter. The heuristic algorithm solution values are compared to optimal solution values. The results show that the heuristic algorithm can yield solutions within a few percent of the optimal solutions with performance improving as the number of jobs to be scheduled increases

Optimal Algorithms for Scheduling under Time-of-Use Tariffs

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time-slots to be used for scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for.Comment: 17 pages; A preliminary version of this paper with a subset of results appeared in the Proceedings of MFCS 201

A statistical comparison of metaheuristics for unrelated parallel machine scheduling problems with setup times

Manufacturing scheduling aims to optimize one or more performance measures by allocating a set of resources to a set of jobs or tasks over a given period of time. It is an area that considers a very important decision-making process for manufacturing and production systems. In this paper, the unrelated parallel machine scheduling problem with machine-dependent and job-sequence-dependent setup times is addressed. This problem involves the scheduling of tasks on unrelated machines with setup times in order to minimize the makespan. The genetic algorithm is used to solve small and large instances of this problem when processing and setup times are balanced (Balanced problems), when processing times are dominant (Dominant P problems), and when setup times are dominant (Dominant S problems). For small instances, most of the values achieved the optimal makespan value, and, when compared to the metaheuristic ant colony optimization (ACOII) algorithm referred to in the literature, it was found that there were no significant differences between the two methods. However, in terms of large instances, there were significant differences between the optimal makespan obtained by the two methods, revealing overall better performance by the genetic algorithm for Dominant S and Dominant P problems.FCT—Fundação para a Ciência e Tecnologia through the R&D Units Project Scope UIDB/00319/2020 and EXPL/EME-SIS/1224/2021 and PhD grant UI/BD/150936/2021