Unrelated Parallel Machine Scheduling Research Articles

Symbiotic organisms search algorithm for the unrelated parallel machines scheduling with sequence-dependent setup times.

This paper addresses the problem of makespan minimization on unrelated parallel machines with sequence dependent setup times. The symbiotic organisms search (SOS) algorithm is a new and popular global optimization technique that has received wide acceptance in recent years from researchers in continuous and discrete optimization domains. An improved SOS algorithm is developed to solve the parallel machine scheduling problem. Since the standard SOS algorithm was originally developed to solve continuous optimization problems, a new solution representation and decoding procedure is designed to make the SOS algorithm suitable for the unrelated parallel machine scheduling problem (UPMSP). Similarly, to enhance the solution quality of the SOS algorithm, an iterated local search strategy based on combining variable numbers of insertion and swap moves is incorporated into the SOS algorithm. More so, to further improve the SOS optimization speed and performance, the longest processing time first (LPT) rule is used to design a machine assignment heuristic that assigns processing machines to jobs based on the machine dynamic load-balancing mechanism. Subsequently, the machine assignment scheme is incorporated into SOS algorithms and used to solve the UPMSP. The performances of the proposed methods are evaluated by comparing their solutions with other existing techniques from the literature. A number of statistical tests were also conducted to determine the variations in performance for each of the techniques. The experimental results showed that the SOS with LPT (SOS-LPT) heuristic has the best performance compared to other tested method, which is closely followed by SOS algorithm, indicating that the two proposed algorithms’ solution approaches are reasonable and effective for solving large-scale UPMSPs.

Metaheuristic algorithms to allocate and schedule of the rescue units in the natural disaster with fatigue effect

During each year, natural disasters like floods, hurricanes, tornadoes, earthquakes, and mass movements cause enormous damages to the people and infrastructure. Designing an effective decision support model to allocate and schedule of the rescue units can reduce economic losses and casualties in the natural disasters. By assuming the incidents as jobs and rescue units as machines, we can formulate the research problem as an unrelated parallel machine scheduling problem. In this paper, a mixed integer linear programming model is proposed to minimize the sum of the weighted completion times and delays at the start of relief operations. After relieving several incidents, rescuers will become tired and then need more time to relieve the remaining incidents which were assigned to them; therefore, we consider this phenomenon as fatigue effect in this research. The rescue units also have different capabilities, and each incident just can be allocated to a rescue unit that is able to do it. Due to NP-hardness of the research problem, three metaheuristic algorithms, namely simulated annealing (SA) algorithm, particle swarm optimization (PSO) algorithm, and a method based on hybrid SA and PSO (SA-PSO), are developed to solve the research problem. Finally, the developed metaheuristic algorithms are ranked by applying the technique for order of preference by similarity to ideal solution. The experimental results illustrate that the SA algorithm and the hybrid SA-PSO are better than others in terms of CPU time and solution quality, respectively.

A Hybrid Genetic Algorithm for Solving the Unrelated Parallel Machine Scheduling Problem with Sequence Dependent Setup Times

The parallel machine scheduling problem is a well known combinatorial optimization problem with several applications in computer science, telecommunications and operations management. Several studies have shown that exact approaches for this problem are not useful in practical situations due to the high computational costs involved. This paper describes a hybrid genetic algorithm for solving the unrelated parallel machine scheduling problem with sequence dependent setup times. Computational results with simulated data are presented and discussed. A case study on the granite industry is presented.The proposed approach outperformed three traditional dispatch rules presented in the current literature.

Algorithms for the unrelated parallel machine scheduling problem with a resource constraint

We consider the unrelated parallel machine scheduling problem with a renewable resource constraint (UPMR). For the two-machine variant of the problem, we propose a very efficient mixed-integer linear programming (MILP) model. For more than two machines, we propose a two-stage heuristic, which first uses a MILP model to calculate a lower bound and assign jobs to machines, and then uses a constraint programming (CP) model to schedule jobs on machines. If the solution of the two-stage heuristic is not proven optimal, the problem is solved using a CP model for the complete UPMR, with a hot start provided by the two-stage heuristic. New large benchmark problem instances with up to 1000 jobs are generated. Extensive computational experiments are carried out on these, as well as on smaller instances from the literature. Our algorithms obtain excellent solutions for much larger problem instances than previously proposed methods. For the UPMR with two machines, our MILP model solves all test instances to optimality in very modest computation times, greatly outperforming previously proposed methods. For the variant with more than two machines, our overall algorithm, which combines the two-stage heuristic with a full CP model, finds for the smaller instances from the literature better than or the same solutions as all previously proposed methods in considerably less computation time. Difficult types of problem instances are also identified for future research.

A constraint programming approach for solving unrelated parallel machine scheduling problem

Abstract This paper addresses the non-preemptive unrelated parallel machine scheduling problem (PMSP) with job sequence and machine dependent setup times. This is a widely seen NP-hard (non-deterministic polynomial-time) problem with the objective to minimize the makespan. This study provides a noval constraint programming (CP) model with two customized branching strategies that utilize CP’s global constraints, interval decision variables, and domain filtering algorithms. The performance of the CP model is evaluated against the state-of-art algorithms. In addition, we compare the performance of the default branching method in the CP solver against the two customized variants. In terms of average solution quality, the computational results indicate that the CP model slightly outperforms all of the state-of-art algorithms in solving small problem instances, is able to prove the optimality of 283 currently best-known solutions. It is also effective in finding good quality feasible solutions for the larger problem instances.

Integrated scheduling of m-truck, m-drone, and m-depot constrained by time-window, drop-pickup, and m-visit using constraint programming

The idea of deploying unmanned aerial vehicles, also known as drones, for final-mile delivery in logistics operations has vitalized this new research stream. One conceivable scenario of using a drone in conjunction with a traditional delivery truck to distribute parcels is discussed in earlier literature and termed the parallel drone scheduling traveling salesman problem (PDSTSP). This study extends the problem by considering two different types of drone tasks: drop and pickup. After a drone completes a drop, the drone can either fly back to depot to deliver the next parcels or fly directly to another customer for pickup. Integrated scheduling of multiple depots hosting a fleet of trucks and a fleet of drones is further studied to achieve an operational excellence. A vehicle that travels near the boundary of the coverage area might be more effective to serve customers that belong to the neighboring depot. This problem is uniquely modeled as an unrelated parallel machine scheduling with sequence dependent setup, precedence-relationship, and reentrant, which gives us a framework to effectively consider those operational challenges. A constraint programming approach is proposed and tested with problem instances of m-truck, m-drone, m-depot, and hundred-customer distributed across an 8-mile square region.

A hybrid ABC-TS algorithm for the unrelated parallel-batching machines scheduling problem with deteriorating jobs and maintenance activity

This paper studies an unrelated parallel machine scheduling problem with deteriorating maintenance activities, parallel-batching processing, and deteriorating jobs. Practically, deteriorating maintenance activities mean that durations of maintenance activities will increase with their starting time. The objective is to make the joint decisions on jobs assignments, the maintenance arrangements, jobs batching, and batches sequencing on each machine to minimize the makespan. Firstly, we formulate a mixed integer programming model for the problem. Then, we analyze a special case where all jobs have been assigned to machines and provide polynomial time optimal algorithms. Furthermore, since the studied problem is NP-hard, we develop a hybrid ABC-TS algorithm combining artificial bee colony (ABC) and Tabu Search (TS) to solve the problem in a reasonable time. Extensive computational experiments are conducted and the results validate the effectiveness and robustness of our proposed algorithms.

Non-clairvoyant online scheduling of synchronized jobs on virtual clusters

Although virtualization technology is recently applied to next-generation distributed high-performance computing systems, theoretical aspects of scheduling jobs on these virtualized environments are not sufficiently studied, especially in online and non-clairvoyant cases. Virtualization of computing resources results in interference and virtualization overheads that negatively impact the load balancing objectives on commonly used cluster of multi-core physical machines. We present a technique for non-clairvoyant online scheduling of globally synchronized jobs, each of which spawns tasks to execute compute-intensive works. Our technique considers both load balancing of physical cores and per job synchronization cost minimization. We show that in the presence of arbitrary virtualization overheads, interference effects and synchronization cost, the problem can be reduced to an online unrelated parallel machine scheduling, which is solved using routing of virtual circuits. We present a new opportunity cost model to reduce the problem to the routing of virtual circuits and prove the effectiveness of our scheduling technique using mathematical analysis and simulative experiments.

A memetic differential evolution algorithm for energy-efficient parallel machine scheduling

This paper considers an energy-efficient bi-objective unrelated parallel machine scheduling problem to minimize both makespan and total energy consumption. The parallel machines are speed-scaling. To solve the problem, we propose a memetic differential evolution (MDE) algorithm. Since the problem involves assigning jobs to machines and selecting an appropriate processing speed level for each job, we characterize each individual by two vectors: a job-machine assignment vector and a speed vector. To accelerate the convergence of the algorithm, only the speed vector of each individual evolves and a list scheduling heuristic is applied to derive its job-machine assignment vector based on its speed vector. To further enhance the algorithm, we propose efficient speed adjusting and job-machine swap heuristics and integrate them into the algorithm as a local search approach by an adaptive meta-Lamarckian learning strategy. Computational results reveal that the incorporation of list scheduling heuristic and local search greatly strengthens the algorithm. Computational experiments also show that the proposed MDE algorithm outperforms SPEA-II and NSGA-II significantly.

An Improved Firefly Algorithm for the Unrelated Parallel Machines Scheduling Problem With Sequence-Dependent Setup Times

Research in the area of unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times has received little attention from the research community. However, this problem is NP-hard even without considering the setup times, and when sequence-dependent setup times are included, finding optimal solutions becomes very difficult, especially for the problems with large dimension. In this paper, a firefly algorithm (FA) which is refined with a local search solution improvement mechanism is presented to solve this problem, with the objective of reaching a near-optimum solution. Since the classical FA was originally designed for continuous optimization problems, a new solution representation scheme is designed to make the FA suitable for a combinatorial optimization problem such as the UPMSP. Three different popular metaheuristic algorithms are developed in parallel to verify and measure the effectiveness of the proposed algorithm. More so, the success of the novel firefly scheduling method is measured by comparing the quality of its solutions against the best-known methods from the literature. An exhaustive computational and statistical analysis is carried out to show an excellent performance of the new method on a large set of problem instances. The numerical results show that the improved FA is competitive, fast, and efficient and provide good quality solutions for both small and large problem instances.

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

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.

Hybrid scheduling and maintenance problem using artificial neural network based meta-heuristics

PurposeThe purpose of this paper is to present a new mathematical model for the unrelated parallel machine scheduling problem with aging effects and multi-maintenance activities.Design/methodology/approachThe authors assume that each machine may be subject to several maintenance activities over the scheduling horizon and a machine turn into its initial condition after maintenance activity and the aging effects start anew. The objective is to minimize the weighted sum of early/tardy times of jobs and maintenance costs.FindingsAs this problem is proven to be non-deterministic polynomial-time hard (NP-hard), the authors employed imperialist competitive algorithm (ICA) and genetic algorithm (GA) as solution approaches, and the parameters of the proposed algorithms are calibrated by a novel parameter tuning tool called Artificial Neural Network (ANN). The computational results clarify that GA performs better than ICA in quality of solutions and computational time.Originality/valuePredictive maintenance (PM) activities carry out the operations on machines and tools before the breakdown takes place and it helps to prevent failures before they happen.

Heuristic Approach to Unrelated Parallel Machines Scheduling under Availability and Resource Constraints

In present paper we consider scheduling problem for the arrangement of oil and gas field. The primary challenge determining associated problems in this area is computation of the optimal schedules of wells (well bushes) construction using different drilling equipment. We adapt unrelated parallel machine scheduling with release dates to solve the problem. Real conditions impose additional resource constraints to the standard unrelated parallel machines scheduling with release dates. We propose mathematical formulation of the problem and two efficient algorithms to its solving. Finally, we give illustrative example and the results of testing for the proposed approach. Computational experiments have shown high accuracy and acceptable performance time of the developed algorithm.

A rule-based genetic algorithm with an improvement heuristic for unrelated parallel machine scheduling problem with time-dependent deterioration and multiple rate-modifying activities

In this article, we consider an unrelated parallel machine scheduling (UPMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The actual processing time of a job is defined by a linear function of a gap between starting time of the job and ending time of the recent RMA. The starting rate of the actual processing time of jobs is restored to the original processing time through the application of RMAs. In the UPMS problem, we simultaneously determine the schedule of jobs and the number and positions of RMAs to minimize the makespan. To solve the problem, a mixed integer linear programming (MILP) model for the problem is developed to find the optimal solution. Then, we propose a novel rule-based genetic algorithm (GA) with a chromosome representing job assigning sequence to one of the machines and the schedule of jobs and the number and positions of RMAs in each machine are determined by a completion time rule-based dispatching heuristic during the decoding process of the chromosome. To enhance the solution effectiveness, an improvement heuristic is implemented to the GA. Extensive computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms.

Energy-conscious unrelated parallel machine scheduling under time-of-use electricity tariffs

This paper investigates an energy-conscious unrelated parallel machine scheduling problem under time-of-use (TOU) electricity pricing scheme, in which the electricity price varies throughout a day. The problem lies in assigning a group of jobs to a set of unrelated parallel machines and then scheduling jobs on each separate machine so as to minimize the total electricity cost. We first build an improved continuous-time mixed-integer linear programming (MILP) model for the problem. To tackle large-size problems, we then propose a two-stage heuristic. Specifically, at the first stage, jobs are assigned to machines aiming at minimizing the total electricity cost under the preemptive circumstance. At the second stage, the jobs assigned to each machine are scheduled using an insertion heuristic. Computational results on a real-life instance for turning process and random test instances demonstrate that the proposed MILP approach is able to solve small-size problems while the two-stage heuristic is appropriate for large-size problems. The case study for turning process also reveals that the proposed optimization approaches can contribute to cleaner production.

Iterated Greedy with Random Variable Neighborhood Descent for Scheduling Jobs on Parallel Machines with Deterioration Effect

In this paper, we study an unrelated parallel machine scheduling problem in which the jobs cause deterioration of the machines. This deterioration decreases the performance of the machines, and therefore, the processing times of the jobs are increased over time. The problem is to find the processing sequence of jobs on each machine in order to reduce the deterioration of the machines and consequently minimize the makespan. This problem is NP-hard when the number of machines is greater or equal than two, and hence we propose a heuristic based on the Iterated Greedy meta-heuristic coupled with a variant of the Variable Neighborhood Descent method that uses a random ordering of neighborhoods in local search phase. The performance of our heuristic, named IG-RVND, is compared with the state-of-the-art meta-heuristic proposed in the literature for the problem under study. The results show that the our heuristic outperform the existing algorithm by a significant margin.

A hybrid multi-objective evolutionary algorithm approach for handling sequence- and machine-dependent set-up times in unrelated parallel machine scheduling problem

This paper addresses a fuzzy mixed-integer non-linear programming (FMINLP) model by considering machine-dependent and job-sequence-dependent set-up times that minimize the total completion time, the number of tardy jobs, the total flow time and the machine load variation in the context of unrelated parallel machine scheduling (UPMS) problem. The above-mentioned multi-objectives were considered based on non-zero ready times, machine- and sequence-dependent set-up times and secondary resource constraints for jobs. The proposed approach considers unrelated parallel machines with inherent uncertainty in processing times and due dates. Since the problem is shown to be NP-hard in nature, it is a challenging task to find the optimal/near-optimal solutions for conflicting objectives simultaneously in a reasonable time. Therefore, we introduced a new multi-objective-based evolutionary artificial immune non-dominated sorting genetic algorithm (AI-NSGA-II) to resolve the above-mentioned complex problem. The performance of the proposed multi-objective AI-NSGA-II algorithm has been compared to that of multi-objective particle swarm optimization (MOPSO) and conventional non-dominated sorting genetic algorithm (CNSGA-II), and it is found that the proposed multi-objective-based hybrid meta-heuristic produces high-quality solutions. Finally, the results obtained from benchmark instances and randomly generated instances as test problems evince the robust performance of the proposed multi-objective algorithm.

Solving a New Multi-objective Unrelated Parallel Machines Scheduling Problem by Hybrid Teaching-learning Based Optimization

This paper considers a scheduling problem of a set of independent jobs on unrelated parallel machines (UPMs) that minimizesthe maximum completion time (i.e., makespan or ), maximum earliness ( ), and maximum tardiness ( ) simultaneously. Jobs have non-identical due dates, sequence-dependent setup times and machine-dependentprocessing times. A multi-objective mixed-integer linear programming (MILP) is considered then solved with the e-constraint method in small-sized problems.The related results are compared with the results obtained by meta-heuristic algorithms.Furthermore, an effectivehybrid multi-objective teaching–learningbased optimization (HMOTLBO) algorithm is proposed, whose performance is compared with a non-dominated sorting genetic algorithm (NSGA-II) fortest problems generated at random. The associated results show that the proposed HMOTLBO outperformsthe NSGA-II in terms of different metrics.

Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources

In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature. The other one, which is based on the resemblance to strip packing problems, is an original contribution of this paper. As the models presented are incapable of solving medium-sized instances to optimality, we propose three matheuristic strategies for each of these two models. The algorithms proposed are tested over an extensive computational experience. Results show that the matheuristic strategies significantly outperform the mathematical models.

Approximation algorithms for scheduling unrelated parallel machines with release dates

In this paper we propose approaches to optimal scheduling of unrelated parallel machines with release dates. One approach is based on the scheme of dynamic programming modified with adaptive narrowing of search domain ensuring its computational effectiveness. We discussed complexity of the exact schedules synthesis and compared it with approximate, close to optimal, solutions. Also we explain how the algorithm works for the example of two unrelated parallel machines and five jobs with release dates. Performance results that show the efficiency of the proposed approach have been given.