Parallel Computing for the Non-permutation Flow Shop Scheduling Problem with Time Couplings Using Floyd-Warshall Algorithm

Bożejko, Wojciech; Rudy, Jarosław; Idzikowski, Radosław

doi:10.1007/978-3-030-67063-4_1

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…This reduced the running time of the method, allowing it to obtain better multi-criteria solutions (Pareto fronts). In another paper [25], it was shown that it was possible to compute the goal function for non-permutation FSSP with time couplings in time O(log 2 (nm)) instead of O(nm). Unfortunately, the method requires a very large number of processors, even for small problem sizes.…”

Section: Parallel Computingmentioning

confidence: 99%

“…For the sequential algorithm, one directly applies Formulas ( 24) and ( 25), resulting in a running time of O(n) for n jobs. As for a parallel algorithm, the first idea was to use Algorithm 2 and adjust it to the job shift scan by replacing the standard summation of c = a + b with c = max{a + b, 0} as per Formulas ( 24) and (25). However, such an approach does not work as will be shown with another example.…”

Section: Parallel Job Shift Scanmentioning

confidence: 99%

“…The aim of the paper was to propose a novel parallel computing technique for the faster computation of the goal function for FSSP-MMI and to develop a solving method that is: (1) capable of solving large-size FSSP-MMI problems in reasonable time; and (2) working fast enough for small-and medium-sized FSSP-MMI problems to be applicable as a local-search subroutine in larger algorithms. A parallel algorithm for FSSP-MMI was previously proposed [25], but it required massive numbers of processors, even for small problems. We aimed to rectify this drawback.…”

Section: Introductionmentioning

confidence: 99%

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Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

Rudy

2021

Applied Sciences

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In this paper, a flow shop scheduling problem with minimal and maximal machine idle time with the goal of minimizing makespan is considered. The mathematical model of the problem is presented. A generalization of the prefix sum, called the job shift scan, for computing required shifts for overlapping jobs is proposed. A work-efficient algorithm for computing the job shift scan in parallel for the PRAM model with n processors is proposed and its time complexity of O(logn) is proven. Then, an algorithm for computing the makespan in time O(mlogn) in parallel using the prefix sum and job shift scan is proposed. Computer experiments on GPU were conducted using the CUDA platform. The results indicate multi-thread GPU vs. single-thread GPU speedups of up to 350 and 1000 for job shift scan and makespan calculation algorithms, respectively. Multi-thread GPU vs. single-thread CPU speedups up to 4.5 and 14.7, respectively, were observed as well. The experiments on the Taillard-based problem instances using a simulated annealing solving method and employing the parallel makespan calculation show that the method is able to perform many more iterations in the given time limit and obtain better results than the non-parallel version.

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Section: Parallel Computingmentioning

confidence: 99%

Section: Parallel Job Shift Scanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

Rudy

2021

Applied Sciences

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Solving Non-Permutation Flow Shop Scheduling Problem with Time Couplings

2021

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In this paper, a non-permutation variant of the Flow Shop Scheduling Problem with Time Couplings and makespan minimization is considered. Time couplings are defined as machine minimum and maximum idle time allowed. The problem is inspired by the concreting process encountered in industry. The mathematical model of the problem and solution graph representation are presented. Several problem properties are formulated, including the time complexity of the goal function computation and block elimination property. Three solving methods, an exact Branch and Bound algorithm, the Tabu Search metaheuristic, and a baseline Genetic Algorithm metaheuristic, are proposed. Experiments using Taillard-based problem instances are performed. Results show that, for the Tabu Search method, the neighborhood based on the proposed block property outperforms other neighborhoods and the Genetic Algorithm under the same time limit. Moreover, the Tabu Search method provided high quality solutions, with the gap to the optimal solution for the smaller instances not exceeding 2.3%.

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Parallel Computing for the Non-permutation Flow Shop Scheduling Problem with Time Couplings Using Floyd-Warshall Algorithm

Cited by 2 publications

References 18 publications

Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

Solving Non-Permutation Flow Shop Scheduling Problem with Time Couplings

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