Solving Non-Permutation Flow Shop Scheduling Problem with Time Couplings

Idzikowski, Radosław; Rudy, Jarosław; Gnatowski, Andrzej

doi:10.3390/app11104425

Cited by 4 publications

(5 citation statements)

References 43 publications

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“…Finally, both the minimal and maximal idle time constraints can be enforced at the same time. This can be used to model some time-sensitive processes in construction, for example, the concreting process [23].…”

Section: Problem Constraintsmentioning

confidence: 99%

“…A possible method of constructing schedule C from solution π is described by Algorithm 1. The method is nearly identical to the one shown for the non-permutation variant of the problem in [23]. In line 1, the completion time for processing job π(1) on machine 1 is set, since that job has no constraints.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In this paper, a permutation flow shop scheduling problem with makespan criterion and minimal and maximal machine idle time (FSSP-MMI) is considered. A similar, nonpermutation variant was previously considered in [23]. FSSP-MMI is a variant of the well-known permutation flow shop scheduling problem (FSSP) [24].…”

Section: Introductionmentioning

confidence: 99%

“…FSSP-MMI is a variant of the well-known permutation flow shop scheduling problem (FSSP) [24]. The problem can be used to model some practical processes, e.g., the concreting process (which was described in [23]). Moreover, this problem is also a generalization of several other variants, including: (a) no-idle; (b) minimal idle time; (c) maximal idle time; and (d) classic FSSP.…”

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: Problem Constraintsmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Other examples are (3,12,4,2), (7,9,8) and (7,11). This concept is similar to the notion of critical block commonly used in the context of shop scheduling problems [16,50]. Throughout, for a C-path P, T(P) will denote its tardiness, i.e., the sum of the tardiness values of all the jobs contained in it.…”

Section: Local Search Proceduresmentioning

confidence: 99%

One-Machine Scheduling with Time-Dependent Capacity via Efficient Memetic Algorithms

Mencía

2021

Mathematics

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This paper addresses the problem of scheduling a set of jobs on a machine with time-varying capacity, with the goal of minimizing the total tardiness objective function. This problem arose in the context scheduling the charging times of a fleet of electric vehicles and it is NP-hard. Recent work proposed an efficient memetic algorithm for solving the problem, combining a genetic algorithm and a local search method. The local search procedure is based on swapping consecutive jobs on a C-path, defined as a sequence of consecutive jobs in a schedule. Building on it, this paper develops new memetic algorithms that stem from new local search procedures also proposed in this paper. The local search methods integrate several mechanisms to make them more effective, including a new condition for swapping pairs of jobs, a hill climbing approach, a procedure that operates on several C-paths and a method that interchanges jobs between different C-paths. As a result, the new local search methods enable the memetic algorithms to reach higher-quality solutions. Experimental results show significant improvements over existing approaches.

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Q-Learning-Based Priority Dispatching Rule Preference Model for Non-Permutation Flow Shop

Zhao,

Liu

2024

J. Adv. Manuf. Syst.

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Non-permutation flow shop scheduling (NPFS) is an extension of the traditional permutation flow shop scheduling, with a broader solution space. The effectiveness of reinforcement learning in solving flow shop scheduling problems has been demonstrated through its powerful combinatorial optimization capabilities. However, the design and training of the end-to-end policy network is complex, leading to long online training time and limited adaptability of offline training. To overcome these problems, we introduced a NPFS dynamic decision-making process and then proposed a novel NPFS method that combines the Q-learning algorithm with the priority dispatching rule (PDR) set. The NPFS dynamic decision-making process involves decomposing the entire process into multiple sub-job queues for scheduling. The PDR demonstrates better scheduling performance when applied to smaller job queues. By utilizing the Q-learning algorithm, PDRs with superior performance are assigned to sub-scheduling queues based on the generation process of sub-job sequences, resulting in an optimized NPFS strategy. The limited number of PDRs in the PDR set and the small number of sub-job queues in the NPFS process contribute to the efficiency of Q-learning in solving NPFS problem. Finally, we demonstrate the superiority of the proposed NPFS method by a series of numerical experiments using the machine-based assignment PDR method and NSGA-II algorithms as performance benchmarks.

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Solving Non-Permutation Flow Shop Scheduling Problem with Time Couplings

Cited by 4 publications

References 43 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

One-Machine Scheduling with Time-Dependent Capacity via Efficient Memetic Algorithms

Q-Learning-Based Priority Dispatching Rule Preference Model for Non-Permutation Flow Shop

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