Permutation Flow Shop Scheduling Research Articles

An improved fruit fly optimization algorithm with Q-learning for solving distributed permutation flow shop scheduling problems

AbstractThe distributed permutation flow shop scheduling problem (DPFSP) is one of the hottest issues in the context of economic globalization. In this paper, a Q-learning enhanced fruit fly optimization algorithm (QFOA) is proposed to solve the DPFSP with the goal of minimizing the makespan. First, a hybrid strategy is used to cooperatively initialize the position of the fruit fly in the solution space and the boundary properties are used to improve the operation efficiency of QFOA. Second, the neighborhood structure based on problem knowledge is designed in the smell stage to generate neighborhood solutions, and the Q-learning method is conducive to the selection of high-quality neighborhood structures. Moreover, a local search algorithm based on key factories is designed to improve the solution accuracy by processing sequences of subjobs from key factories. Finally, the proposed QFOA is compared with the state-of-the-art algorithms for solving 720 well-known large-scale benchmark instances. The experimental results demonstrate the most outstanding performance of QFOA.

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

An Iterative Greedy Algorithm With Q-Learning Mechanism for the Multiobjective Distributed No-Idle Permutation Flowshop Scheduling

An Iterative Greedy Algorithm With <i>Q</i>-Learning Mechanism for the Multiobjective Distributed No-Idle Permutation Flowshop Scheduling

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

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.

A hybrid genetic programming algorithm for the distributed assembly scheduling problems with transportation and sequence-dependent setup times

This paper investigates a distributed assembly permutation flow-shop scheduling problem with transportation and sequence-dependent set-up times (DAPFSP-TSDST). A hybrid genetic programming (HGP) algorithm is proposed to optimize the makespan of the assembly stage, which inherits the merits of genetic programming (GP) and neighbourhood search operators. In HGP, a hybrid problem-specific initialization heuristic is developed to make populations more diverse. Multiple neighbourhood search operators are employed as the leaf nodes, which are vital for the success of GP. A product shift strategy is proposed to strengthen its exploitability. In addition, a simulated annealing criterion is adopted to make the HGP explore more thoroughly. Finally, statistical and computational experiments are carried out on the benchmark instances. The results exhaustively identify the notable competitiveness of the HGP algorithm in coping with the DAPFSP-TSDST.

Permutation flow shop scheduling with makespan objective and truncated learning effects

Permutation flow shop scheduling with makespan objective and truncated learning effects

An upper bound for the inter-exit time of two jobs in an m-machine flow shop

AbstractThis paper addresses the class of permutation flow shop scheduling where jobs, after their completion, must be grouped in batches. This is a common scheme in industrial environments, where products undergo multiple process steps in different shops and, when completed, must be transported to customers or the next production step. A new optimisation criterion is used, the inter-exit time, i.e., the difference between the completion times of two jobs. An upper bound is proposed and demonstrated for a general permutation flow shop with m machines.

A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Learning to Optimize Permutation Flow Shop Scheduling via Graph-Based Imitation Learning

The permutation flow shop scheduling (PFSS), aiming at finding the optimal permutation of jobs, is widely used in manufacturing systems. When solving large-scale PFSS problems, traditional optimization algorithms such as heuristics could hardly meet the demands of both solution accuracy and computational efficiency, thus learning-based methods have recently garnered more attention. Some work attempts to solve the problems by reinforcement learning methods, which suffer from slow convergence issues during training and are still not accurate enough regarding the solutions. To that end, we propose to train the model via expert-driven imitation learning, which accelerates convergence more stably and accurately. Moreover, in order to extract better feature representations of input jobs, we incorporate the graph structure as the encoder. The extensive experiments reveal that our proposed model obtains significant promotion and presents excellent generalizability in large-scale problems with up to 1000 jobs. Compared to the state-of-the-art reinforcement learning method, our model's network parameters are reduced to only 37% of theirs, and the solution gap of our model towards the expert solutions decreases from 6.8% to 1.3% on average. The code is available at: https://github.com/longkangli/PFSS-IL.

A distributed permutation flow-shop considering sustainability criteria and real-time scheduling

Recent advancements in production scheduling have arisen in response to the need for adaptation in dynamic environments. This paper addresses the challenge of real-time scheduling within the context of sustainable production. We redefine the sustainable distributed permutation flow-shop scheduling problem using an online mixed-integer programming model. The proposed model prioritizes minimizing makespan while simultaneously constraining energy consumption, reducing the number of lost working days and increasing job opportunities within permissible limits. Our approach considers machines operating in different modes, ranging from manual to automatic, and employs two real-time scheduling strategies: predictive-reactive and proactive-reactive scheduling. We evaluate two rescheduling policies: continuous and event-driven. To demonstrate the model's applicability, we present a case study in auto workpiece production. We manage model complexity through various reformulations and heuristics, such as Lagrangian relaxation and Benders decomposition for initial optimization as well as four problem-specific heuristics for real-time considerations. For solving large-scale instances, we employ simulated annealing and tabu search metaheuristic algorithms. Our findings underscore the benefits of the predictive-reactive scheduling strategy and the efficiency of the event-driven rescheduling policy. By addressing dynamic scheduling challenges and integrating sustainability criteria, this study contributes valuable insights into real-time scheduling and sustainable production.

No-Wait Flow Shop scheduling problem: a systematic literature review and bibliometric analysis

One of the most widely studied problems in flow shop scheduling is not allowing jobs to wait to be processed at the next stage. This constraint causes the job to be processed immediately at the next stage without waiting, so this problem is popularly called the No-Wait Flow Shop. This article aims to provide a comprehensive review of the No-Wait Flow Shop Scheduling (NWFS) problem based on a survey of published articles from 1999 to 2023. The article review is based on a systematic literature review, and bibliometric analysis is also presented based on the network processed using VOSviewer. One hundred twenty articles were collected from the Scopus database, which was reviewed based on NWFS variants, objective functions, and optimization procedures. The no-wait permutation flow shop scheduling (NWPFS) problem is a variant that researchers have widely investigated. Meta-heuristic procedures are widely applied to solve NWFS problems. In addition, the objective function of minimizing makespan is an objective function that researchers often apply. NWFS research gaps and future research trends are also presented in this paper.

Ensemble evolutionary algorithms equipped with Q‐learning strategy for solving distributed heterogeneous permutation flowshop scheduling problems considering sequence‐dependent setup time

AbstractA distributed heterogeneous permutation flowshop scheduling problem with sequence‐dependent setup times (DHPFSP‐SDST) is addressed, which well reflects real‐world scenarios in heterogeneous factories. The objective is to minimise the maximum completion time (makespan) by assigning jobs to factories, and sequencing them within each factory. First, a mathematical model to describe the DHPFSP‐SDST is established. Second, four meta‐heuristics, including genetic algorithms, differential evolution, artificial bee colony, and iterated greedy (IG) algorithms are improved to optimally solve the concerned problem compared with the other existing optimisers in the literature. The Nawaz‐Enscore‐Ham (NEH) heuristic is employed for generating an initial solution. Then, five local search operators are designed based on the problem characteristics to enhance algorithms' performance. To choose the local search operators appropriately during iterations, Q‐learning‐based strategy is adopted. Finally, extensive numerical experiments are conducted on 72 instances using 5 optimisers. The obtained optimisation results and comparisons prove that the improved IG algorithm along with Q‐learning based local search selection strategy shows better performance with respect to its peers. The proposed algorithm exhibits higher efficiency for scheduling the concerned problems.

A regional biogeography-based optimization algorithm for the distributed assembly permutation flow-shop scheduling problem with fuzzy processing time

For solving the distributed assembly flow shop scheduling problem with fuzzy processing time (FDAPFSP), a regional biogeography-based optimization algorithm (RBBO) is proposed to minimize the maximum fuzzy completion time. The mathematical model is provided. In RBBO, all habitats are divided into regions based on the habitat suitability index, and the habitats of each region are subject to cross-regional migration and replacement procedures. A critical factory optimization strategy is developed to enhance local search capability. Taguchi method is used to determine the parameters of RBBO. In ten FDAPFSP instances, comparative testing of RBBO algorithm with various heuristic and swarm intelligence algorithms are conducted. The computation results show that in ten FDAPFSP cases, the proposed RBBO outperforms other algorithms in nine out of ten FDAPFSP cases.

A Q-learning memetic algorithm for energy-efficient heterogeneous distributed assembly permutation flowshop scheduling considering priorities

Most studies on distributed assembly permutation flowshop scheduling do not consider product priorities and factory heterogeneity. This causes delays in critical products and cannot reflect the real-world production situation. This paper focuses on the energy-efficient heterogeneous distributed assembly permutation flowshop scheduling considering priorities (EHDAPFS-P) to minimize total tardiness and total energy consumption simultaneously. Unlike traditional models, factory heterogeneity and product priorities are considered to better reflect the production environment and customer satisfaction in real-world situations. Then, a Q-learning memetic algorithm (QLMA) is proposed to solve this problem: (i) a high-quality initial population is obtained using a hybrid initialization strategy that combines four problem-specific heuristics; (ii) six efficient neighborhood structures are tailored to guide the population to converge to the promising areas; (iii) the most useful neighborhood structure is selected among the six structures using the Q-learning algorithm to accelerate the convergence, thus maximizing the cumulative and future improvements according to the population state; and (iv) an energy-saving strategy is developed to optimize the total energy consumption without deteriorating the total tardiness. The proposed QLMA is compared with seven state-of-the-art algorithms on 261 benchmark instances to demonstrate its superiority or at least competitiveness.

A Knowledge-Guided End-to-End Optimization Framework Based on Reinforcement Learning for Flow Shop Scheduling

Designing an effective and efficient end-to-end optimization framework with good generalization for shop scheduling is an emerging topic in the informational manufacturing system. Existing end-to-end frameworks have achieved satisfactory results for COPs such as traveling salesman problem and vehicle routing problem. However, the performances of these methods in solving complex COPs such as shop scheduling need to be improved. In this paper, a knowledge-guided end-to-end optimization framework based on reinforcement learning is proposed to solve the permutation flow shop scheduling problem (PFSP). Firstly, a new policy network is designed based on the problem characteristics to deal with different scales of PFSPs and achieve iterative end-to-end generation. Secondly, an improved policy-based reinforcement learning algorithm by using the knowledge accumulated during the training process is designed to enhance the training quality. Thirdly, a knowledge-guided improvement strategy is introduced through the cooperation of local search and supervised learning to improve the learning of the policy. Simulation results and comparisons show that the knowledge-guided end-to-end optimization framework can obtain better results than different kinds of commonly-used optimization methods in limited computation time for solving the PFSP.

An improved iterated greedy algorithm for distributed mixed no-wait permutation flowshop problems with makespan criterion

The distributed permutation flowshop scheduling is a critical issue in various industries, involving jobs allocation and scheduling among multiple flowshops. This paper extends the research to explore the Distributed Mixed No-Wait Permutation Flowshop Scheduling Problems (DMNWPFSP) with minimizing makespan. The innovation lies in an optimized mathematical model, hybrid heuristic algorithms, an improved iterated greedy algorithm (IIG), and high-quality solutions. Extensive experimental results demonstrate the effectiveness and superiority of the proposed IIG in terms of scheduling quality, computational efficiency, and robustness compared to existing approaches. The outcomes of this work contribute to the field of distributed flowshop scheduling, providing valuable insights for practitioners seeking to enhance production efficiency and competitiveness.

Parameter less hybrid IG-Jaya approach for permutation flow shop scheduling problem

Parameter less hybrid IG-Jaya approach for permutation flow shop scheduling problem

An Optimization Model for Smart and Sustainable Distributed Permutation Flow Shop Scheduling

Smart production scheduling has gained significant attention due to advancements in industrial informatics and technologies that enable the monitoring, control, and adaptation of task scheduling in response to disruptive events. These events can include machine breakdowns, variations in task processing times, and the arrival of new or unexpected tasks. Concurrently, sustainable production scheduling aims to optimize task scheduling by considering economic, environmental, and social factors. This paper introduces a novel optimization model for the development of smart and sustainable production scheduling in a distributed permutation flow shop. The proposed model aims to minimize the makespan while simultaneously limiting the number of lost working days and energy consumption. It also strives to increase job opportunities within acceptable limits. To evaluate the proposed model, we conduct numerical simulations using various examples and a real-case study focusing on auto workpiece production. The results demonstrate the superior performance of the proposed model. Sensitivity analyses are performed to assess the model's ability to deal with disruptions and uncertainties while satisfying economic, environmental, and social considerations.

An adaptive dynamic neighborhood crow search algorithm for solving permutation flow shop scheduling problems

An adaptive dynamic neighborhood crow search algorithm for solving permutation flow shop scheduling problems

A self-learning knowledge-based MOEA/D for distributed heterogeneous assembly permutation flowshop scheduling with batch delivery

With the requirements of just-in-time and make-to-order, it is necessary to consider the batch delivery in distributed heterogeneous assembly flow shop scheduling as well as the minimization of inventory and tardiness costs. Hence, this work proposes a new mixed integer linear programming model and a self-learning knowledge-based multi-objective evolutionary algorithm based on decomposition. In this algorithm, 4 problem-specific properties are extracted and embedded in the designed solution representation, forward-reverse objective calculation and local search operators. A new hybrid initialization with six knowledge-based NEH heuristics and a random generation is developed to generate better initial solutions. A self-learning selection strategy is developed to coordinate the above knowledge-based local search operators. The experimental study, based on 900 small and 540 large instances, demonstrates that the designed components such as hybrid initialization and self-learning selection strategy are effective, and the proposed algorithm is superior to 6 existing algorithms in the literature in solving this new problem.