Hybrid Flow Shop Scheduling Problem Research Articles

An improved memetic algorithm for distributed hybrid flow shop scheduling problem with operation inspection and reprocessing

An improved memetic algorithm for distributed hybrid flow shop scheduling problem with operation inspection and reprocessing

A parallel deep adaptive large neighbourhood search algorithm for distributed heterogeneous hybrid flow shops with mixed-model assembly scheduling

ABSTRACT Nowadays, manufacturing enterprises must have fast response and flexible production capabilities to meet personalized and diversified market demands. Mixed-model production and distributed production have become the preferred production methods for enterprises. This article studies a distributed heterogeneous hybrid flow shop scheduling problem with a mixed-model assembly line (DHHFSP-MMAL), which consists of manufacturing and assembly stages. The DHHFSP-MMAL is modelled by a mixed integer linear programming (MILP) model. Three constructive heuristics and a parallel deep adaptive large neighbourhood search (PDALNS) problem are presented. A constructive heuristic with a group strategy is employed to obtain an initial solution. Several deep destroy-and-repair operators are proposed where problem-specific greedy local search methods are applied. The PDALNS assigns weights to destroy-and-repair operators to guide the selection of operators. The parallel computing technique is introduced to increase the efficiency of training. The experiments demonstrate that the PDALNS algorithm is an efficient and effective algorithm for solving the DHHFSP-MMAL problem.

Scheduling analysis of automotive glass manufacturing systems subject to sequence-independent setup time, no-idle machines, and permissive maximum total tardiness constraint

With the increasing demand for automotive glass, improving the efficiency of automotive glass manufacturing systems can make full use of production resources and reduce the waste of natural and social resources. Therefore, this work aims to provide an efficient method for a real-world two-stage hybrid flow shop scheduling problem with small batches in an automotive glass manufacturing system. For the investigated problem, there is a significant setup time at the first stage, the second stage is served by machines that should not be interrupted, and each batch has a due date. Such constraints make this scheduling problem challenging. To solve this problem, a mixed integer linear programming model is established. Also, two properties and three theorems are given to enhance the problem-solving process. Subsequently, an efficient genetic algorithm is carefully designed to solve large-scale problems by considering the properties of the system. Meanwhile, an improvement scheme is proposed to decrease the running time of the algorithm, and experimental results show that this scheme can reduce the running time by 280 s at most from the average results of different scale problems. Finally, extensive experiments are carried out and a real-world case is solved to demonstrate the efficiency and effectiveness of the designed genetic algorithm. Also, the Taguchi method is adopted to tune the parameters for the designed algorithm.

A Shuffled Frog Leaping Algorithm with Q-Learning for Distributed Hybrid Flow Shop Scheduling Problem with Energy-Saving

Abstract Energy saving has always been a concern in production scheduling, especially in distributed hybrid flow shop scheduling problems. This study proposes a shuffled frog leaping algorithm with Q-learning (QSFLA) to solve distributed hybrid flow shop scheduling problems with energy-saving(DEHFSP) for minimizing the maximum completion time and total energy consumption simultaneously. The mathematical model is provided, and the lower bounds of two optimization objectives are given and proved. A Q-learning process is embedded in the memeplex search of QSFLA. The state of the population is calculated based on the lower bound. Sixteen search strategy combinations are designed according to the four kinds of global search and four kinds of neighborhood structure. One combination is selected to be used in the memeplex search according to the population state. An energy-saving operator is presented to reduce total energy consumption without increasing the processing time. One hundred forty instances with different scales are tested, and the computational results show that QSFLA is a very competitive algorithm for solving DEHFSP.

Reentrant hybrid flow shop scheduling with stockers in automated material handling systems using deep reinforcement learning

In smart factories, automated material handling system (AMHSs) replace manual material handling to increase production efficiency, in which stockers serve as the temporary storage for work-in-process inventories. Furthermore, costly machines and complex processes in advanced manufacturing lead to the need for multiple reentrant processes of the same workstation. However, previous works on scheduling problems rarely considered the function of stockers and reentrant processes, and their approaches were mostly based on metaheuristic algorithms. Recent advances in artificial intelligence enable the possibility of solving scheduling problems using deep reinforcement learning (DRL). Therefore, this work investigates the reentrant hybrid flow shop scheduling problem with stockers (RHFS2) inspired by AMHSs, and solves it by DRL. Firstly, the states, actions, and rewards of the Markov decision process for this problem are designed; and then, two deep Q network (DQN) approaches based on the actions for determining machines and jobs, respectively, are proposed. Simulation results demonstrate that our proposed DQN approaches outperform for finding better solutions of different-scale problems than classical metaheuristic algorithms.

An Adaptive Two-Class Teaching-Learning-Based Optimization for Energy-Efficient Hybrid Flow Shop Scheduling Problems with Additional Resources

Energy-efficient scheduling problems with additional resources are seldom studied in hybrid flow shops. In this study, an energy-efficient hybrid flow shop scheduling problem (EHFSP) with additional resources is studied in which there is asymmetry in the machine. An adaptive two-class teaching-learning-based optimization (ATLBO) which has multiple teachers is proposed to simultaneously minimize the makespan and the total energy consumption. After two classes are formed, a teacher phase is first executed, which consists of teacher self-learning and teacher training. Then, an adaptive learner phase is presented, in which the quality of two classes is used to adaptively decide the learner phase or the reinforcement search of the temporary solution set. An adaptive formation of classes is also given. Extensive experiments were conducted and the computational results show that the new strategies are effective and that ATLBO was able to provide better results than comparative algorithms reported in the literature in at least 54 of 68 instances.

A Sequential Hybrid Optimization Algorithm (SHOA) to Solve the Hybrid Flow Shop Scheduling Problems to Minimize Carbon Footprint

In today’s world, a situational awareness of sustainability is becoming increasingly important. Leaving a better world for future generations is becoming the main interest of many studies. It also puts pressure on managers to change production methods in most industries. Reducing carbon emissions in industry today is crucial to saving our planet. Theoretical research and practical industry requirements diverge, even though numerous researchers have tackled various strategies to handle carbon emission problems. Therefore, this work considers the carbon emission problem of the furniture manufacturing industry in Hosur, Tamilnadu, India. The case study company has a manufacturing system that resembles a hybrid flow shop (HFS) environment. As the HFS scheduling problems are NP-hard in nature, exact solution techniques could not be used to solve the problems. Hence, a sequential hybrid optimization algorithm (SHOA) has been developed in this paper to minimize the carbon footprint. In the SHOA, the pigeon-inspired optimization algorithm (PIOA) is hybridized sequentially with the firefly algorithm (FA). A computational experimental design is proposed to analyze the efficiency of the introduced strategy, and the solutions indicate that the developed approach could reduce the carbon footprint by up to 9.82%. The results motivate us to implement the proposed algorithm in the manufacturing industry to reduce the carbon footprint.

Modeling and optimization of the hybrid flow shop scheduling problem with sequence-dependent setup times

The hybrid flow shop scheduling problem (HFSP) is an extension of the classic flow shop scheduling problem and widely exists in real industrial production systems. In real production, sequence-dependent setup times (SDST) are very important and cannot be neglected. Therefore, this study focuses HFSP with SDST (HFSP-SDST) to minimize the makespan. To solve this problem, a mixed-integer linear programming (MILP) model to obtain the optimal solutions for small-scale instances is proposed. Given the NP-hard characteristics of HFSP-SDST, an improved artificial bee colony (IABC) algorithm is developed to efficiently solve large-sized instances. In IABC, permutation encoding is used and a hybrid representation that combines forward decoding and backward decoding methods is designed. To search for the solution space that is not included in the encoding and decoding, a problem-specific local search strategy is developed to enlarge the solution space. Experiments are conducted to evaluate the effectiveness of the MILP model and IABC. The results indicate that the proposed MILP model can find the optimal solutions for small-scale instances. The proposed IABC performs much better than the existing algorithms and improves 61 current best solutions of benchmark instances.

A two-stage cross-neighborhood search algorithm bridging different solution representation spaces for solving the hybrid flow shop scheduling problem

In this paper, we address the classical hybrid flow shop scheduling problem(HFSP) to minimize makespan. This problem is known to be NP-hard and widely exists in many industrial systems such as electronics, paper, textile, and manufacturing industries. The existing work has shown that searching in multiple solution representation spaces is beneficial to improving the performance of the algorithm. However, the connection of the solutions in different solution representation spaces was ignored. To address this issue, this paper proposes a two-stage cross-neighborhood search algorithm (TSCNSA) for solving the hybrid flow shop scheduling problem. TSCNSA contains two individuals, each of which is responsible for searching in a solution representation space. The algorithm is divided into two stages: exploration and exploitation. In the exploration stage, the two individuals search in the solution representation space generated by the job-based encoding method and two decoding methods respectively to locate the potential area. In the exploitation stage, the two individuals search in the solution representation space generated by the operation-based encoding and two decoding methods respectively. The information obtained in the exploration stage will be transferred in the exploitation stage. Besides, each individual searches in its neighborhood and then generates an expert solution in the other solution representation space to guide the search for the other individual. Finally, the performance of the TSCNSA is proved by testing the well-known 586 benchmark instances. 151 new upper bounds are obtained, including 144 instances in Jose's benchmark instances, 2 instances in Liao's benchmark instances, and 5 instances in Carlier's benchmark instances.

Hybrid Flow Shop Scheduling Problem with Energy Utilization using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III) Optimization

Hybrid flow shop scheduling (HFS) is an on sought problem modelling for production manufacturing. Due to its impact on productivity, researchers from different backgrounds have been attracted to solve its optimum solution. The HFS is a complex dilemma and provides ample solutions, thus inviting researchers to propose niche optimization methods for the problem. Recently, researchers have moved on to multi-objective solutions. In real-world situations, HFS is known for multi-objective problems, and consequently, the need for optimum solutions in multi-objective HFS is a necessity. Regarding sustainability topic, energy utilization is mainly considered as one of the objectives, including the common makespan criteria. This paper presents the existing multi-objective approach for solving energy utilization and makespan problems in HFS scheduling using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), and a comparison to other optimization models was subjected for analysis. The model was compared with the most sought algorithm and latest multi-objective algorithms, Strength Pareto Evolutionary Algorithm 2 (SPEA -II), Multi-Objective Algorithm Particle Swarm Optimization (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The research interest starts with problem modelling, followed by a computational experiment with an existing multi-objective approach conducted using twelve HFS benchmark problems. Then, a case study problem is presented to assess all models. The numerical results showed that the NSGA-III obtained 50% best overall for distribution performance metrics and 42% best in convergence performance metrics for HFS benchmark problems. In addition, the case study results show that NSGA-III obtained the best overall convergence and distribution performance metrics. The results show that NSGA-III can search for the best fitness solution without compromising makespan and total energy utilization. In the future, these multi-objective algorithms’ potential can be further investigated for hybrid flow shop scheduling problems.

Reinforcement Learning-Based Multi-Objective of Two-Stage Blocking Hybrid Flow Shop Scheduling Problem

Consideration of upstream congestion caused by busy downstream machinery, as well as transportation time between different production stages, is critical for improving production efficiency and reducing energy consumption in process industries. A two-stage hybrid flow shop scheduling problem is studied with the objective of the makespan and the total energy consumption while taking into consideration blocking and transportation restrictions. An adaptive objective selection-based Q-learning algorithm is designed to solve the problem. Nine state characteristics are extracted from real-time information about jobs, machines, and waiting processing queues. As scheduling actions, eight heuristic rules are used, including SPT, FCFS, Johnson, and others. To address the multi-objective optimization problem, an adaptive objective selection strategy based on t-tests is designed for making action decisions. This strategy can determine the optimization objective based on the confidence of the objective function under the current job and machine state, achieving coordinated optimization for multiple objectives. The experimental results indicate that the proposed algorithm, in comparison to Q-learning and the non-dominated sorting genetic algorithm, has shown an average improvement of 4.19% and 22.7% in the makespan, as well as 5.03% and 9.8% in the total energy consumption, respectively. The generated scheduling solutions provide theoretical guidance for production scheduling in process industries such as steel manufacturing. This contributes to helping enterprises reduce blocking and transportation energy consumption between upstream and downstream.

Robust multi-equipment scheduling for U-shaped container terminals concerning double-cycling mode and uncertain operation time with cascade effects

The integrated scheduling of quay cranes, internal vehicles, and yard cranes in container terminals aims to improve port operations and often requires scheduling robustness under uncertainty with cascade effects. In container terminal operations, uncertainty in equipment operating time poses challenges to effective scheduling, as even small fluctuations can create cascade effects throughout the operations, rendering the original schedule ineffective. This research aims to develop a new method that enables a balance between optimization and robustness in container terminal scheduling. Additionally, the double-cycling operation mode and U-shaped port layout, known for their improved efficiency in container terminals, are gaining increasing attention and hence are incorporated into this study. It creates a three-stage hybrid flow shop scheduling problem with bi-directional flows, waiting time, and uncertain operation time. To address the complex problem, a mixed integer programming model is proposed to characterize the integrated scheduling problem, and an index based on complex network structure entropy is designed to evaluate the anti-cascade effect as well as the robustness of the schedule. The index and makespan serve as the bi-objectives, transforming the original problem into a bi-objective optimization one. The non-dominated sorting genetic algorithm-Ⅱ with appropriate coding and decoding rules is utilized to solve the model and obtain a set of Pareto frontier solutions. The feasibility of the new method is verified through a real case analysis. Specifically, comparative analysis with basic stochastic programming, basic robust optimization, triangular fuzzy programming, and maximum gap method are used to demonstrate the effectiveness of the new method. The paper also provides insightful practical implications for port managers, and the genericity of the method could also contribute to its practical values spreading to a wider scope of beneficiaries, such as manufacturing warehousing and distribution management.

The application of heterogeneous graph neural network and deep reinforcement learning in hybrid flow shop scheduling problem

The hybrid flow shop scheduling problem (HFSP) is a fundamental optimization problem in the process industries. HFSP needs to consider both job selection and machine allocation. The existing HFSP solution methods represented by deep reinforcement learning (DRL) are challenging to extract complex state features and lack certain adaptability in dealing with large-scale HFSP. To solve HFSP with a large scale and relatively strong flexibility, we propose an end-to-end DRL architecture based on the heterogeneous graph neural network to learn an optimal scheduling policy. First of all, by adding a set of machine nodes, the disjunctive graph of the traditional flexible scheduling problem is extended and transformed into a heterogeneous graph, which intuitively represents the allocation relationship between operations and machines, and it is regarded as the scheduling state at different times; secondly, a new HFSP heterogeneous graph neural network (HGNN) algorithm is established to embed potential relationships between different types of nodes and edges, and an embedding of the entire graph is generated; finally, we use the graph-level representation vectors of heterogeneous graphs as input to the proximal policy optimization (PPO) algorithm for learning the optimal scheduling policy. The experimental results show that compared with several well-known heuristic algorithms, the scheduling policy obtained by the architecture through learning can have good generalization performance in simple and complex problems, respectively, and has a relatively high solution efficiency.

Integration of deep reinforcement learning and multi-agent system for dynamic scheduling of re-entrant hybrid flow shop considering worker fatigue and skill levels

In real-life manufacturing systems, production management is often affected by urgent demands and unexpected interruptions, such as new job insertions, machine breakdowns and operator unavailability. In this context, agent-based techniques are useful and able to respond quickly to dynamic disturbances. The ability of agents to recognize their environment and make decisions can be further enhanced by deep reinforcement learning (DRL). This paper investigates a novel dynamic re-entrant hybrid flow shop scheduling problem (DRHFSP) considering worker fatigue and skill levels to minimize the total tardiness of all production tasks. An integrated architecture of DRL and MAS (DRL-MAS) is proposed for real-time scheduling in dynamic environments. Two DRL models are proposed for different sub-decisions, where a reward-shaping technique combining long-term and short-term returns is proposed for the job sequence and machine selection sub-decisions, and an attention-based network is proposed for the worker assignment sub-decision for efficient feature extraction and decision making. Numerical experiments and case studies demonstrate the superior performance of the proposed DRL models compared with existing scheduling strategies.

Electromagnetism-like mechanism algorithm for hybrid flow-shop scheduling problems

<span>Given the interest and complexity, of the hybrid flow shops (HFS) problem in industry, he has been extensively considered, the HFS, is a complex combinatorial problem supported in many original world applications. We consider a hybrid flow shop FH4(P3, P2)||C<sub>max</sub> to applied in this paper. In this papers we attempt to optimize the makespan which refers to the last task completion time by an adequate meta-heuristic algorithm based on electromagnetism mechanism (EM). We also present analysis on the performance of the EM-algorithm adapted to HFS scheduling problems. The electromagnetism-like mechanism method gave us efficient and fair results comparing to particle swarm and genetic algorithm.</span>

An adaptive artificial bee colony for hybrid flow shop scheduling with batch processing machines in casting process

Hybrid flow shop scheduling problem (HFSP) with real-life constraints has been extensively considered; however, HFSP with batch processing machines (BPM) at a middle stage is seldom investigated. In this study, HFSP with BPM at a middle stage in hot & cold casting process is considered and an adaptive artificial bee colony (AABC) is proposed to minimise makespan. To produce high quality solutions, an adaptive search process with employed bee phase and adaptive search step is implemented. Adaptive search step, which may be onlooker bee phase or cooperation or empty, is decided by evolution quality and an adaptive threshold. Cooperation is performed between the improved solutions of one employed bee swarm and the unimproved solutions of another swarm. Six search operators are constructed and search operator is adaptively adjusted. A new scout phase is also given. A lower bound is provided and proved. Extensive experiments are conducted. The computational results validate that new strategies such as cooperation are effective and efficient and AABC can obtain better results than methods from existing literature on the considered problem.

Mathematical model and knowledge-based iterated greedy algorithm for distributed assembly hybrid flow shop scheduling problem with dual-resource constraints

With the development of economic globalization, distributed hybrid flow shop scheduling problem (DHFSSP) has become prevalent in realistic manufacturing systems. Moreover, to accord with the actual production scenarios and satisfy the requirement of manufacturing market, it is imperative to comprehensively explore various complex manufacturing scenarios (e.g., production assembly) and production-constrained resources (e.g., worker resources) in DHFSSP. However, the integration mode of DHFSSP, assembly shop problem (ASP), and dual-resource constraints (DRC) has not been reported in existing literature. Thus, to fill out this research gap, this paper first attempts to investigate DAHFSSP-DRC with minimization the total tardiness (TTD). To solve this problem, a mixed-integer linear programming (MILP) model and a knowledge-based iterated greedy algorithm (KBIG) are presented. The novelties of KBIG are as follows: (1) An efficient decoding is developed to improve the solution’s quality; (2) A knowledge-based NEH (KB-NEH) initialization strategy is presented to generate an initial solution; (3) A knowledge-based destruction and construction is designed to improve the exploration capability; (4) A product-based local search is proposed to enhance the exploitation capability. Additionally, to validate the proposed model, we implement CPLEX to solve it on 24 small-sized instances. To verify the effectiveness of the proposed KBIG, extensive experiments are conducted to compare with other 7 comparison algorithms on 405 large-sized instances. Experimental results illustrate that KBIG is superior to its competitors.

Automated rail-water intermodal transport container terminal handling equipment cooperative scheduling based on bidirectional hybrid flow-shop scheduling problem

The importance of rail-water intermodal transport is becoming more and more prominent in recent years. As a key node of rail-water intermodal transportation, the operation efficiency of automated container terminal directly affects the overall transportation efficiency. However, there are few studies on the collaborative scheduling of automated container terminal equipment in rail-water intermodal transportation. Therefore, this paper focuses on the ‘Automated Quay Crane (AQC)-Automated Straddle Carrier (ASC)-Automated Rail Mounted Gantry Crane (ARMG)’ operation system and addresses the operational efficiency requirements of the Automated Rail-Water Intermodal Transport Container Terminal (ARWITCT), Based on the bidirectional Hybrid Flow-shop Scheduling Problem (HFSP), a scheduling optimization model for the ARWITCT is established with the objective of minimizing the maximum completion time. To solve this complex scheduling problem, Particle Swarm Optimization based on Adaptive Tent Chaos Mapping (PSO-ATCM) is designed. In this algorithm, a parameter adaptive adjustment strategy and a Tent Chaos Mapping Optimization Strategy are introduced to help PSO jump out of local optimum. Problem-feature-based encoding and decoding methods are designed for the problem. An ‘insertion-translation’ mechanism is used to judge and resolve the conflicts between import and export containers during the decoding process. The effect of proposed scheduling model and the performance of the proposed algorithm are validated via comprehensive comparison experiments. To validate the effectiveness of proposed scheduling model, we compare the unidirectional HFSP model with the bidirectional HFSP model. The proposed PSO-ATCM is compared with standard Genetic Algorithm, Particle Swarm Optimization algorithm and Adaptive Genetic Algorithm. Computational results demonstrate that the proposed model is effective and PSO-ATCM performs better than other three compared algorithms.

A multi-objective complex product assembly scheduling problem considering transport time and worker competencies

The hybrid flow shop scheduling problem (HFSP) is a research hotspot in the shop scheduling problem. However, few studies have investigated HFSP involving parallel machine scheduling and worker competencies. Therefore, this study investigates a complex product assembly line scheduling problem considering parallel team scheduling, worker competencies, and transport time. The makespan, transport time, imbalance degree of team workload, and imbalance degree of cycle time are taken as optimization objectives. First, a mathematical model considering transport time and worker competencies is developed, and then a mixed encoding and decoding method is proposed. Second, an algorithm that hybridizes the genetic algorithm and simulated annealing algorithm is proposed, involving an improved Nawaz-Enscore-Ham heuristic method and a strengthened elite retention strategy to improve the quality of the solution. Finally, based on nine examples generated from real production statuses, the proposed algorithm is compared with the other four algorithms. The results show that the proposed algorithm is superior in terms of the quality and efficiency of solutions.

A Population Diversity-Based Artificial Bee Colony Algorithm for Assembly Hybrid Flow Shop Scheduling with Energy Consumption

Assembly shop scheduling and energy-efficient scheduling have attracted much attention in the past decades; however, energy consumption is often ignored in assembly hybrid flow shop scheduling. Neglecting energy consumption will greatly diminish the progress of sustainable manufacturing. In this study, an assembly hybrid flow shop scheduling problem considering energy consumption (EAHFSP) is investigated, and a population diversity-based artificial bee colony algorithm (DABC) is proposed to minimize the makespan and total energy consumption (TEC) simultaneously. Diversified search strategies based on rank value are introduced to the employed bee phase; a novel probability selection method in the onlooker bee phase is designed to control the selection pressure; moreover, a diversity control strategy is applied to improve the diversity of food sources and avoid falling into stagnation. A number of experiments based on 44 extended benchmark instances from the literature and a real case are conducted to test the performance of the DABC algorithm. The statistical results show that the DABC algorithm is superior to the other four state-of-the-art algorithms on over 70% of the instances corresponding to metrics IGD and c, which means that the DABC algorithm is effective and competitive in solving the considered EAHFSP.