Hybrid Flow Shop Problem Research Articles

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

MODEL PENJADWALAN BACKWARD HYBRID FLOW SHOP 2 STAGE UNTUK MEMINIMASI MEAN FLOWTIME

The scheduling problem is a common challenge when it comes to executing tasks, making the resolution of this issue crucial for decision-making in production activities. The problem addressed in this research is the company's desire to conduct production without waiting times between stages to maintain the quality of pharmaceutical raw materials. Additionally, the production results must meet predefined due dates. The production system formed is a Hybrid Flow Shop system, which is an extension of the Flow Shop concept where one or all stages have identical parallel machines. The objective of this study is to minimize the time between job start and job completion, defined in scheduling problems as the minimization of mean Flow time. The research collected data from 5 products in the company to model according to the research objectives. Process times for each stage and due dates for each product have been predetermined. After modeling and processing using the LINGO application, the optimal result obtained is backward scheduling with an average flow time of 12.6. This demonstrates that the model in this research effectively addresses the Hybrid Flow Shop problem using backward scheduling to minimize mean flow time

Multi-objective Evolutionary Algorithm with Variable Neighborhood Search for Optimizing Green Scheduling in a Re-Entrant Hybrid Flow Shop with Dynamic Events

In previous studies on re-entrant hybrid flow shops, the impact of dynamic events was often ignored despite being a common occurrence in practical production. To address this issue and simultaneously reduce energy consumption, a multi-objective evolutionary algorithm with variable neighborhood search (MOEA-VNS) has been proposed to optimize the green scheduling problem in a re-entrant hybrid flow shop with dynamic events (RHFS-GDS).The approach involves creating a green dynamic scheduling optimization model, which aims to minimize the makespan, total energy consumption, and stability of rescheduling solutions. A hybrid green scheduling decoding method is then employed to select machines for each operation and calculate fitness. Additionally, three neighborhood structures are designed to improve the population diversity and optimality of the MOEA-VNS algorithm. Two rescheduling strategies are also adopted to handle dynamic events that may occur during production. Experimental results demonstrate that these approaches are effective in solving the RHFS-GDS problem and can guide actual production. By incorporating dynamic events and rescheduling strategies into the optimization process, the proposed MOEA-VNS algorithm provides a comprehensive solution to the complex challenges faced by re-entrant hybrid flow shops in practical production environments.

Energy-efficient scheduling for a hybrid flow shop problem while considering multi-renewable energy

At present, the concept of green and sustainable development has been recognised by everyone. For industrial applications, the concept is both a matter of energy consumption and a matter of production methods. Based on the hybrid flow shop problem, a multi-energy supply system is constructed, and external renewable energy microgrid is introduced to further improve the low-carbon level. From the perspectives of energy supply and internal load, the output of wind power and photovoltaic, energy storage cost and energy consumption cost in the flow shop on a certain day are analysed under the demand–response electricity price. After considering the natural endowments and demand differences of different microgrids, construct a multi-energy complementarity model, determine the coordination transaction strategy among microgrids and obtain the solution of the subproblem and the equilibrium solution of the whole problem. Finally, an example is given to evaluate the effectiveness of the proposed strategy under time-of-use prices. The results show that the proposed strategy can effectively improve the utilisation rate of renewable energy in the flow shop while reducing the overall operating cost.

Q-Learning-Assisted Meta-Heuristics for Scheduling Distributed Hybrid Flow Shop Problems

Q-Learning-Assisted Meta-Heuristics for Scheduling Distributed Hybrid Flow Shop Problems

An Iterated Greedy Algorithm With Reinforcement Learning for Distributed Hybrid FlowShop Problems With Job Merging

An Iterated Greedy Algorithm With Reinforcement Learning for Distributed Hybrid FlowShop Problems With Job Merging

A tri-individual iterated greedy algorithm for the distributed hybrid flow shop with blocking

Scheduling problem with blocking is an attractive research direction due to its wide practical applications. However, in the distributed hybrid flow shop problem (DHFSP), there are few studies on blocking constraints. In this article, we study a distributed hybrid flow shop scheduling problem with blocking constraints (DBHFSP), where the goal is to minimize the maximum completion time, and propose a tri-individual iterated greedy (TIG) algorithm based on the characteristics of the DBHFSP. First, an active decoding strategy is designed to reduce the idle time of machines. Afterward, a framework of multiple iterative solutions is designed to enhance the diversity of the solutions, in which the multiple solutions are generated through a neighborhood search. Then, a heuristic rule based on blocking constraint is proposed to generate promising initial solutions. In addition, an insertion-based search strategy based on rotating critical factories is designed to accelerate the convergence speed of the TIG algorithm. Finally, the proposed algorithm is compared with state-of-the-art algorithms and classical intelligent optimization algorithms. The experimental results show that the TIG algorithm is superior to the comparison algorithm in solving the DBHFSP.

A cooperative adaptive genetic algorithm for reentrant hybrid flow shop scheduling with sequence-dependent setup time and limited buffers

This paper deals with a reentrant hybrid flow shop problem with sequence-dependent setup time and limited buffers where there are multiple unrelated parallel machines at each stage. A mathematical model with the minimization of total weighted completion time is constructed for this problem. Considering the complexity of the problem at hand, an effective cooperative adaptive genetic algorithm (CAGA) is proposed. In the algorithm, a dual chain coding scheme and a staged-hierarchical decoding approach are, respectively, designed to encode and decode each solution. Six dispatch heuristics and a dynamic adjustment method are introduced to define initial population. To balance the exploration and exploitation abilities, three effective operations are implemented: (1) two new crossover and mutation operators with collaborative mechanism are imposed on genetic algorithm; (2) an adaptive adjustment strategy is introduced to re-optimize better solutions after mutation operations, where ant colony search algorithm and modified greedy heuristic are intelligently switched; (3) a reset strategy with dynamic variable step strategy is embedded to re-generate some non-improved solutions. A Taguchi method of design of experiment is adopted to calibrate the parameter values in the presented algorithm. Comparison experiments are executed on test instances with different scale problems. Computational results show that the proposed CAGA is more effective and efficient than several well-known algorithms in solving the studied problem.

Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches

This paper presents a comprehensive approach for minimizing makespan in the challenging two-stage hybrid flowshop with dedicated machines, a problem known to be strongly NP-hard. This study proposed a constraint programming approach, a novel heuristic based on a priority rule, and Tabu search procedures to tackle this optimization problem. The constraint programming model, implemented using a commercial solver, serves as the exact resolution method, while the heuristic and Tabu search explore approximate solutions simultaneously. The motivation behind this research is the need to address the complexities of scheduling problems in the context of two-stage hybrid flowshop with dedicated machines. This problem presents significant challenges due to its NP-hard nature and the need for efficient optimization techniques. The contribution of this study lies in the development of an integrated approach that combines constraint programming, a novel heuristic, and Tabu search to provide a comprehensive and efficient solution. The proposed constraint programming model offers exact resolution capabilities, while the heuristic and Tabu search provide approximate solutions, offering a balance between accuracy and efficiency. To enhance the search process, the research introduces effective elimination rules, which reduce the search space and simplify the search effort. This approach improves the overall optimization performance and contributes to finding high-quality solutions. The results demonstrate the effectiveness of the proposed approach. The heuristic approach achieves complete success in solving all instances for specific classes, showcasing its practical applicability. Furthermore, the constraint programming model exhibits exceptional efficiency, successfully solving problems with up to n=500 jobs. This efficiency is noteworthy compared to instances solved by other exact solution approaches, indicating the scalability and effectiveness of the proposed method.

A knowledge-driven multiobjective algorithm for distributed hybrid flowshop with group and carryover setup in glass manufacturing systems

The distributed hybrid flow shop problem (DHFSP) exists widely in real workshop production processes. Its process optimization has important academic significance and application value, and has become one of the research hotspots in the field of production scheduling. In this study, a multiobjective DHFS problem with carryover setup time and group constraints (DHFGSP) is considered with the background of glass processing, and the objectives are the completion time and time of use price. First, a mathematical programming model is established according to the processing flow of glass production. Second, an improved nondominated sorting genetic algorithm-II (INSGAII) is adopted to optimize the problem. Third, the evolutionary strategies based on problem knowledge are developed, and a local search strategy based on critical factories is designed. Finally, the proposed algorithm is compared with several of the most advanced multiobjective algorithms, which shows that INSGA-II has better performance for solving DHFGSP.

Hybrid Flow Shop with Setup Times Scheduling Problem

The two-stage hybrid flow shop problem under setup times is addressed in this paper. This problem is NP-Hard. on the other hand, the studied problem is modeling different real-life applications especially in manufacturing and high performance-computing. Tackling this kind of problem requires the development of adapted algorithms. In this context, a metaheuristic using the genetic algorithm and three heuristics are proposed in this paper. These approximate solutions are using the optimal solution of the parallel machines under release and delivery times. Indeed, these solutions are iterative procedures focusing each time on a particular stage where a parallel machines problem is called to be solved. The general solution is then a concatenation of all the solutions in each stage. In addition, three lower bounds based on the relaxation method are provided. These lower bounds present a means to evaluate the efficiency of the developed algorithms throughout the measurement of the relative gap. An experimental result is discussed to evaluate the performance of the developed algorithms. In total, 8960 instances are implemented and tested to show the results given by the proposed lower bounds and heuristics. Several indicators are given to compare between algorithms. The results illustrated in this paper show the performance of the developed algorithms in terms of gap and running time.

An Evaluation of Mathematical Programming and Lower-Bound Methods for Hybrid Flow Shop Problems With a Makespan Criterion

This paper considers the hybrid flow shop scheduling problem, where jobs are processed in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> stages with the same route of the stage. Each stage has identical parallel machines for processing jobs. Some mathematical programming formulations and lower bound calculations have been proposed in the literature for such cases. Nevertheless, there is a lack of complete comparisons of these mathematical programming formulations and lower bounds in the hybrid flow shop literature. In this paper, we propose a new mixed integer programming model and two new lower bounds based on the bin-packing concept for the considered problem. To evaluate the proposed model, two sets of small and small-to-medium problems are used to compare our model with the existing models. Moreover, two propositions are discussed for lower bounds. The experimental results show that the proposed mixed integer programming model efficiently found optimal solutions because it needs a smaller number of binary variables and a smaller number of constraints, and the proposed lower bound can also serve as a strong indicator to evaluate the distances between the solutions obtained by heuristic algorithms and the optimal solution.

Multi-resource collaborative scheduling problem of automated terminal considering the AGV charging effect under COVID-19

Since the COVID-19 ravaged the global terminals, the Automated Container Terminal (ACT) has become one of important approach to promote the stronger quick response capacity to deal with the uncertainty that COVID-19 brought to the terminal. This research takes Automated Guided Vehicle (AGV) and their effects into account the multi-resource collaborative scheduling model to tradeoff ACT operational efficiency and energy savings. Firstly, the dual-cycle strategy of QC and the pooling strategy of AGV are given, which coordinates the scheduling of Quay Cranes (QCs), Yard Cranes (YCs) and other equipment. Furthermore, a multi-resource collaborative scheduling optimization model is proposed which roots from the principle of the Blocking-type Hybrid Flow Shop Problem (B–HFSP) with the objectives of minimizing the makespan of QC and the transportation energy consumption. And simultaneously, a mixed algorithm SA-GA is designed for solving this mixed integer programming model by an optimizing effect of Simulated Annealing on Genetic algorithms. Numerical experiments show that the model in this research is effective. The convergence of SA-GA is effective for small-scale cases and superior for large-scale cases. Considering both goals of high efficiency and energy saving, the Pareto solution set and collaborative scheduling solution take a priority to ensure that the bottlenecked QC runs efficiently. Here and now the average idle rate of QC is about [14%, 35%] lower than that of other equipment. The collaborative scheduling model constructed above not only has reference value for other multi-device and multi-stage scheduling problem, but also enhance the integrated decision-making ability of the ACT in the post-epidemic era.

Improved formulations and new valid inequalities for a Hybrid Flow Shop problem with time-varying resources and chaining time-lag

This paper proposes revised and improved mathematical integer formulations for the Hybrid Flow Shop problem under time-varying resources and chaining time-lag constraints. First, we provide a structural classification and a complexity analysis of the tackled problem. Then, we prove the correctness of our novel modeling techniques. To reinforce the formulations, two valid inequalities are developed. The revised formulations are benchmarked, and the results show that the valid inequalities improve significantly the performance. Finally, we propose a hybrid model that outperforms the best formulations and can be applied in an industrial application.

Deep Reinforcement Learning Approach for Material Scheduling Considering High-Dimensional Environment of Hybrid Flow-Shop Problem

Manufacturing sites encounter various scheduling problems, which must be dealt with to efficiently manufacture products and reduce costs. With the development of smart factory technology, many elements at manufacturing sites have become unmanned and more complex. Moreover, owing to the mixing of several processes in one production line, the need for efficient scheduling of materials has emerged. The aim of this study is to solve the material scheduling problem of many machines in a hybrid flow-shop environment using deep reinforcement learning. Most previous work has ignored some conditions, which were critical for solving practical problems. Such critical conditions make the scheduling more complex and difficult to solve. They expand the size of the state and large action space and make learning in an environment with many machines problematic. In this study, a reinforcement learning approach was developed considering practical factors such as the processing time and material transfer to solve realistic manufacturing scheduling problems. Additionally, a method to simplify the high-dimensional environmental space at manufacturing sites for efficient learning was established to solve the problem of learning in a high-dimensional space. Through experiments, we showed that our approach could optimally schedule material scheduling in multi-process lines, which contributes to realistic manufacturing intelligence.

Batching and scheduling in a continuous-discrete hybrid flowshop: Lagrangian relaxation-based heuristic algorithms

ABSTRACT We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently.

An efficient self-adaptive artificial bee colony algorithm for the distributed resource-constrained hybrid flowshop problem

Distributed factory processing has attracted the attention and application of many companies because of the low cost and high flexibility. In the present study, the self-adaptive artificial bee colony algorithm (SABC) is presented to solve the distributed resource-constrained hybrid flowshop scheduling (DRCHFS) problems aiming to minimize the makespan. In the proposed algorithm, the two-dimensional vector solution representation is employed. Then, resource constraint in the decoding process is considered. In addition, a self-adaptive perturbation structure and local search strategy based on the critical factory are investigated to enhance searching abilities. The proposed algorithm is tested based on a randomly generated set of the real shop scheduling system, and then numerically analyze and compare the proposed algorithm with the existing heuristic algorithms to verify its effectiveness.

A collaborative iterative greedy algorithm for the scheduling of distributed heterogeneous hybrid flow shop with blocking constraints

The hybrid flow shop and distributed flow shop problems have been extensively studied due to their wide industrial applications. However, the distributed heterogeneous hybrid flow shop problems (DHHFSP) with blocking constraints have not yet been well studied up to date. This paper considers how to arrange a variety of jobs to different heterogeneous factories, and each factory has a minimal makespan. The innovations of this paper lie in presenting a mathematical model of the DHHFSP with blocking constraints and designing a collaborative iterative greedy (CIG) algorithm. The CIG contains the problem-specific initialization strategy, the neighborhood search strategy, the destruction-reconstruction strategy, and the local intensification strategy. The cross-factory and inner-factory neighborhood search strategies based on two swap operators are adopted to reduce the blocking time. The local intensification strategy is developed to optimize the scheduling sequence of each factory. The proposed algorithm is empirically compared with five state-of-the-art algorithms on 60 different instance sets. The experimental results show that the proposed algorithm significantly outperforms the compared ones in terms of objective values and relative percentage deviation values.

An improved iterated greedy algorithm for the energy-efficient blocking hybrid flow shop scheduling problem

• A mathematical model of a blocking hybrid flow shop scheduling problem with energy consumption criteria is proposed. • A simple global perturbation based on a half-swap operator is proposed to further search for the potentially best solution. • A local perturbation strategy based on a swap operator is designed to ensure the convergence of the algorithm. • The proposed algorithm is applied to 140 test instances with different scales and compared with state-of-the-art algorithms and can obtain the best solution to the BHFSP. With the continuous development of national economies, problems of various energy consumption levels and pollution emissions in manufacturing have attracted attention from researchers. Most existing research has focused on reducing economic costs and energy consumption. However, the Hybrid Flow Shop Scheduling Problem with energy-efficient criteria has not yet been well studied, especially with blocking constraints. This paper is the first to present a mathematical model of the blocking hybrid flow shop problem with an energy-efficient criterion and a modified Iterative Greedy algorithm based on a swap strategy designed to optimize the constructed model. In the proposed algorithm, first, a heuristic is adopted to generate the initial solution. Second, a local perturbation strategy based on a swap operator is designed to ensure the convergence of the algorithm. Third, a simple global perturbation strategy based on a half-swap operator is proposed as a means to further search for the potentially best solution with the traditional simulated annealing criterion. The proposed algorithm is applied to 150 test instances at different scales and compared to state-of-the-art algorithms. The experimental results demonstrate that the proposed algorithm outperforms the compared algorithms and can obtain a better solution.

Competitive scheduling in a hybrid flow shop problem using multi-leader–multi-follower game - A case study from Iran

It is logical that organizations pay more attention to their major customers which have more impacts on their abilities or benefits. In many real cases, decision makers in scheduling system must prioritize the sequence of processing orders according to the agent of orders while the classic production scheduling do not have the ability to consider the relationships between agents. These problems can be modeled by the Stackelberg problems in the field of game theory. In this study, an agent-based hybrid flow shop problem is formulated by using the multi-leader multi-follower mathematical model. Each level is evaluated by Nash equilibrium and Nash bargaining with the new co-evolutionary and genetic algorithm. The proposed model is validated in a real case problem in the tire manufacturing industry. The results show that Nash equilibrium is superior to Nash bargaining for all agents.