Distributed Permutation Flowshop Scheduling Problem 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

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

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.

Solving the Distributed Permutation Flow-Shop Scheduling Problem Using Constrained Programming

The permutation flow-shop scheduling problem is a classical problem in scheduling that aims at identifying the optimal sequence of jobs that should be processed in a number of machines in an effort to minimize makespan or some other performance criterion. The distributed permutation flow-shop scheduling problem adds multiple factories where copies of the machines exist and asks for minimizing the makespan on the longest-running location. In this paper, the problem is approached using Constraint Programming and its specialized scheduling features, such as interval variables and non-overlap constraints, while a novel heuristic is proposed for computing lower bounds. Two constraint programming models are proposed: one that solves the Distributed Permutation Flow-shop Scheduling problem, and another one that drops the constraint of processing jobs under the same order for all machines of each factory. The experiments use an extended public dataset of problem instances to validate the approach’s effectiveness. In the process, optimality is proved for many problem instances known in the literature but has yet to be proven optimal. Moreover, a high speed of reaching optimal solutions is achieved for many problems, even with moderate big sizes (e.g., seven factories, 20 machines, and 20 jobs). The critical role that the number of jobs plays in the complexity of the problem is identified and discussed. In conclusion, this paper demonstrates the great benefits of scheduling problems that stem from using state-of-the-art constraint programming solvers and models that capture the problem tightly.

A cooperative iterated greedy algorithm for the serial distributed permutation flowshop scheduling problem

This paper addresses a serial distributed permutation flowshop scheduling problem (SDPFSP) inspired by a printed circuit board assembly process that contains two production stages linked by a transportation stage, where the scheduling problem in each production stage can be seen as a distributed permutation flowshop scheduling problem (DPFSP). A sequence-based mixed-integer linear programming model is established. A solution representation consisting of two components, one component per stage, is presented and a makespan calculation method is given for the representation. Two suites of accelerations based on the insertion neighbourhood are proposed to reduce the computational complexity. A cooperative iterated greedy (CIG) algorithm is developed with two subloops, each of which optimises a component of the solution. A collaboration mechanism is used to conduct the collaboration of the two subloops effectively. Problem-specific operators including the NEH-based heuristics, destruction, reconstruction and three local search procedures, are designed. Extensive computational experiments and statistical analysis verify the validity of the model, the effectiveness of the proposed CIG algorithm and the superiority of the proposed CIG over the existing methods for solving the problem under consideration.

A problem-specific knowledge based artificial bee colony algorithm for scheduling distributed permutation flowshop problems with peak power consumption

A distributed permutation flowshop scheduling problem (DPFSP) with peak power consumption is addressed in this work. The instantaneous energy consumption of each factory cannot exceed a threshold. First, a mathematical model is developed to describe the concerned problem. Second, an improved artificial bee colony (IABC) algorithm is proposed. Based on problem-specific knowledge, three new solution generation operators, e.g., shift, swap, and speed adjust, are designed for employ bees and onlooker bees. A local search operation is developed to improve the quality of current best-known solution in each iteration. 450 instances are solved to evaluate the performance of IABC via comparing to seven state-of-the-art algorithms. The average relative percentage increase (ARPI) of IABC ranks 1 among all compared algorithms. The results and discussions show that the proposed IABC algorithm has strong competitiveness for solving the DPFSP with peak power consumption.

An effective fruit fly optimization algorithm for the distributed permutation flowshop scheduling problem with total flowtime

Distributed permutation flowshop scheduling problem (DPFSP) has always been a hot issue. The optimization goal of minimizing the total flowtime is of great significance to the environment of multi-factory. In this paper, a discrete fruit fly optimization algorithm (DFFO) is proposed to solve the DPFSP with the total flowtime criterion. In the proposed DFFO, an initialization method considering the population quality and diversity is adopted. In the smell-based search stage, three perturbation operators, the Shift-based operator, the Exchange-based operator and the Hybrid operator are designed respectively, and each fruit fly improves its state through a specific neighborhood strategy. In addition, we propose an improved reference local search (MRLS) method to enhance the exploitation ability of fruit flies. In the vision-based search stage, fruit flies use a well-designed combination update mechanism to lead fruit flies to more potential areas. In order to enhance the exploration ability, we use random reinforcement method for the population. The parameters are evaluated using an orthogonal experimental design to determine the appropriate values of the key parameters. In addition, we test the DFFO and the state-of-art algorithms from the literature on 720 large-scale instances. The experimental results show that DFFO is a very effective metaheuristic.

Acceleration-based artificial bee colony optimizer for a distributed permutation flowshop scheduling problem with sequence-dependent setup times

The distributed permutation flowshop scheduling problem (DPFSP) has attracted a lot of attentions in recent years. Furthermore, sequence-dependent setup time (SDST) often occurs in the job’s production, and total flowtime becomes a more important and meaningful objective for the modern dynamic productive environment. Therefore, the DPFSP with SDST under minimization of total flowtime is investigated in this paper, and the mathematical model is established. To solve the problem, this paper presents three constructive heuristics and an effective discrete artificial bee colony (EDABC) method based on the acceleration. In the EDABC, the constructive heuristics are used to initialize population. Moreover, based on the problem-specific of sequence-dependent, the employed bees stage, onlooker bees stage and scout bees stage are improved by exploring the acceleration methods to evaluate the neighboring solutions. Further, to strengthen the performance of the proposed algorithm, three effective problem-oriented local search methods are developed, including referenced local search (RLS), improved local search 1 (ILS1) and improved local search 2 (ILS2). RLS is used to the best solution after the initialization, and ILS1 and ILS2 are designed in the framework of improved variable neighborhood descent. The extensive computational experiences are carried out, and the results show that the proposed methods, including three heuristics and EDABC, have outstanding performance for the SDST/DPFSP to minimize the total flowtime.

A discrete artificial bee colony method based on variable neighborhood structures for the distributed permutation flowshop problem with sequence-dependent setup times

• The DPFSP with SDST under minimization of total flowtime is investigated in the paper; • We propose a constructive heuristic framework, which contains three constructive heuristics, to obtain good initial solutions for our DABC vns ; • By analyzing the characteristics of problem-specific, four different neighborhood structures are proposed and selectively applied in three stages to obtain more feasible neighborhood solutions; • A new population update strategy is adopted in scout bee phase to help algorithm explore new promising area; • The experimental evaluation is used to verify the validity of constructive heuristics and DABC vns . In today's global economy, distributed manufacturing has become increasingly appropriate. Job setup time is invariably a factor in manufacturing, and needs to be considered when making scheduling decisions. This study aims to minimize the total flow time by solving a distributed permutation flowshop scheduling problem (DPFSP) with a sequence-dependent setup time (SDST) to minimize total flowtime. First, to manage the DPFSP/SDST effectively, we propose a constructive heuristic framework based on the LR heuristic, which contains three constructive heuristics to obtain good initial solutions. Second, a discrete artificial bee colony (DABC) method based on variable neighborhood structures (DABC vns ) is proposed. By analyzing the problem-specific characteristics in the DABC vns , four different neighborhood structures are proposed, which are selectively applied in three stages of DABC vns to obtain more feasible neighborhood solutions. In addition, two variable neighborhood descent algorithms are proposed, which are each based on local search methods. The algorithms are developed to improve the best solution obtained in initial population and the best solution generated in the three stages. Finally, we conduct an experiment to calibrate the parameter of the DABC vns method. To evaluate the performance of the proposed method compared to six other algorithms, comprehensive computational experiments are conducted. The simulation results indicate that the proposed method delivers the best quality solutions for the DPFSP/SDST in the minimization of total flowtime.

Real-time scheduling for distributed permutation flowshops with dynamic job arrivals using deep reinforcement learning

Distributed manufacturing plays an important role for large-scale companies to reduce production and transportation costs for globalized orders. However, how to real-timely and properly assign dynamic orders to distributed workshops is a challenging problem. To provide real-time and intelligent decision-making of scheduling for distributed flowshops, we studied the distributed permutation flowshop scheduling problem (DPFSP) with dynamic job arrivals using deep reinforcement learning (DRL). The objective is to minimize the total tardiness cost of all jobs. We provided the training and execution procedures of intelligent scheduling based on DRL for the dynamic DPFSP. In addition, we established a DRL-based scheduling model for distributed flowshops by designing suitable reward function, scheduling actions, and state features. A novel reward function is designed to directly relate to the objective. Various problem-specific dispatching rules are introduced to provide efficient actions for different production states. Furthermore, four efficient DRL algorithms, including deep Q-network (DQN), double DQN (DbDQN), dueling DQN (DlDQN), and advantage actor-critic (A2C), are adapted to train the scheduling agent. The training curves show that the agent learned to generate better solutions effectively and validate that the system design is reasonable. After training, all DRL algorithms outperform traditional meta-heuristics and well-known priority dispatching rules (PDRs) by a large margin in terms of solution quality and computation efficiency. This work shows the effectiveness of DRL for the real-time scheduling of dynamic DPFSP.

The distributed flowshop scheduling problem with delivery dates and cumulative payoffs

In the classic distributed permutation flowshop scheduling problem (DPFSP), there are more studies on the minimization of makespan, total flow time, total tardiness, etc. This paper studies a new problem with a new optimization goal, the DPFSP with delivery dates and cumulative payoffs. It is a variation of the DPFSP with job release dates that maximizes the total payoff with a stepwise job objective function. The main contributions are summarized as follows. (1) A mathematical model is built to formulate the new problem. (2) The characteristics of the problem are explored, and the upper and lower bounds of the problem are given. Based on the problem-specific knowledge, an algorithm named Insert-Pruning is proposed to improve the efficiency of search. (3) Nine heuristic algorithms are proposed, including DRI, DRA, DEI, DEA, DNI, DNA, DII, DIA and DFF. (4) Combined with the characteristics of the problem, some modifications and improvements have been made to the IG algorithm to solve it, including the destruction method, the local search method and the acceptance criterion. (5) The experimental results show that the presented algorithm significantly outperforms the existing algorithms in the literature. In comparison with other competing algorithms in different dimensions, our algorithm has shown better performance, which verifies the effectiveness of this algorithm.

A new solution to distributed permutation flow shop scheduling problem based on NASH Q-Learning

Aiming at Distributed Permutation Flow-shop Scheduling Problems (DPFSPs), this study took the minimization of the maximum completion time of the workpieces to be processed in all production tasks as the goal, and took the multi-agent Reinforcement Learning (RL) method as the main frame of the solution model, then, combining with the NASH equilibrium theory and the RL method, it proposed a NASH Q-Learning algorithm for Distributed Flow-shop Scheduling Problem (DFSP) based on Mean Field (MF). In the RL part, this study designed a two-layer online learning mode in which the sample collection and the training improvement proceed alternately, the outer layer collects samples, when the collected samples meet the requirement of batch size, it enters to the inner layer loop, which uses the Q-learning model-free batch processing mode to proceed, and adopts neural network to approximate the value function to adapt to large-scale problems. By comparing the Average Relative Percentage Deviation (ARPD) index of the benchmark test questions, the calculation results of the proposed algorithm outperformed other similar algorithms, which proved the feasibility and efficiency of the proposed algorithm.

Distributed Flow Shop Scheduling with Sequence-Dependent Setup Times Using an Improved Iterated Greedy Algorithm

To meet the multi-cooperation production demand of enterprises, the distributed permutation flow shop scheduling problem (DPFSP) has become the frontier research in the field of manufacturing systems. In this paper, we investigate the DPFSP by minimizing a makespan criterion under the constraint of sequence-dependent setup times. To solve DPFSPs, significant developments of some metaheuristic algorithms are necessary. In this context, a simple and effective improved iterated greedy (NIG) algorithm is proposed to minimize makespan in DPFSPs. According to the features of DPFSPs, a two-stage local search based on single job swapping and job block swapping within the key factory is designed in the proposed algorithm. We compare the proposed algorithm with state-of-the-art algorithms, including the iterative greedy algorithm (2019), iterative greedy proposed by Ruiz and Pan (2019), discrete differential evolution algorithm (2018), discrete artificial bee colony (2018), and artificial chemical reaction optimization (2017). Simulation results show that NIG outperforms the compared algorithms.

Sustainable distributed permutation flow-shop scheduling model based on a triple bottom line concept

Based on a triple bottom line concept, sustainable development is characterized by the simultaneous pursuit of economic, environmental and social goals. The implementation of this concept in production scheduling can result in the resolution of a sustainable Distributed Permutation Flow Shop Scheduling Problem (DPFSP). The present study conceptually shifts an energy-efficient DPFSP to a sustainable DPFSP, simultaneously contributing to economic, environmental and social improvements. The study aims not only to minimize the total energy consumption related to production, but also, to maximize, for the first time, the social factors linked to job opportunities and lost working days. Different production centers and technologies are considered as new suppositions to establish a sustainable DPFSP. In this regard, a novel multi-objective mixed integer linear model is developed. To manage the high complexity of the proposed model, a novel multi-objective learning-based heuristic is established, as an extension of the Social Engineering Optimizer (SEO). The applicability of the proposed model is determined in the context of the wood industry in Canada. Several simulated tests are considered to verify the model. The proposed heuristic is compared with one of the other well-known, recent and state-of-the art methods. In order to guarantee a fair comparison, the Taguchi method is used to tune the parameters of the algorithms. Finally, sensitivity analyses are done to assess the efficiency of the proposed model.

Heuristics and iterated greedy algorithms for the distributed mixed no-idle flowshop with sequence-dependent setup times

The distributed permutation flowshop scheduling problem (DPFSP) has attracted a lot of attention in recent years, as current production systems frequently operate multiple factories at once. Due to the practical relevance of mixed no-idle flowshop, we address an extension of the DPFSP where there are identical factories, each one with a mixed no-idle flowshop environment. In a mixed no-idle flowshop regular machines exist side-by-side with stages that require a non-stop process. The addressed problem also takes into account sequence-dependent setup times on conventional machines. To the extent of our knowledge, this issue has not yet been examined in the literature despite it can be encountered in current manufacturing systems. For the purpose, we present a MILP formulation, a novel constructive heuristic and iterated greedy algorithms. A new construction scheme based on inter-factory and intra-factory improvement schemes is provided for the novel heuristic to further improve the solution quality given by the method. For the iterated greedy algorithm, we developed a new efficient reconstruction strategy to enhance the exploration capability of the algorithm. Furthermore, a large new benchmark was generated using a well recognized set of instances. The state-of-the-art methods and our proposed algorithms were tested in an extensive statistical and computational experiment. The analysis show that our proposals outperformed the methods from the literature.

A memetic discrete differential evolution algorithm for the distributed permutation flow shop scheduling problem

The distributed manufacturing has become a prevail production mode under the economic globalization. In this article, a memetic discrete differential evolution (MDDE) algorithm is proposed to address the distributed permutation flow shop scheduling problem (DPFSP) with the minimization of the makespan. An enhanced NEH (Nawaz–Enscore–Ham) method is presented to produce potential candidate solutions and Taillard’s acceleration method is adopted to ameliorate the operational efficiency of the MDDE. A new discrete mutation strategy is introduced to promote the search efficiency of the MDDE. Four neighborhood structures, which are based on job sequence and factory assignment adjustment mechanisms, are introduced to prevent the candidates from falling the local optimum during the search process. A neighborhood search mechanism is selected adaptively through a knowledge-based strategy which focuses on the adaptive evaluation for the neighborhood selection. The optimal combinations of parameters in the MDDE algorithm are testified by the design of experiment. The computational results and comparisons demonstrated the effectiveness of the MDDE algorithm for solving the DPFSP.

Effective constructive heuristic and iterated greedy algorithm for distributed mixed blocking permutation flow-shop scheduling problem

Distributed permutation flow-shop scheduling problem (DPFSP) has achieved much attention in recent years, which always assumes that there are infinite buffers between any consecutive machines. However, in many practical industrials, no buffers exist between some consecutive machines due to space constraint or technological requirement, which generate various types of blocking constraint. Hence, a distributed mixed permutation blocking flow-shop scheduling problem (DMBPFSP) is investigated in this paper, which considers three types of blocking constraint and without blocking. The objective is to minimize the maximum makespan among all factories. To address this problem, an improved NEH heuristic (NEH_P) is proposed, which incorporates the re-optimization of partial solutions. Afterwards, an efficient iterated greedy (EIG) algorithm is proposed. In the proposed EIG, the NEH_P heuristic is employed to generate the initial solution with high quality. A problem-specific knowledge based destruction–construction is used to explore the solution space. Three efficient local search procedures are designed to implement exploitation around the critical factory and exploitation across multi-factory. We compare the proposed methods against the closely relevant and high-performing methods in the literature. The computational results indicate that both NEH_P and EIG are very effective for addressing the considered problem.

Local search-based metaheuristics for the robust distributed permutation flowshop problem

Distributed Permutation Flowshop Scheduling Problem (DPFSP) has become a hot issue in recent years. However, DPFSP with uncertain processing times (DPFSP_UPT) has not been addressed so far although real manufacturing systems often encounter various uncertain factors which make processing times uncertain. In this paper, two local-search based metaheuristics, i.e., an Iterated Greedy algorithm (sIG) and an Iterated Local Search algorithm (sILS), are presented to solve the DPFSP_UPT with makespan criterion. A robust model of expect-risk rule is used to describe the DPFSP_UPT. A valid heuristic based on the well-known NEH heuristic is proposed to initialize sIG and sILS. An acceleration algorithm is adapted to save computational efforts. A destruction procedure with dynamic sizes is presented to enhance the exploration capability for sIG. A feature with the characteristic that small changes in the solution can preserve the properties of good solutions in the iterative process is applied by sILS. Both sIG and sILS use multiple local search methods to produce promising solutions by exploiting diverse search areas. Extensive experiments show that the proposed sIG and sILS perform significantly better than the five competing algorithms adapted in the literature, but there is no significant difference between sIG and sILS and each has its own advantages for different instances.

Dağıtılmış Permütasyon Akış Tipi Atölye Çizelgeleme Problemi için Hibrit Benders Ayrıştırma Algoritması ve Yeni Modeller

The distributed permutation flowshop scheduling problem (DPFSP) is a generalization of the regular flowshop scheduling problem where several factories are accessible for processing the jobs. In this paper, two new mathematical models are developed by deriving inspiration from the formulations developed for the multiple-traveling salesman problem (mTSP), and six different pure Benders decomposition algorithms are developed based on different mathematical model formulations. In addition, a hybrid Benders decomposition algorithm is developed through the best performed mathematical. Nine newly developed exact methods are compared in detail with each other, the best mathematical models given by Naderi and Ruiz (2010) and an automatic Benders decomposition algorithm by using the 84 problem instances available in the literature. The consequences of the experiment performed for the comparison of all existing and new exact algorithms have revealed that the proposed hybrid Benders decomposition algorithm has outperformed considerably when compared to the other methods. In this paper, 4 new best solutions are identified for the DPFSP.