Hybrid Flow Shop Scheduling Research Articles

Multi-objective energy-efficient hybrid flow shop scheduling using Q-learning and GVNS driven NSGA-II

The urgent mission for carbon peak and carbon neutrality is demanding greater industrial sustainability. Energy-efficient hybrid flow shop scheduling problem (EEHFSP) has been raising increasing attention in recent years. This paper studies a new EEHFSP with uniform machines to minimize total tardiness, total energy cost, and carbon trading cost. Time-of-use tariffs and power down strategies are simultaneously adopted. A novel multi-objective mixed-integer nonlinear programming model for the problem is proposed. To solve the model, we propose a Q-learning and general variable neighborhood search (GVNS) driven non-dominated sorting genetic algorithm II (QVNS-NSGA-II). The novelty of the algorithm is that we incorporate Q-learning into GVNS to guide premium adaptive operator selection throughout the shaking and local search processes. A distinguishing feature is that the states and actions of Q-learning are set as neighborhood structures and local search operators. The Q-learning-driven GVNS is embedded into NSGA-II to promote the exploration and exploitation capability. Experimental results show that the proposed QVNS-NSGA-II outperforms NSGA-II, improved Jaya, and modified MOEA/D in terms of the quantity, quality of Pareto solutions, and computational efficiency. Sensitivity analysis also derives several managerial implications. The proposed approach can be applied to improve sustainability and productivity for hybrid flow shop manufacturers.

Improved MOEA/D with local search for solving multi-stage distributed reentrant hybrid flow shop scheduling problem

Steel tubes are known as “the vessels of industry” and widely used in oil exploration, drilling, aerospace and other fields. This study focuses on cold-drawn seamless steel tubes, aiming to reduce the high logistics cost and improve the low efficiency in production. This study models three stages of heat treatment, cold drawing, and finishing as a multi-stage distributed reentrant hybrid flow shop scheduling problem (MSDRHFSP). First, a multi-objective optimization model is established to minimize makespan and transferring cost. Second, an improved multi-objective evolutionary algorithm based on decomposition with local search (IMOEA/D-LS) is proposed. The balanced decoding method according to the similarity degree of the jobs (BDMASDJ) is developed to trade off the two objectives. Crossover and mutation operators suitable for MSDRHFSP are designed, and a local search operator is performed. Finally, comprehensive experiments are conducted and the results show that IMOEA/D-LS can solve the MSDRHFSP effectively.

Q-learning driven multi-population memetic algorithm for distributed three-stage assembly hybrid flow shop scheduling with flexible preventive maintenance

The distributed assembly flow shop scheduling (DAFS) problem has received much attention in the last decade, and a variety of metaheuristic algorithms have been developed to achieve the high-quality solution. However, there are still some limitations. On the one hand, these studies usually ignore the machine deterioration, maintenance, transportation as well as the flexibility of flow shops. On the other hand, metaheuristic algorithms are prone to fall into local optimality and are unstable in solving complex combinatorial optimization problems. Therefore, a multi-population memetic algorithm (MPMA) with Q-learning (MPMA-QL) is developed to address a distributed assembly hybrid flow shop scheduling problem with flexible preventive maintenance (DAHFSP-FPM). Specifically, a mixed integer linear programming (MILP) model targeted at the minimal makespan is first established, followed by an effective flexible maintenance strategy to simplify the model. To efficiently solve the model, MPMA is developed and Q-learning is used to achieve an adaptive individual assignment for each subpopulation to improve the performance of MPMA. Finally, two state-of-the-art metaheuristics and their Q-learning-based improvements are selected as rivals of the developed MPMA and MPMA-QL. A series of numerical studies are carried out along with a real-life case of a furniture manufacturing company, to demonstrate that MPMA-QL can provide better solutions on the studied DAHFSP-FPM..

A scheduling mechanism for hybrid flow shops with reworks under general queue time limits

This study addresses multi-stage hybrid flow shop scheduling in which a job is reworked if the queue time between two arbitrary stages exceeds an upper limit. The problem is to determine the allocations of jobs to machines at each stage and the start times of jobs and rework setups/operations when incurred. A mixed integer programming model is proposed for each of the makespan and the total tardiness measures. Then, because the problem is NP-hard, a scheduling mechanism is proposed that consists of three phases: (a) filtering the jobs to be delayed; (b) searching the jobs to be reworked; and (c) dispatching non-delayed and delayed jobs sequentially. Simulation results show that the mechanism proposed in this study outperforms the conventional dispatching approach in the high rework setup time case for the makespan problem and low/high setup time cases for the tardiness problem. The best priority rules of the mechanism under each of the measures are also reported.

Solving a new bi-objective mathematical model for a hybrid flow shop scheduling problem with robots and fuzzy maintenance time

This paper presents a bi-objective mathematical model of a hybrid flow shop scheduling problem (HFSSP) with robots and fuzzy maintenance time. The proposed model minimizes the mean completion time of jobs and the total cost of the processes based on maintenance costs and incurred transportation costs via robots. A fuzzy chance-constrained programming (FCCP) model is used to present its deterministic-equivalent problem. It is then solved by two multi-objective decision-making approaches, namely LP-metric and goal attainment (GA). A sensitivity analysis of the weights of the objective functions is conducted and the behavior of the model is studied for each instance. Also, a TOPSIS (the technique for order of preference by similarity to ideal solution) method is used to rank the efficiency of the proposed solution approaches. Future research areas are also suggested.

A Variant Iterated Greedy Algorithm Integrating Multiple Decoding Rules for Hybrid Blocking Flow Shop Scheduling Problem

This paper studies the hybrid flow shop scheduling problem with blocking constraints (BHFSP). To better understand the BHFSP, we will construct its mixed integer linear programming (MILP) model and use the Gurobi solver to demonstrate its correctness. Since the BHFSP exists parallel machines in some processing stages, different decoding strategies can obtain different makespan values for a given job sequence and multiple decoding strategies can assist the algorithm to find the optimal value. In view of this, we propose a hybrid decoding strategy that combines both forward decoding and backward decoding to select the minimal objective function value. In addition, a hybrid decoding-assisted variant iterated greedy (VIG) algorithm to solve the above MILP model. The main novelties of VIG are a new reconstruction mechanism based on the hybrid decoding strategy and a swap-based local reinforcement strategy, which can enrich the diversity of solutions and explore local neighborhoods more deeply. This evaluation is conducted against the VIG and six state-of-the-art algorithms from the literature. The 100 tests showed that the average makespan and the relative percentage increase (RPI) values of VIG are 1.00% and 89.6% better than the six comparison algorithms on average, respectively. Therefore, VIG is more suitable to solve the studied BHFSP.

A summary of algorithm research on hybrid flow-shop scheduling problem

The hybrid flow shop scheduling problem is a flow shop scheduling problem that combines the two scheduling characteristics of the classical flow shop and the parallel machine. It is also one of the research hotspots in the field of shop scheduling. In this paper, the algorithm for solving the problem is reviewed, and the research status of the related expansion problems of the mixed flow workshop is summarized. Finally, combined with the development trend, the existing problems in the current research are analyzed, possible solutions are proposed, and the application of the algorithm for solving the problem of mixed flow shop scheduling in new fields in the future is discussed.

Hybrid Flow-Shop Scheduling Problems with Missing and Re-Entrant Operations Considering Process Scheduling and Production of Energy Consumption

A hybrid flow shop scheduling model with missing and re-entrant operations was designed to minimize the maximum completion time and the reduction in energy consumption. The proposed dual-population genetic algorithm was enhanced with a range of improvements, which include the design of a three-layer gene coding method, hierarchical crossover and mutation techniques, and the development of an adaptive operator that considered gene similarity and chromosome fitness values. The optimal and worst individuals were exchanged between the two subpopulations to improve the exploration ability of the algorithm. An orthogonal experiment was performed to obtain the optimal horizontal parameter set of the algorithm. Furthermore, an experiment was conducted to compare the proposed algorithm with a basic genetic algorithm, particle swarm optimization algorithm, and ant colony optimization, which were all performed on the same scale. The experimental results show that the fitness value of the proposed algorithm is above 15% stronger than the other 4 algorithms on a small scale, and was more than 10% stronger than the other 4 algorithms on a medium and large scale. Under the condition close to the actual scale, the results of ten repeated calculations showed that the proposed algorithm had higher robustness.

A systematic literature review on energy-efficient hybrid flow shop scheduling

A systematic literature review on energy-efficient hybrid flow shop scheduling

Integrating sustainability into production scheduling in hybrid flow-shop environments.

Global energy consumption is projected to grow by nearly 50% as of 2018, reaching a peak of 910.7 quadrillion BTU in 2050. The industrial sector accounts for the largest share of the energy consumed, making energy awareness on the shop floors imperative for promoting industrial sustainable development. Considering a growing awareness of the importance of sustainability, production planning and control require the incorporation of time-of-use electricity pricing models into scheduling problems for well-informed energy-saving decisions. Besides, modern manufacturing emphasizes the role of human factorsin production processes. This study proposes a new approach for optimizing the hybrid flow-shop scheduling problems (HFSP) considering time-of-use electricity pricing, workers' flexibility, and sequence-dependent setup time (SDST). Novelties of this study are twofold: to extend a new mathematical formulation and to develop an improved multi-objective optimization algorithm. Extensive numerical experiments are conducted to evaluate the performance of the developed solution method, the adjusted multi-objective genetic algorithm (AMOGA), comparing it with the state-of-the-art, i.e., strength Pareto evolutionary algorithm (SPEA2), and Pareto envelop-based selection algorithm (PESA2). It is shown that AMOGA performs better than the benchmarks considering the mean ideal distance, inverted generational distance, diversification, and quality metrics, providing more versatile and better solutions for production and energy efficiency.

Agent-based simulation and optimization of hybrid flow shop considering multi-skilled workers and fatigue factors

In the past few decades, more and more studies have begun to consider the impact of human factors on manufacturing systems. This paper studies a hybrid flow shop scheduling problem considering multi-skilled workers and fatigue factors. An agent-based simulation system is established to cope with the uncertainties in the worker fatigue model. Furthermore, this paper proposes a novel simulation-based optimization (SBO) framework, which combines genetic algorithm (GA) and reinforcement learning (RL) to address the hybrid flow shop scheduling problem. Numerical experiments are conducted on several instances with different production configurations. In particular, a pharmaceutical production facility is modeled as a hybrid flow shop to demonstrate the feasibility and effectiveness of the proposed SBO method.

A Dual-Population Genetic Algorithm with Q-Learning for Multi-Objective Distributed Hybrid Flow Shop Scheduling Problem

In real-world production processes, the same enterprise often has multiple factories or one factory has multiple production lines, and multiple objectives need to be considered in the production process. A dual-population genetic algorithm with Q-learning is proposed to minimize the maximum completion time and the number of tardy jobs for distributed hybrid flow shop scheduling problems, which have some symmetries in machines. Multiple crossover and mutation operators are proposed, and only one search strategy combination, including one crossover operator and one mutation operator, is selected in each iteration. A population assessment method is provided to evaluate the evolutionary state of the population at the initial state and after each iteration. Two populations adopt different search strategies, in which the best search strategy is selected for the first population and the search strategy of the second population is selected under the guidance of Q-learning. Experimental results show that the dual-population genetic algorithm with Q-learning is competitive for solving multi-objective distributed hybrid flow shop scheduling problems.

Multi-Objective Hybrid Flow-Shop Scheduling in Parallel Sequential Mode While Considering Handling Time and Setup Time

Hybrid flow-shop scheduling based on the parallel sequential movement mode (HFSP-PSMM) is an extended application of hybrid flow-shop scheduling that ensures that the equipment works continuously during the processing cycle. However, current research has only investigated the flow-shop scheduling of single-equipment processing, and ignores the effect of auxiliary time. Therefore, this paper investigates a multi-equipment hybrid flow-shop scheduling problem based on the parallel sequential movement mode and considers the setup time and handling time. The mathematical model of the HFSP-PSMM was developed with the handling and makespan numbers as the optimization objectives. The NSGA-II-V based on the NSGA-II was designed by combining the problem characteristics. New crossover, mutation, and selection strategies were proposed and variable neighborhood search operations were implemented for the optimal set of Pareto solutions. Finally, through an algorithm comparison, performance testing, and an example simulation, the effectiveness of the NSGA-II-V for solving the HFSP-PSMM was verified.

An improved multi-population genetic algorithm with a greedy job insertion inter-factory neighborhood structure for distributed heterogeneous hybrid flow shop scheduling problem

Distributed heterogeneous hybrid flow shop scheduling problem (DHHFSP) is an extension of the classical hybrid flow shop scheduling problem (HFSP), which is an NP-hard problem. In the context of economic globalization, DHHFSP considers the collaboration and heterogeneity among multiple factories. The neighborhood structure plays an important role in continuously improving the current individuals for DHHFSP. The existing work has fully studied the inner-factory neighborhood structure, but the research on the inter-factory neighborhood structure is still immature. A greedy job insertion inter-factory neighborhood structure and a new move evaluation method are designed to ensure the efficiency of neighborhood movement. And an improved multi-population genetic algorithm (IMPGA) is proposed to solve the DHHFSP with makespan. To enhance the convergence speed and robustness of the IMPGA, a guided sub-populations information interaction and a re-initialization procedure with an individual resurrection strategy are designed respectively. In computational experiments, there are 480 instances (including the same proportion of small, medium, and large-scale problems) randomly generated. The proposed IMPGA obtains the best solutions for 457 instances. The analysis of experimental results shows that IMPGA significantly outperforms the reported state-of-the-art algorithms for DHHFSP. Finally, the proposed method is used to solve a polyester film manufacturing company case effectively.

A Heuristic-Based Adaptive Iterated Greedy Algorithm for Lot-Streaming Hybrid Flow Shop Scheduling Problem with Consistent and Intermingled Sub-Lots

Owing to the different quantities and processing times of sub-lots, intermingling sub-lots with each other, instead of fixing the production sequence of sub-lots of a lot as in the existing studies, is a more practical approach to lot-streaming flow shops. Hence, a lot-streaming hybrid flow shop scheduling problem with consistent and intermingled sub-lots (LHFSP-CIS) was studied. A mixed integer linear programming (MILP) model was established, and a heuristic-based adaptive iterated greedy algorithm (HAIG) with three modifications was designed to solve the problem. Specifically, a two-layer encoding method was proposed to decouple the sub-lot-based connection. Two heuristics were embedded in the decoding process to reduce the manufacturing cycle. Based on this, a heuristic-based initialization is proposed to improve the performance of the initial solution; an adaptive local search with four specific neighborhoods and an adaptive strategy has been structured to improve the exploration and exploitation ability. Besides, an acceptance criterion of inferior solutions has been improved to promote global optimization ability. The experiment and the non-parametric Kruskal-Wallis test (p = 0) showed the significant advantages of HAIG in effectiveness and robustness compared with five state-of-the-art algorithms. An industrial case study verifies that intermingling sub-lots is an effective technique to enhance the utilization ratio of machines and shorten the manufacturing cycle.

A hybridization of PSO and VNS to solve the machinery allocation and scheduling problem under a machinery sharing arrangement

This paper presents the hybrid Particle Swarm Optimization and the Variable Neighborhood Search (PSO-VNS) to solve the machinery and equipment allocation and scheduling to help the growers expand the production level to meet the increased demands and growing interest, and to increase profitability. This problem can be formulated as the Machinery and Equipment Allocation and Scheduling Problem (MEASP) which is special type of a hybrid flow shop scheduling problem (HFS) with sequence dependent setup times, machine eligibility, machine grouping, blocking, tooling constraint, and time windows (HFS |SDST, rcrc, Grouping, blocking, Tool, Tw | Cmax). The objective of this research is to minimize the total completion time for sugarcane cultivation. A Mixed Integer Linear Programming (MILP) model was developed to handle small-scale problems. The hybrid Particle Swarm Optimization and the Variable Neighborhood Search (PSO-VNS) was used for large-scale problems. Two new velocity update formulae and a position update formula were incorporated into the Particle Swarm Optimization (PSO), and four types of neighborhood strategies were developed for the VNS. The experimental results show that all the PSO-VNS methods outperform the traditional PSO due to the effectiveness of the newly proposed velocity and position update formulae in finding the optimal solutions, the PSO-VNS-6 methods, on the average, can reduce the computational time by 58.43% from the original PSO and improve the solution quality by 11.71%.

A Multiobjective Optimization Approach for Multiobjective Hybrid Flowshop Green Scheduling with Consistent Sublots

Hybrid flowshop scheduling problems are encountered in many real-world manufacturing scenarios. With increasingly fierce market competition, the production mode of multiple varieties and small batches has gradually been accepted by enterprises, where the technology of lot streaming is widely used. Meanwhile, green criteria, such as energy consumption and carbon emissions, have attracted increasing attention to improving protection awareness. With these motivations, this paper studies a multiobjective hybrid flowshop green scheduling problem with consistent sublots (MOHFGSP_CS), aiming to minimize two objectives, i.e., makespan and total energy consumption, simultaneously. To solve this complex problem, we first formulate a novel multiobjective optimization model. However, due to the NP-hard nature of the problem, the model is computationally prohibitive as the problem scale increases. Thus, a multiobjective discrete artificial bee colony algorithm (MDABC) based on decomposition is proposed. There are three phases in this algorithm: the VND-based employed bee phase, the adjustment weight onlooker bee phase, and the population interaction scout bee phase. In the experimental study, various small-scale and large-scale instances are collected to verify the effectiveness of the multiobjective optimization model and the MDABC. Comprehensive computational comparisons and statistical analysis show that the developed strategies and MDABC show superior performance.

Toward automated algorithm configuration for distributed hybrid flow shop scheduling with multiprocessor tasks

Due to the large volume of requests and the need to speed up the provision of services, production companies are migrating from a single service center to distributed centers. To support this migration, it is necessary to make intelligence decisions that benefit from automatic design of search algorithms. Considering these, this paper addresses the distributed hybrid flow shop scheduling problem with multiprocessor tasks (DHFSP-MT) as an extension of the hybrid flow shop scheduling problem with multiprocessor tasks (HFSP-MT) to minimize the maximum completion time among distributed factories. To provide effective decision support, we apply a novel framework called conditional markov chain search (CMCS) to automate the generation of heuristics, which is presented for the first time in the distributed shop scheduling problem to the best of our knowledge. We express the HFSP-MT as a markov decision process (MDP) and solve it through a hybrid Q-learning-local search algorithm. By using the characteristics of the problem under study, we introduce two new concepts, weight and impact, which are used to develop an initial construction algorithm and two local search methods. To balance jobs between factories at runtime, we propose a load balancing method, which transfers selected jobs from certain source factories to destination factories. We compare the proposed CMCS with two state-of-the-art metaheuristic algorithms from the literature using publicly available benchmark instances. The computational results show that the proposed CMCS provides better performance than that of the existing algorithms on solving the considered DHFSP-MT.

A multi-class teaching–learning-based optimization for multi-objective distributed hybrid flow shop scheduling

Distributed hybrid flow shop scheduling problem (DHFSP) has attracted some attention. In this study, DHFSP with sequence-dependent setup times is studied and a multi-class teaching–learning-based optimization (MTLBO) is proposed to minimize makespan and maximum tardiness simultaneously. A two-string representation is adopted. s classes are formed to improve search efficiency by implementing reward and punishment mechanism among them. Class evaluation is introduced and two teacher phases and one learner phase are applied in the evolution of each class. Elimination process acts on the worst class to avoid the waste of computing resource. A number of experiments are conducted and the computational results demonstrate that MTLBO is a very competitive method for DHFSP.

Environmentally friendly strategy for hybrid flow shop scheduling with the unrelated parallel machines

With the increasing environmental pressure, reducing the environmental impact on hybrid flow shops (HFS) has attracted extensive attention because of its broad industrial applications. The selection of machines in the implementation of HFS is a complex decision-making process that hinders the optimization efficiency in shops. However, this issue has not been addressed thoroughly. In light of this, a multi-objective mathematical model is formulated for the minimization of makespan and energy consumption of the hybrid flow shop scheduling problem (HFSP). The environmental performance of machines is calculated by the proposed evaluation index and is ranked on the basis of the integrated entropy and fuzzy technique for order performance by similarity to ideal solution method. Moreover, to solve the multi-objective model of HFSP, an improved differential evolution algorithm with a heuristic active decoding rule that incorporates the ranking of environmental performance of machines into the iterative process of the algorithm is presented. Finally, a case study is presented to evaluate the effectiveness of the proposed method and to prove the feasibility of the ranking-based differential evolution algorithm (RBDE). The result shows that the proposed RBDE outperforms RBNSGA-II and RBPSO in searching for non-dominated solutions that can solve the environmental production of HFSP effectively.