Hybrid Flow Shop Scheduling Problem Research Articles

An efficient Q-learning integrated multi-objective hyper-heuristic approach for hybrid flow shop scheduling problems with lot streaming

Efficient scheduling in flow shop environments with lot streaming remains a critical challenge in various industrial settings, necessitating innovative approaches to optimize production processes. This study investigates a hybrid flow shop scheduling problem dominant in real-world printed circuit board assembly shops. A novel multi-objective hyper-heuristic combining Q-learning, i.e., two-stage improved spider monkey optimization (TS-ISMO), is tailored to address the complexities of the flow shop scheduling problems. The proposed method aims to simultaneously optimize conflicting objectives such as minimizing makespan, total energy consumption, and total tardiness time while incorporating lot streaming considerations. For multi-objective hyper-heuristic techniques, the algorithm dynamically selects and adapts a diverse set of low-level heuristics to explore the solution space comprehensively and strike a balance among competing objectives. The proposed TS-ISMO algorithm incorporates several significant features aimed at enhancing its performance. These features encompass hybrid heuristics for solution initialization, a contribution value method for comprehensive convergence and diversity assessment, diverse evolutionary state judgments to promote the algorithm’s balance between exploration and exploitation capabilities, and a Q-learning strategy for self-adaptive parameter tuning. The integration of Q-learning facilitates intelligent parameter control, enabling the algorithm to autonomously adjust its behavior based on past experiences and evolution dynamics. This adaptive mechanism enhances convergence speed and solution quality by effectively guiding the search process toward promising regions of the solution space. Extensive computational experiments are conducted on benchmark instances of hybrid flow shop scheduling problems with lot streaming to evaluate the performance of the proposed algorithm. Comparative analyses against state-of-the-art approaches demonstrate its superior solution quality and computational efficiency.

An Enhanced Algorithm for Hybrid Flow Shop Scheduling Using Discrete Sparrow Optimization and Rough Set Theory

Aiming at the shortcomings of the sparrow search algorithm, such as it is easy to fall into local optimum and unable to solve discrete optimization problems, an improved discrete sparrow search algorithm is proposed. Firstly, the position update formula of the original sparrow search algorithm is abstracted, a new discrete heuristic position update strategy is designed according to the different identities of individuals, and the encoding and decoding methods are designed for the hybrid flow shop scheduling problem; Secondly, the rough data-deduction theory is introduced, and the feasibility and rationality of the above theory are explained by mathematical proofs, which provides theoretical support for the algorithm and improves the interpretability; Then, the nature of upper approximation is adopted to expand the search space, improve the population diversity, avoid prematurity of the algorithm, combine division and rough data-deduction to propose three strategies to promote information sharing among populations, regulate the exploitation ability and exploration ability of populations, and reduce the probability of the algorithm falling into local optimum; Finally, the improved discrete sparrow search algorithm is used to solve the hybrid flow shop scheduling problem. Simulation experiments are carried out on three small-scale practical examples and Liao's classic test set to verify the feasibility of the improved discrete sparrow search algorithm to solve the hybrid flow shop scheduling problem, and to prove the superiority of the proposed algorithm and the effectiveness of the improved strategy through comparison experiments with other algorithms.

Algorithm for solving multi-objective hybrid flow shop scheduling problem

Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem, a multi-objective mathematical model is established with the goal of minimizing the maximum completion time, total machine energy consumption and machine processing cost. An improved multi-objective evolution algorithm based on decomposition (IMOEAD) is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. Normal distribution crossover and adaptive Gaussian mutation are used to improve the global and local search capabilities of the algorithm. Individuals are selected in the neighborhood of the weight vector to generate new solutions. The non-dominated rank and crowding distance are used to update the external archive. The inverse generation distance, generation distance and number of non-dominated solutions are used as performance indicators. Through a large number of case simulations, the algorithm is compared with the non-dominated sorting genetic algorithm II and the multi-objective evolution algorithm based on decomposition. The results verify the effectiveness of the algorithm.

A bi-population cooperative scatter search algorithm for distributed hybrid flow shop scheduling with machine breakdown

The occurrence of machine breakdowns is a frequent and dynamic phenomenon in the production process. The implementation of effective preventive measures can mitigate such events and result in reduced production costs. This paper investigates the distributed hybrid flow shop scheduling problem with machine breakdown (DHFSSPB) considering short maintenance time. The bi-population cooperative scatter search (BCSS) algorithm is proposed to address the DHFSSPB, wherein the search for the optimal scheduling sequence is transformed into genetic evolution aiming to obtain a gene chain with both minimum lower bound and minimum cost attributes. Firstly, the DHFSSPB problem is modeled through a combination of predictive maintenance strategy and right-shift rescheduling rule. Subsequently, a diversification approach is developed to facilitate attribute inheritance, enhance the efficiency of job allocation, and establish a reference set. The reference set is partitioned into two subpopulations based on lower bound attributes and cost attributes, respectively. The corresponding hybrid search strategies are designed to enhance the efficiency of job sorting and machine selection for subpopulations with distinct attributes. The cooperative evolution between subpopulations occurs through the competitive interaction and fusion of individuals. An enhanced reinforcement learning approach is proposed to expedite the acceleration of individual attribute evolution by leveraging evolutionary knowledge acquired from populations, thereby effectively guiding the evolutionary trajectories of individuals. Additionally, a method for evaluating the population during the learning process is developed based on problem characteristics to enhance learning efficiency. Experimental results demonstrate that BCSS outperforms the comparative algorithm in solving the DHFSSPB.

A heuristic method for multi-objective hybrid flow shop scheduling problem with parent-child relationships and space constraints

ABSTRACT In modern ship manufacturing, a ship is divided into hundreds of blocks in the design stage, and the productivity of the block manufacturing process is vital to ship delivery. This paper investigates the production scheduling problem of ship blocks with the parent-child relationship; this relationship is characterised by the fact that sibling jobs at the same BOM layer must be processed on adjacent machines at their assembly stages. We formulate this problem as a multi-objective hybrid flow shop scheduling problem: the first objective is to minimise the total deviation from the target time of the jobs and the second one is to minimise the total processing time. To solve this problem, we propose a heuristic method based on the multi-objective genetic algorithm, in which an adjacent machine priority method is first proposed to generate feasible solutions that satisfy the space constraints. Then, we improve the individual quality in crossover and mutation of the algorithm via tabu search. We verify the performance of our algorithm by test instances generated from real manufacturing data of a shipbuilding company. Results show that the proposed method outperforms the existing algorithms when identifying the Pareto optimal solutions, especially for large-sized problems.

Two-stage learning scatter search algorithm for the distributed hybrid flow shop scheduling problem with machine breakdown

The distributed hybrid flow shop scheduling problem with machine breakdown is investigated to reduce the negative impact on real production caused by machine breakdown events. (DHFSPMB). DHFSPMB comprises two subproblems: the maintenance problem with machine breakdown and the distributed hybrid flow shop scheduling problem (DHFSP). A rescheduling method is designed to address the maintenance problem. Subsequently, a two-stage learning scatter search (TLSS) algorithm is proposed for optimizing the DHFSP when the machines break down. Firstly, a mixed integer programming model for DHFSPMB is constructed. Secondly, TLSS employs an improved reinforcement learning approach to enhance the capability of exploration by guiding the direction of global search. A two-stage approach is designed to address the lack of knowledge in the early periods of learning. Finally, a hybrid search strategy is devised to enhance the development capability of TLSS. The experimental results demonstrate that the TLSS algorithm outperforms the comparison algorithms in effectively addressing the DHFSPMB.

A multi-objective Immune Balancing Algorithm for Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling

Driven by economic globalization, global supply chain collaboration has gained significant importance, fostering the emergence of distributed manufacturing. This paper addresses the Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling (DHBIAHFS) problem within the pharmaceutical industry. Jobs are allocated to factories for processing, batched within defined lot sizes for transportation, and subsequently assembled into products to minimize the maximum completion time and tardy product count. Effective lot sizing during transport is emphasized between factories and assembly machines. Drawing inspiration from the biological immune system’s balancing mechanisms, we propose a Multi-objective Immune Balancing Algorithm (MOIBA) equipped with learning and repairing mechanisms. Each solution is structured with three nested sequences, and composite heuristic evaluations are employed to generate high-quality initial solutions. The performance of each solution is assessed based on both fitness and diversity metrics. Customized crossover and mutation operators are introduced with dynamically adjusted probabilities reflective of immune response dynamics. Quantitative analysis validates our mathematical model and the distinct components of MOIBA. We compare MOIBA’s efficiency against six other effective multi-objective strategies using three performance metrics. Stability and robustness assessments, conducted through variance examination and statistical testing, offer insights into MOIBA’s consistency and reliability across diverse problem instances.

Combining meta-heuristics and Q-learning for scheduling lot-streaming hybrid flow shops with consistent sublots

This study addresses a hybrid flow shop scheduling problem by considering consistent sublots (HFSP_CS) in lot-streaming. The objective is to minimize the maximum completion time (makespan). By mathematically formulating the HFSP_CS, a mathematical model is established. Next, novel combinations of four meta-heuristics and Q-learning-based improvement tactics are proposed for tackling the related problems for the first time. Drawing upon problem-specific characteristics, five local search operators are employed and selected appropriately by utilizing Q-learning throughout the iterations. Furthermore, the model's veracity is demonstrated through the utilization of the CPLEX solver. Then, by resolving 128 instances, the enhanced algorithms showcase their effectiveness. The results show that the artificial bee colony algorithm integrated with Q-learning is the most competitive algorithm among the tested algorithms.

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.

A multi-objective dynamical artificial bee colony for energy-efficient fuzzy hybrid flow shop scheduling with batch processing machines

Energy-efficient hybrid flow shop scheduling problem (EHFSP) with batch processing machines (BPMs) is rarely considered, let alone EHFSP with BPMs and uncertainty. In this study, an energy-efficient fuzzy hybrid flow shop scheduling problem (EFHFSP) with BPMs at a middle stage and no precedence between some stages is solved, and a multi-objective dynamical artificial bee colony algorithm (MODABC) is presented to simultaneously minimize fuzzy makespan and total fuzzy energy consumption. To produce high quality solutions, a swarm decision is used to dynamically determine the employed bee swarm and onlooker bee swarm, a dynamical employed bee phase is implemented, and an onlooker bee phase with adaptive communication is given. The diversity reinforcement strategy and an adaptive scout phase are also adopted. Extensive experiments are conducted, and the optimal combination of key parameters for the proposed algorithm is determined by the Taguchi method. The computational results demonstrate that the new strategies of MODABC are effective, and MODABC is very competitive in solving the considered EFHFSP.

Multi-stage hybrid flow shop scheduling problem with lag, unloading, and transportation times

Multi-stage hybrid flow shop scheduling problem with lag, unloading, and transportation times

Tri-objective lot-streaming scheduling optimization for hybrid flow shops with uncertainties in machine breakdowns and job arrivals using an enhanced genetic programming hyper-heuristic

Lot-streaming scheduling has been widely recognized as a means to improve shop productivity, but there is few research on lot-streaming scheduling problems under dynamic disturbances. To fill the gap, lot-streaming scheduling optimization approach for hybrid flow shops with uncertainties in machine breakdowns and job arrivals is proposed. A mathematical model is formulated with objectives of minimizing maximum tardiness, total idle energy consumption of the machine, and maximum makespan. Since the Genetic Programming Hyper Heuristic algorithm has better results in solving dynamic scheduling problems, a Collaborative Harmony Search-based Genetic Programming Hyper Heuristic (CHS-GPHH) is presented to solve the dynamic lot-streaming hybrid flow shop scheduling problem (DLS-HFSSP) with the two dynamic events occurring simultaneously. In the improved algorithm, a neighborhood structure based on harmony search is developed for lot splitting. To verify the effectiveness of the proposed approach, the various comparative studies c are conducted on the lot-streaming dynamic hybrid flow shop scheduling. The results demonstrate the effectiveness of each improvement component of the CHS-GPHH, and verify that CHS-GPHH is an effective approach to deal with DLS-HFSSP with the in all the scenarios.

Co-Evolutionary Algorithm for Two-Stage Hybrid Flow Shop Scheduling Problem with Suspension Shifts

Demand fluctuates in actual production. When manufacturers face demand under their maximum capacity, suspension shifts are crucial for cost reduction and on-time delivery. In this case, suspension shifts are needed to minimize idle time and prevent inventory buildup. Thus, it is essential to integrate suspension shifts with scheduling under an uncertain production environment. This paper addresses the two-stage hybrid flow shop scheduling problem (THFSP) with suspension shifts under uncertain processing times, aiming to minimize the weighted sum of earliness and tardiness. We develop a stochastic integer programming model and validate it using the Gurobi solver. Additionally, we propose a dual-space co-evolutionary biased random key genetic algorithm (DCE-BRKGA) with parallel evolution of solutions and scenarios. Considering decision-makers’ risk preferences, we use both average and pessimistic criteria for fitness evaluation, generating two types of solutions and scenario populations. Testing with 28 datasets, we use the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) to quantify benefits. Compared to the average scenario, the VSS shows that the proposed algorithm achieves additional value gains of 0.9% to 69.9%. Furthermore, the EVPI indicates that after eliminating uncertainty, the algorithm yields potential improvements of 2.4% to 20.3%. These findings indicate that DCE-BRKGA effectively supports varying decision-making risk preferences, providing robust solutions even without known processing time distributions.

Theoretical analysis and implementation of mandatory operations-based accelerated search in graph space for hybrid flow shop scheduling

For the hybrid flow shop scheduling problem (HFSP), this study addresses its high computational burden associated with insertion operations due to over-much objective function calculations as the number of jobs increases. Unfortunately, the search solution space and existing accelerated local search methods exhibit limitations. We find that there are many operations on the critical path that do not affect the completion time, especially when there are multiple critical paths. However, deleting mandatory operations must make the original makespan value smaller. Moreover, only specific insertion positions have the potential to decrease the makespan of the changed sequence. In view of this, we emphasize the need for improved accelerated local search techniques tailored to overcome these limitations, and propose the theoretical analysis and methods of an accelerated local search based on effective insertion of mandatory operations in the graph for the HFSP with makespan criterion. More specifically, first, we represent a solution using a solution graph, and introduce four definitions related to mandatory operations in the graph space. Second, we propose five theorems and their corresponding proofs. Third, we present a mandatory operations-based accelerated iterated greedy algorithm (MOAIG) in the graph space according to the above theorems. Finally, we conduct many experiments on two well-known benchmarks (a total of 576 instances). Through statistical analysis, it becomes evident that the computational time required for calculating the makespan associated with operations-based insertion has decreased significantly. The development of the mandatory operations-based effective insertion accelerated local search is a promising approach to significantly mitigate the time complexity by reducing the numbers of operations perturbed and insertion positions involved in the calculation, and makes up for gaps in existing accelerated insertion methods for HFSP.

Distributed assembly shop scheduling problem for complex products considering multiskilled worker assignment and transportation time

The distributed assembly hybrid flow shop scheduling problem (DAHFSP) is a type of distributed shop scheduling problem, and each distributed shop can be regarded as a hybrid flow shop. In distributed assembly processes for complex products such as satellites and missiles, transportation time and worker assignment have important effects on production scheduling. Based on real production situations, this study proposes a novel DAHFSP considering worker assignment and transportation time, aiming to minimise the makespan and the imbalance degree of worker workloads. First, to solve these problems, we construct a mathematical model and design a two-layer chromosome coding scheme including worker assignment and task sequence. Then, in the local search stage, we propose a mutation-based search method and an elite search method. On that basis, we propose a multi-objective evolutionary algorithm with reinforced elite retention strategy (MOEA-RERS). Finally, based on a set of 12 test instances generated by actual enterprise production data, we compare the MOEA-RERS algorithm with five multi-objective evolutionary algorithms. The results show that the MOEA-RERS algorithm is superior to other algorithms in terms of solution quality and distribution.

Minimising makespan in distributed assembly hybrid flowshop scheduling problems

To enhance the manufacturing flexibility, resilience, and production efficiency, the integration of scheduling for distributed manufacturing with assembly systems has become a pivotal driver of production planning evolution. In this research endeavour, we present a Mixed-Integer Linear Programming model and an innovative Iterated Epsilon-Greedy Reinforcement Learning algorithm to address the distributed assembly hybrid flowshop scheduling problem. Empirical validation, conducted through computational experiments on a benchmark problem set, is used to gain important managerial insights. The computational results demonstrate that the proposed algorithms significantly reduce the makespan for the addressed problem. This study has the potential to make valuable contributions to ongoing research endeavours within the realm of multi-stage shop scheduling, an area that continues to warrant progressive advancement.

A metaheuristic algorithmic framework for solving the hybrid flow shop scheduling problem with unrelated parallel machines

The hybrid flow shop scheduling problem (HFSP), as a realistic extension of the classical flow shop scheduling problem, widely exists in real-world industrial production systems. In practice, the fact that machines are unrelated is important and cannot be neglected. This study focuses on the HFSP with unrelated parallel machines (HFSP-UPM) to minimize the makespan. To address this problem, a hybrid representation that combines single-sequence coding and full-sequence coding is developed to search for solution space that is not covered by common encoding methods. An initialization block integrating random heuristic strategies is proposed for improving the quality of the initial sparrow swarm. To improve the diversity of a sparrow swarm further, a perturbation block embedded with a set of historical best positions and an enhancement strategy are developed. A critical set based local search block is designed for high-intensity local exploitation of promising regions when necessary. Several benchmark cases from the literature as well as some randomly generated instances characterized by the distribution of real data from factory studies are employed to participate in the test. The test results reveal the effectiveness of the proposed perturbation block and local search block. Compared to state-of-the-art metaheuristic algorithms, the enhanced sparrow search algorithm (ESSA) demonstrates higher convergence accuracy when handling instances. The value of the gap between a solution found by the ESSA and a feasible solution found by the mixed-integer programming (MIP) model can reach 0.6%.

An improved co-evolutionary memetic algorithm based on novel schedule type and unconditional feasibility for hybrid flow-shop scheduling problem

The hybrid flow-shop scheduling problem (HFSP) is used in a wide range of industries and is very hard to solve. There has been a great deal of research on HFSP with the objective of makespan, but related research mainly focused on the algorithmic level, ignoring characters of HFSP. In this paper, through the study of the characters of HFSP itself, together with the design of the algorithm, new records on benchmarks are obtained. Firstly, the property of unconditional feasibility of HFSP (UFH) is formally proven. Based on UFH, the disjunctive-graph-based encoding scheme is considered convenient and accurate to HFSP, and the constraints for feasible neighborhood solutions are superfluous to HFSP. New specialized neighborhood structures are developed for HFSP accordingly. Secondly, traditional schedule types (such as active schedule) are found to be further explored. A novel type of schedule, all-active schedule (AAS) is proposed to tap the potential of one scheduling process. Thirdly, an improved co-evolutionary memetic algorithm (ICMA) based on UFH and AAS is proposed to solve HFSP. To balance exploration and exploitation, the co-evolutionary framework with multiple groups is adopted. Path reconnection is used as a crossover operator, and a non-dominated selection mechanism is also employed. In the end, the effectiveness of ICMA is experimentally demonstrated. 1 new solution on Carlier benchmark (proposed in 2000) and 45 new solutions on Jose benchmark (proposed in 2020) are found by ICMA, outperforming all previous outstanding algorithms.

A simulated annealing metaheuristic approach to hybrid flow shop scheduling problem

This study investigates a complex hybrid flow shop scheduling problem prevalent in the industrial sector, characterized by dedicated machines, availability dates, and delivery times. The primary objective is to minimize the total completion time (makespan) in a two-stage workshop setting. We conducted a comprehensive literature review, revealing a scarcity of research on this specific configuration, and employed the Simulated Annealing metaheuristic as our main resolution method. Special emphasis was placed on the meticulous parameterization and configuration of this metaheuristic, crucial for navigating the complexity of the problem.Our findings demonstrate the remarkable effectiveness of the Simulated Annealing method, particularly in achieving low deviation from the lower bound in larger problem sizes and specific instance classes. This consistency highlights the method’s robustness and suitability for complex scheduling scenarios. The study also reveals varying degrees of problem solvability across different instance classes, with computation times generally reasonable except in more challenging scenarios.

A variable-representation discrete artificial bee colony algorithm for a constrained hybrid flow shop

In the realm of hybrid flow shop environments, existing literature predominantly overlooks a practical scenario that jobs with different constraints often need to be simultaneously processed. This article addresses a constrained hybrid flow shop scheduling problem (CHFSP) in which certain jobs are bound by a common deadline while other jobs are not. We first propose constructive heuristics to generate initial solutions, completely based on the characteristics of the problem. Additionally, we present a variable-representation discrete artificial bee colony algorithm (VRDABC). The algorithm introduces a novel variable solution representation along with a tailored decoding method, allowing an extensive exploration of the solution space while maintaining a remarkable search speed. By leveraging the distinctive solution representation, we design an insertion operation, a multi-phase evolutionary process, and an efficient phase-transition mechanism, thereby enabling the VRDABC to successfully address this problem. Experimental validations, including algorithmic components analysis and algorithmic comparison, confirm the effectiveness and potential of our approach in producing high-quality solutions. Through the theoretical explanation and experimental analysis, the VRDABC presents an influential contribution to the constrained hybrid flow shop scheduling problem.