Non-permutation Flow Shop Scheduling Research Articles

Q-Learning-Based Priority Dispatching Rule Preference Model for Non-Permutation Flow Shop

Non-permutation flow shop scheduling (NPFS) is an extension of the traditional permutation flow shop scheduling, with a broader solution space. The effectiveness of reinforcement learning in solving flow shop scheduling problems has been demonstrated through its powerful combinatorial optimization capabilities. However, the design and training of the end-to-end policy network is complex, leading to long online training time and limited adaptability of offline training. To overcome these problems, we introduced a NPFS dynamic decision-making process and then proposed a novel NPFS method that combines the Q-learning algorithm with the priority dispatching rule (PDR) set. The NPFS dynamic decision-making process involves decomposing the entire process into multiple sub-job queues for scheduling. The PDR demonstrates better scheduling performance when applied to smaller job queues. By utilizing the Q-learning algorithm, PDRs with superior performance are assigned to sub-scheduling queues based on the generation process of sub-job sequences, resulting in an optimized NPFS strategy. The limited number of PDRs in the PDR set and the small number of sub-job queues in the NPFS process contribute to the efficiency of Q-learning in solving NPFS problem. Finally, we demonstrate the superiority of the proposed NPFS method by a series of numerical experiments using the machine-based assignment PDR method and NSGA-II algorithms as performance benchmarks.

Hybrid deep convolution network and differential evolution algorithm for solving non-permutation flow shop scheduling problem

With explosive growth of industrial big data, workshop scheduling faces problems such as high complexity, multi-dimensionality and low stability. Recent years, the wide application of deep learning provides new idea for scheduling problem. In this paper, a hybrid deep convolution network and differential evolution algorithm is proposed to solve the non-permutation flow shop scheduling problem with the goal of minimizing total completion time. Mining relationship between job attributes and process priority by deep convolutional network is core idea of this method. In this paper, differential evolution algorithm is used to obtain the data set for deep learning, and neighborhood search algorithm is used to optimize scheduling solution. Additionally, a method combining k-means algorithm and data statistics is proposed, which provides a reasonable way for priority division. The experimental results show that this method can greatly improve scheduling efficiency.

Integrated optimization of non-permutation flow shop scheduling and maintenance planning with variable processing speed

Integrated optimization of production scheduling and maintenance planning has received tremendous attention from academia and industry, but the impacts of variable processing speeds on the integrated optimization are either unconsidered or supposed to be constant in the most existing publications. To remedy this shortcoming, this paper addresses an integrated optimization problem of non-permutation flow-shop scheduling and maintenance planning (including preventive maintenance and replacement) with adjustable processing speeds for minimizing the total production cost. To better analyze the problem, there are five problem properties are derived to describe the relationship among processing speed, processing sequence and maintenance planning. Based on this, an improved genetic algorithm with variable processing speed selection (IGAVPSS) is proposed to deal with the concerned problem. In the numerical simulation, the effectiveness and superiority of extended advanced-postpone balancing strategy, proposed internal operators, IGAVPSS algorithm and variable processing speeds are firstly demonstrated through experimental comparisons. After that, a real application is presented to verify the benefits of the proposed IGAVPSS, and the results show that the newly generated scheduling plan based on the proposed IGAVPSS can reduce up to 42.29% of the total production cost compared with the existing company’s scheduling plan.

Solving non-permutation flow-shop scheduling problem via a novel deep reinforcement learning approach

The non-permutation flow-shop scheduling problem (NPFS) is studied. We model it as a Markov decision process, creating a massive arena for reinforcement learning (RL) algorithms to work. While RL approaches with function approximation generate a significant number of sequences of highly linked states, few studies have examined the connection between the state sequences but merely shuffled their orders. To this end, this paper proposes a novel deep reinforcement learning algorithm, named LSTM-TD(0), to address NPFS. Specifically, we design fifteen state features to represent a production state at each scheduling point and fourteen actions to choose an unprocessed operation on a given machine. This study applies long short-term memory (LSTM) network to capture the intrinsic connection of the state sequences in RL-based scheduling approaches. Moreover, we enhance the LSTM model with the one-step temporal difference (TD(0)) algorithm to select each action impartially in relation to the state value, avoiding the frequent overestimation of action values in Q-learning. The proposed LSTM-TD(0) was trained using two LSTM networks and enhanced by redesigning the reward value. A series of comparative experiments were conducted between simple heuristic rules, metaheuristic rules, general DRL methods, and LSTM-TD(0) using a group of well-known benchmark problems with different scales. Comparative results have confirmed both the superiority and universality of LSTM-TD(0) over its competitors. Scalability tests reveal that our approach can generalize to instances of different sizes without retraining or knowledge transferring.

Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem

This study investigates the optimization of non-permutation flow-shop scheduling problems and lot-sizing simultaneously. Contrary to previous works, we first study the energy awareness of non-permutation flow-shop scheduling and lot-sizing using modified novel meta-heuristic algorithms. In this regard, first, a mixed-integer linear mathematical model is proposed. This model aimed to determine the size of each sub-category and determine each machine's speed within each sub-category to minimize makespan and total consumed energy simultaneously. In order to optimize this model, Multi-objective Ant Lion Optimizer (MOALO), Multi-objective Keshtel Algorithm (MOKA), and Multi-objective Keshtel and Social Engineering Optimizer (MOKSEA) are proposed. First, the validation of the mathematical model is evaluated by implementing it in a real case of the food industry using GAMS software. Next, the Taguchi design of the experiment is applied to adjust the meta-heuristic algorithms' parameters. Then the efficiency of these meta-heuristic algorithms is evaluated by comparing with Epsilon-constraint (EPC), Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO) using several test problems. The results demonstrated that the MOALO, MOKA, and MOKSEO algorithms could find optimal solutions that can be viewed as a set of Pareto solutions, which means the used algorithm has the necessary validity. Moreover, the proposed hybrid algorithm can provide Pareto solutions in a shorter time than EPC and higher quality than NSGA-II and MOPSO. Finally, the model's key parameters were the subject of sensitivity analysis; the results showed a linear relationship between the processing time and the first and second objective functions.

Automatic generation of iterated greedy algorithms for the non-permutation flow shop scheduling problem with total completion time minimization

In this paper we address the non-permutation flow shop scheduling problem, a more general variant of the flow shop problem in which the machines can have different sequences of jobs. We aim to minimize the total completion time. We propose a template to generate iterated greedy algorithms, and use an automatic algorithm configuration to obtain efficient methods. This is the first automated approach in the literature for the non-permutation flow shop scheduling problem. The algorithms start by building a high-quality permutation solution, which is then improved during a second phase that generates non-permutation solutions by changing the job order on some machines. The obtained algorithms are evaluated against two well-known benchmarks from the literature. The results show that they can find better schedules than the state-of-the-art methods for both the permutation and non-permutation flow shop scheduling problems in comparable experimental conditions, as evidenced by comprehensive computational and statistical testing. We conclude that using non-permutation schedules is a viable alternative to reduce the total completion time that production managers should consider.

Multi-objective permutation and non-permutation flow shop scheduling problems with no-wait: a systematic literature review

Flow shop scheduling is a type of scheduling where sequence follows for each job on a set of machines for processing. In practice, jobs in flow shops can arrive at irregular times, and the no-wait constraint allows the changes in the job order to flexibly manage such irregularity. The flexible flow shop scheduling problems with no-wait have mainly addressed for flow optimization on the shop floor in manufacturing, processing, and allied industries. The scope of this paper is to identify the literature available on permutation and non-permutation flow shop scheduling with no-wait constraint. This paper organizes scheduling problems based on performance measures of variability and shop environments. The extended summary of two/three-machine and m-machine problems has been compiled, including their objectives, algorithms, parametric considerations, and their findings. A systematic appearance of both conceptual and analytical results summarizes various advances of the no-wait constraint. The paper includes independently investigated problems and suggestions for future research directions.

A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems

In this paper we introduce a novel approach to the combinatorial analysis of flow shop scheduling problems for the case of two jobs, assuming that processing times are unknown. The goal is to determine the dominance properties between permutation flow shop (PFS) and non-permutation flow shop (NPFS) schedules. In order to address this issue we develop a graph-theoretical approach to describe the sets of operations that define the makespan of feasible PFS and NPFS schedules (critical paths). The cardinality of these sets is related to the number of switching machines at which the sequence of the previous operations of the two jobs becomes reversed. This, in turn, allows us to uncover structural and dominance properties between the PFS and NPFS versions of the scheduling problem. We also study the case in which the ratio between the shortest and longest processing times, denoted ρ, is the only information known about those processing times. A combinatorial argument based on ρ leads to the identification of the NPFS schedules that are dominated by PFS ones, restricting the space of feasible solutions to the NPFS problem. We also extend our analysis to the comparison of NPFS schedules (with different number of switching machines). Again, based on the value of ρ, we are able to identify NPFS schedules dominated by other NPFS schedules.

Efficient heuristic for solving non-permutation flow-shop scheduling problems with maximal and minimal time lags

Flow-shop scheduling problem is an attractive subject in the scheduling field, which has attracted the attention of many researchers in the past five decades. However, few studies focused on non-permutation flow-shop problems with time lag consideration. In the present work, the non-permutation flow-shop scheduling problem with time lags has been studied to minimize the makespan as a performance measure. First, we obtain a near-optimal permutation solution using the permutation flow-shopproblem (PFSP) heuristic. Then, an effective iterated greedy heuristic, which can identify high-quality non-permutation solutions, is presented. Using the neighbourhood non-PFSP searching heuristic, we searched for non-PFSP schedules using the proposed heuristic algorithms in the second stage. Finally, the computational results were used to evaluate the performance and effectiveness of the proposed heuristic. The proposed heuristics were able to find near optimal non-PFSP solutions with very short computational time. Thus, the proposed algorithms is efficient and can be used in industrial applications. Moreover, the proposed heuristic algorithms are very simple to implement, which is attractive for industrial applications.

Non-permutation flow shop scheduling problem with preemption-dependent processing time

AbstractIn this paper, the non-permutation flow shop scheduling problem with preemption-dependent processing times is considered. A mixed integer programming formulation is proposed to tackle the problem. The optimization objective considered is the minimization of the total tardiness. The model is tested against random instances. The results allow us to identify the effect of some parameters such as coefficient of preemption-dependent processing time, number of preemptions and the selected machine for preemption on the total tardiness.

A hybrid genetic algorithm for non-permutation flow shop scheduling problems with unavailability constraints

This article deals with the non-permutation flow shop scheduling problems with non-availability intervals. Specifically, two kinds of unavailability constraints are investigated and the jobs are non-resumable in both cases. In the first case, the non-availability intervals are periodically fixed and known in advance. In the second case, the intervals are flexible and the machines’ continuous working time cannot exceed a maximum allowed time. Two mixed binary integer programming models are provided for deriving the optimal schedules, respectively. The problems of minimising makespan in such flow shops are proved Non-deterministic Polynomial-time hard in strong sense. Then a hybrid incremental genetic algorithm (HIGA) that combines an incremental evolution strategy framework, a local refinement and a population diversity supervision scheme is proposed to solve the large-sized problems efficiently. The numerical experiments under different problem parameters’ settings indicate that the HIGA can achieve quite satisfactory performance compared with genetic algorithm and a constructive heuristic based on Nawaz, Enscore, Ham.

Non-permutation flow shop scheduling with order acceptance and weighted tardiness

This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.

Two simple and effective heuristics for minimizing the makespan in non-permutation flow shops

We propose a constructive and an iterated local search heuristic for minimizing the makespan in the non-permutation flow shop scheduling problem. Both heuristics are based on the observation that optimal non-permutation schedules often exhibit a permutation structure with a few local job inversions. In computational experiments we compare our heuristics to the best heuristics for finding non-permutation and permutation flow shop schedules, and evaluate the reduction in makespan and buffer size that can be achieved by non-permutation schedules.

Quay crane scheduling with dual cycling

In this article, the dual cycling quay crane scheduling problem (D-QCSP) with hatches is addressed to minimize the operation cycles of quay cranes. The problem is decomposed into two sub-problems: the intra-group stage (sequencing stacks within each hatch) and the inter-group stage (scheduling all hatches). A new stack sequencing method is constructed for stacks of each hatch, which is modelled as a two-machine non-permutation flow shop scheduling problem. By removing inner gaps using left-shifting, the adapted hatch scheduling sub-problem is modelled as a two-machine grouped flow shop scheduling problem, which contains more precise processing times. A composite heuristic is proposed for the D-QCSP. Based on the derived lower bound, the heuristic is compared with the best existing heuristics on a large number of instances. Experimental results illustrate that the proposal outperforms the existing methods on all instances and dual cycling needs many fewer quay crane operating cycles than single cycling.

The Nonpermutation Flowshop Scheduling Problem: Adjustment and Bounding Procedures

We consider the makespan minimization in a flowshop environment where the job sequence does not have to be the same for all the machines. Contrarily to the classical permutation flowshop scheduling problem, this strongly NP-hard problem received very scant attention in the literature. In this paper, some improved single-machine-based adjustment procedures are proposed, and a new two-machine-based one is introduced. Based on these adjustments, new lower and upper bounding schemes are derived. Our experimental analysis shows that the proposed procedures provide promising results.

Nonpermutation flow line scheduling by ant colony optimization

AbstractA flow line is a conventional manufacturing system where all jobs must be processed on all machines with the same operation sequence. Line buffers allow nonpermutation flowshop scheduling and job sequences to be changed on different machines. A mixed-integer linear programming model for nonpermutation flowshop scheduling and the buffer requirement along with manufacturing implication is proposed. Ant colony optimization based heuristic is evaluated against Taillard's (1993) well-known flowshop benchmark instances, with 20 to 500 jobs to be processed on 5 to 20 machines (stages). Computation experiments show that the proposed algorithm is incumbent to the state-of-the-art ant colony optimization for flowshop with higher job to machine ratios, using the makespan as the optimization criterion.

Hybrid firefly-simulated annealing algorithm for the flow shop problem with learning effects and flexible maintenance activities

Job scheduling and maintenance activities scheduling are two important issues in production management, which are often addressed separately. In this paper, the non-permutation flow shop scheduling problem with learning effects and flexible maintenance activities is studied. Each machine has a number of preventive maintenance activities that should be finished within specific time intervals. The aim is to simultaneously determine the sequence of jobs and the finish time of maintenance activities for minimising the sum of tardiness costs and maintenance costs. A mixed integer linear programming model is proposed to formulate the problem. Owing to the high complexity of the problem, an improvement heuristic method and a hybrid meta-heuristic algorithm based on the simulated annealing algorithm and firefly algorithm is presented to find nearly optimal solutions for medium and large problems. To obtain better and more robust solutions, the Taguchi method is used in order to calibrate the hybrid algorithm parameters. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution approaches.

Non-permutation flowshop scheduling with dual resources

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem.

Native metaheuristics for non-permutation flowshop scheduling

The most general flowshop scheduling problem is also addressed in the literature as non-permutation flowshop (NPFS). Current processors are able to cope with the $$(n!)^{m}$$ combinatorial complexity of NPFS scheduling by metaheuristics. After briefly discussing the requirements for a manufacturing layout to be designed and modeled as non-permutation flowshop, a disjunctive graph (digraph) approach is used to build native solutions. The implementation of an Ant Colony Optimization (ACO) algorithm has been described in detail; it has been shown how the biologically inspired mechanisms produce eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions. ACO algorithms are an example of native non-permutation (NNP) solutions of the flowshop scheduling problem, opening a new perspective on building purely native approaches. The proposed NNP-ACO has been assessed over existing native approaches improving most makespan upper bounds of the benchmark problems from Demirkol et al. (1998).

Scheduling flow lines with buffers by ant colony digraph

► Non-permutation/permutation flow line/flowshop scheduling models in manufacturing. ► Mixed integer model, digraph representation and pseudo code for NPFS–ACO. ► Native ACO approaches compared on Taillard and Demirkol benchmarks. This work starts from modeling the scheduling of n jobs on m machines/stages as flowshop with buffers in manufacturing. A mixed-integer linear programing model is presented, showing that buffers of size n − 2 allow permuting sequences of jobs between stages. This model is addressed in the literature as non-permutation flowshop scheduling (NPFS) and is described in this article by a disjunctive graph (digraph) with the purpose of designing specialized heuristic and metaheuristics algorithms for the NPFS problem. Ant colony optimization (ACO) with the biologically inspired mechanisms of learned desirability and pheromone rule is shown to produce natively eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions found by other heuristics. The proposed ACO has been critically compared and assessed by computation experiments over existing native approaches. Most makespan upper bounds of the established benchmark problems from Taillard (1993) and Demirkol, Mehta, and Uzsoy (1998) with up to 500 jobs on 20 machines have been improved by the proposed ACO.