Non-permutation Flow Shop Scheduling Problem Research Articles

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.

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.

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.

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.

Minimizing total flow time for the non-permutation flow shop scheduling problem with learning effects and availability constraints

The flow shop scheduling problem is an attractive subject in the field of scheduling, which has attracted the attention of many researchers in the past five decades. In this paper, the non-permutation flow shop scheduling problem with the learning effects and machine availability constraints has been studied for minimizing the total flow time as a performance measure. First, a mixed integer linear programming model has been proposed for the modeling of the problem and then, an effective improving heuristic method, which is able to find proper non-permutation solutions, has been presented. Finally, the computational results are used for evaluation the performance and effectiveness of the proposed heuristic.

Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.

Solving non-permutation flowshop scheduling problems by an effective iterated greedy heuristic

Flowshop scheduling problems have received considerable research attention over the last five decades. This study proposes an iterated greedy heuristic for non-permutation flowshop scheduling problems. To validate and verify the proposed heuristic, computational experiments have been conducted on a well-known benchmark problem set, and the results are compared with 20 simple constructive heuristics and a state-of-the-art meta-heuristic performed on the same benchmark instances. In terms of both solution quality and computational expense, this study successfully develops an efficient and effective approach for non-permutation flowshop scheduling problems.

Multi-heuristic desirability ant colony system heuristic for non-permutation flowshop scheduling problems

Ant colony optimization (ACO) is a novel intelligent meta-heuristic originating from the foraging behavior of ants. An efficient heuristic of ACO is the ant colony system (ACS). This study presents a multi-heuristic desirability ACS heuristic for the non-permutation flowshop scheduling problem, and verifies the effectiveness of the proposed heuristic by performing computational experiments on a well-known non-permutation flowshop benchmark problem set. Over three-quarters of the solutions to these experiments are superior to the current best solutions in relevant literature. Since the proposed heuristic is comprehensible and effective, this study successfully explores the excellent potential of ACO for solving non-permutation flowshop scheduling problems.

General flow-shop scheduling with resource constraints

The paper deals with a version of the general non-permutation flow-shop scheduling problem in which the duration of each operation on certain machines is a linear function of the allotted part of a constrained resource (e.g. energy, fuel, catalyzer, oxygen, raw material, money) and the objective is to determine both a sequence of the operations on each machine and an allocation of resource to each operation in order to minimize the over-all completion time. The algorithm for solving this problem is based on the disjunctive graph theory and branch and bound technique. Due to the present elimination properties, the search tree is strongly restricted. It applies a special system of fixing precedence relations in each node of the search tree yielding strong lower and upper bounds. To quickly obtain a strong upper bound a special heuristic method is used (to calculate a good initial solution) and the descendants in the search tree are chosen in order of the non-decreasing lower bounds. Some computational resul...