No-wait Flow Shop Scheduling Problem Research Articles

Minimizing the Sum of Makespan and Total Weighted Tardiness in a No-Wait Flowshop

This paper presents a cloud theory-based iterated greedy (CTIG) algorithm for solving the no-wait flowshop scheduling problem (NWFSP) with the objective of minimizing the sum of makespan and total weighted tardiness. The performance of the proposed CTIG algorithm is evaluated by comparing its computational results to those of the best-to-date meta-heuristic algorithm, particle swarm optimization (PSO), as presented in this paper. The experimental results concerning two sets of benchmark problem instances in this paper demonstrate that the CTIG algorithm obtains more (near) optimal solution in less computational time than the PSO algorithm. The computational results in this paper fill the research gap in the development of a novel algorithm to improve the solution quality in the case of the NWFSP with the objective of minimizing the sum of makespan and total weighted tardiness.

Evolutionary Hybrid Particle Swarm Optimization Algorithm for Solving NP-Hard No-Wait Flow Shop Scheduling Problems

The no-wait flow shop is a flowshop in which the scheduling of jobs is continuous and simultaneous through all machines without waiting for any consecutive machines. The scheduling of a no-wait flow shop requires finding an appropriate sequence of jobs for scheduling, which in turn reduces total processing time. The classical brute force method for finding the probabilities of scheduling for improving the utilization of resources may become trapped in local optima, and this problem can hence be observed as a typical NP-hard combinatorial optimization problem that requires finding a near optimal solution with heuristic and metaheuristic techniques. This paper proposes an effective hybrid Particle Swarm Optimization (PSO) metaheuristic algorithm for solving no-wait flow shop scheduling problems with the objective of minimizing the total flow time of jobs. This Proposed Hybrid Particle Swarm Optimization (PHPSO) algorithm presents a solution by the random key representation rule for converting the continuous position information values of particles to a discrete job permutation. The proposed algorithm initializes population efficiently with the Nawaz-Enscore-Ham (NEH) heuristic technique and uses an evolutionary search guided by the mechanism of PSO, as well as simulated annealing based on a local neighborhood search to avoid getting stuck in local optima and to provide the appropriate balance of global exploration and local exploitation. Extensive computational experiments are carried out based on Taillard’s benchmark suite. Computational results and comparisons with existing metaheuristics show that the PHPSO algorithm outperforms the existing methods in terms of quality search and robustness for the problem considered. The improvement in solution quality is confirmed by statistical tests of significance.

Optimization of makespan for the distributed no-wait flow shop scheduling problem with iterated greedy algorithms

The distributed production lines widely exist in modern supply chains and manufacturing systems. This paper aims to address the distributed no-wait flow shop scheduling problem (DNWFSP) with the makespan criterion by using proposed iterated greedy (IG) algorithms. Firstly, several speed-up methods based on the problem properties of DNWFSP are investigated to reduce the evaluation time of neighborhood with O(1) complexity. Secondly, an improved NEH heuristic is proposed to generate a promising initial solution, where the iteration step of the insertion step of NEH is applied to the factory after inserting a new job. Thirdly, four neighborhood structures (i.e. Critical_swap_single, Critical_insert_single, Critical_swap_multi, Critical_insert_multi) based on factory assignment and job sequence adjustment are employed to escape from local optima. Fourthly, four local search methods based on neighborhood moves are proposed to enhance local searching ability, which contains LS_insert_critical_factory1, LS_insert_critical_factory2, LS_swap, and LS_insert. Finally, to organize neighborhood moves and local search methods efficiently, we incorporate them into the framework of variable neighborhood search (VNS), variable neighborhood descent (VND) and random neighborhood structure (RNS). Furthermore, three variants of IG algorithms are presented based on the designed VNS, VND and RNS. The parameters of the proposed IG algorithms are tuned through a design of experiments on randomly generated benchmark instances. The effectiveness of the initialize phase and local search methods is shown by numerical comparison, and the comparisons with the recently published algorithms demonstrate the high effectiveness and searching ability of the proposed IG algorithms for solving the DNWFSP. Ultimately, the best solutions of 720 instances from the well-known benchmark set of Naderi and Ruiz for the DNWFSP are proposed.

A discrete Water Wave Optimization algorithm for no-wait flow shop scheduling problem

In this paper, a discrete Water Wave Optimization algorithm (DWWO) is proposed to solve the no-wait flowshop scheduling problem (NWFSP) with respect to the makespan criterion. Inspired by the shallow water wave theory, the original Water Wave Optimization (WWO) is constructed for global optimization problems with propagation, refraction and breaking operators. The operators to adapt to the combinatorial optimization problems are redefined. A dynamic iterated greedy algorithm with a changing removing size is employed as the propagation operator to enhance the exploration ability. In refraction operator, a crossover strategy is employed by DWWO to avoid the algorithm falling into local optima. To improve the exploitation ability of local search, an insertion-based local search scheme which is utilized as breaking operator, is applied to search for a better solution around the current optimal solution. A ruling out inferior solution operator is also introduced to improve the convergence speed. The global convergence performance of the DWWO is analyzed with the Markov model. In addition, the computational results based on well-known benchmarks and statistical performance comparisons are presented. Experimental results demonstrate the effectiveness and efficiency of the proposed DWWO algorithm for solving NWFSP.

An extended teaching-learning based optimization algorithm for solving no-wait flow shop scheduling problem

The no-wait flow shop scheduling problem (NWFSSP) performs an important function in the manufacturing industry. Inspired by the overall process of teaching-learning, an extended framework of meta-heuristic based on the teaching-learning process is proposed, which consists of four parts, i.e. previewing before class, teaching phase, learning phase, reviewing after class. This paper implements a hybrid meta-heuristic based on probabilistic teaching-learning mechanism (mPTLM) to solve the NWFSSP with the makespan criterion. In previewing before class, an initial method that combines a modified Nawaz-Enscore-Ham (NEH) heuristic and the opposition-based learning (OBL) is introduced. In teaching phase, the Gaussian distribution is employed as the teacher to guide learners to search more promising areas. In learning phase, this paper presents a new means of communication with crossover. In reviewing after class, an improved speed-up random insert local search based on simulated annealing (SA) is developed to enhance the local searching ability. The computational results and comparisons based on Reeves, Taillard and VRF’s benchmarks demonstrate the effectiveness of mPTLM for solving the NWFSSP.

General variable neighborhood search algorithm to minimize makespan of the distributed no-wait flow shop scheduling problem

This paper addresses minimizing makespan of the distributed no-wait flow shop scheduling problem where there are several identical factories that work in parallel. There are jobs with series of operations that should be allocated to one of these factories and all operations of jobs should be performed in the allocated factories. After starting the first operation of the job, all other operations of the job should be processed without any interruption or delay. The goal is finding allocation and sequence of jobs on each factory such that the completion time of the last job processed in the system is minimized. For the addressed problem, several heuristics available in the literature developed to solve the classical no-wait flowshop scheduling problem have been extended to the addressed problem. Due to NP-hard nature of the addressed problem, a metaheuristic algorithm called General Variable Neighbourhood Search (GVNS) has been proposed which similar to Variable Neighbourhood Search (VNS) algorithm has shaking procedure and local search algorithm but the severity of the shaking procedure depending on the progress of incumbent solution changes. Also, time-saving strategies that allow focusing on promising movements in the search algorithm, as well as the shaking producer of the proposed GVNS algorithm, are incorporated. The performance of the heuristic algorithms and GVNS thorough comprehensive benchmark problems are presented.

Properties of two-machine no-wait flow-shop scheduling with a non-resumable unavailable interval

The properties of two-machine no-wait flow-shop scheduling problem, with a non-resumable unavailable interval are studied. This research discusses two cases: a non-resumable unavailable interval in the first and second machines respectively. The problems’ complexities are proved to be NP-hard. The Gilmore and Gomory Algorithm (GGA) is applied to minimize the makespan, and the conditions that GGA yields the optimal solutions are presented. Sixty numerical examples with ten-job and two-machine are generated to test the proposed theorems. Compared to the results obtained by the Johnson algorithm, the GGA algorithm yields an 8.15% improvement on average. Moreover, the worst-case performance ratios of GGA are proved to be 2.

An ant colonial optimisation approach for no-wait permutation flow shop scheduling

This research aims to address the applications of variants of ant colony optimisation (ACO) approach to solve no-wait flow shop scheduling problem (NW-FSSP). The most suitable ACO algorithm out of basic algorithms has been selected and modified to achieve more purified results. The algorithm was coded in visual basic. The varied algorithm has been applied to the bench mark problems and results were compared with the results achieved previously by other researchers using different meta-heuristics. The research covers detailed steps carried out for application of basic ACO algorithms on bench mark problems, comparison of results achieved by application of basic ACO algorithms, selection of best out of basic algorithms, modification of selected basic algorithm and generation of varied ACO algorithm. The varied ACO algorithm gave reasonably good results for almost all the problems under consideration and was able to handle fairly large sized problems with far less computational time. Comparative analysis depicted that the proposed ACO algorithm performed better than genetic algorithm on large sized problems and better than Rajendran heuristic in almost all problems under considerations.

An ant colonial optimisation approach for no-wait permutation flow shop scheduling

This research aims to address the applications of variants of ant colony optimisation (ACO) approach to solve no-wait flow shop scheduling problem (NW-FSSP). The most suitable ACO algorithm out of basic algorithms has been selected and modified to achieve more purified results. The algorithm was coded in visual basic. The varied algorithm has been applied to the bench mark problems and results were compared with the results achieved previously by other researchers using different meta-heuristics. The research covers detailed steps carried out for application of basic ACO algorithms on bench mark problems, comparison of results achieved by application of basic ACO algorithms, selection of best out of basic algorithms, modification of selected basic algorithm and generation of varied ACO algorithm. The varied ACO algorithm gave reasonably good results for almost all the problems under consideration and was able to handle fairly large sized problems with far less computational time. Comparative analysis depicted that the proposed ACO algorithm performed better than genetic algorithm on large sized problems and better than Rajendran heuristic in almost all problems under considerations.

An Effective Harmony Search Algorithm for Solving a No-Wait Hybrid Flow Shop Scheduling Problem with Machine Availability Constraint

This research investigates a no-wait hybrid flow shop scheduling problem. Minimizing the mean tardiness is considered as the objective to develop the optimal scheduling algorithm. Characteristics of our considered problem leads to the complexity of problem. First, no-wait operations. Second, setup time of each job is separated from its processing time and depends upon its preceding job. Third, all of jobs aren’t available at the first of scheduling. In other word, each job has individual ready time. Finally, machines are not continuously available due to the preventive maintenance. An effective harmony search algorithm is used to tackle the mentioned problem. A series of computational experiments is conducted by comparing our algorithm with previous meta-heuristic algorithms like population based simulated annealing (PBSA), Adopted imperialist competitive algorithm (ICA) and hybridization of PBSA and ICA (ICA+PBSA). To achieve reliable results, Taguchi approach is used to define robust parameters’ values for our proposed algorithm. The computational results with random test problems suggest that our proposed harmony search outperforms the three foregoing algorithms.

On the exact solution of the no-wait flow shop problem with due date constraints

This paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

A High Quality Solution Constructive Heuristic for No-Wait Flow Shop Scheduling Problem

This paper deals with the no-wait flow shop scheduling problem in order to minimize the total time to complete the schedule or makespan. It is introduced a constructive heuristic which builds the production schedule from job partial sequences by using an appropriate mechanism of insertion. An extensive computational experiment has been performed to evaluate the performance of proposed heuristic. Experimental results have clearly shown that the presented heuristic provides better solutions than those from the best heuristics existing.

A new hybrid ant colony algorithm for scheduling of no-wait flowshop

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

A Hungarian penalty-based construction algorithm to minimize makespan and total flow time in no-wait flow shops

This paper presents a penalty-based construction algorithm for the no-wait flow shop scheduling problem with the objective of minimizing makespan and total flow time of jobs. The proposed method, derived from Hungarian penalty method originally used for the classic assignment problem is employed to generate an initial schedule of jobs, which is further improved by an insertion technique to obtain an optimal or near-optimal schedule. The results of computational experiments on a large number of test problems show that the proposed method performs significantly better than the state-of-the-art procedures while requiring comparable computational effort.

Fast local neighborhood search algorithm for the no-wait flow shop scheduling with total flow time minimization

A fast local neighbourhood search (FLNS) algorithm is proposed in this paper to minimise the total flow time in the no-wait flow shop scheduling problem, which is known to be NP-hard for more than two machines. In this work, an unscheduled job sequence is constructed firstly according to the total processing time and standard deviation of jobs on the machines. This job sequence is undergone an initial optimisation using basic neighbourhood search algorithm. Then, an innovative local neighbourhood search scheme is designed to search for the partial neighbourhood in each iterative processing and calculate the neighbourhood solution with an objective increment method. This not only improves the solution quality significantly, but also speeds up the convergence of the solution of the algorithm. Moreover, a probabilistic acceptance criterion is adopted to help our method escape from the local optima. Based on Taillard’s benchmarks, the experimental results show that the proposed FLNS algorithm is superior to major existing algorithms (IHA, IBHLS, GA-VNS and DHS) in terms of both quality and robustness, and can provide best upper bounds. The in-depth statistical analysis demonstrates that the promising performance of our proposed algorithm is also statistically significant.

Heuristics for no-wait flow shop scheduling problem

Heuristics for no-wait flow shop scheduling problem

An Enumeration Algorithm for the No-Wait Flow Shop Problem with Due Date Constraints

This paper develops an enumeration algorithm for the no-wait flow shop scheduling problem with due date constraints. In this problem, waiting time is not allowed between successive operations of jobs. Plus, each job is accompanied by a due date which is dealt with as a hard constraint. The considered performance criterion is makespan. The problem is strongly NP-hard. In this research, a new modelling approach is developed for the problem. This new modelling technique and the resulting observations are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics

The no-wait flowshop scheduling problem (NWFSP) with makespan minimization is a well-known strongly NP-hard problem with applications in various industries. This study formulates this problem as an asymmetric traveling salesman problem, and proposes two matheuristics to solve it. The performance of each of the proposed matheuristics is compared with those of the best existing algorithms on 21 benchmark instances of Reeves and 120 benchmark instances of Taillard. Computational results show that the presented matheuristics outperform all existing algorithms. In particular, all tested instances of the problem, including a subset of 500-job and 20-machine test instances, are solved to optimality in an acceptable computational time. Moreover, the proposed matheuristics can solve very hard and large NWFSPs to optimality, including the benchmark instances of Vallada et al. and a set of 2000-job and 20-machine problems. Accordingly, this study provides a feasible means of solving the NP-hard NWFSP completely and effectively.

An effective co-evolutionary quantum genetic algorithm for the no-wait flow shop scheduling problem

This article proposes a competitive co-evolutionary quantum genetic algorithm for the no-wait flow shop scheduling problem with the criterion to minimize makespan, which is a renowned NP-hard combinatorial optimization problem. An innovative coding and decoding mechanism is proposed. The mechanism uses square matrix to represent the quantum individual and adapts the quantum rotation gate to update the quantum individual. In the algorithm framework, the store-with-diversity is proposed to maintain the diversity of the population. Moreover, a competitive co-evolution strategy is introduced to enhance the evolutionary pressure and accelerate the convergence. The store-with-diversity and competitive co-evolution are designed to keep a balance between exploration and exploitation. Simulations based on a benchmark set and comparisons with several existing algorithms demonstrate the effectiveness and robustness of the proposed algorithm.

A particle swarm optimisation for the no-wait flow shop problem with due date constraints

This paper considers the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, a due date is associated with the completion of each job. The considered objective function is makespan. This problem is proved to be strongly NP-Hard. In this paper, a particle swarm optimisation (PSO) is developed to deal with the problem. Moreover, the effect of some dispatching rules for generating initial solutions are studied. A Taguchi-based design of experience approach has been followed to determine the effect of the different values of the parameters on the performance of the algorithm. To evaluate the performance of the proposed PSO, a large number of benchmark problems are selected from the literature and solved with different due date and penalty settings. Computational results confirm that the proposed PSO is efficient and competitive; the developed framework is able to improve many of the best-known solutions of the test problems available in the literature.