Permutation Flow Shop Scheduling Research Articles

A Hybrid Algorithm for Multi-Objective Optimization of Minimizing Makespan and Total Flow Time in Permutation Flow Shop Scheduling Problems

This paper proposes, a multi-objective optimization of minimizing makespan and total flow time of jobs for permutation flow shop scheduling is considered. Bi-objective issues are comprehended by doling out uniform weight to every objective function in view of its preference or determining every competent solutions. In flow shop scheduling environment, many meta-heuristic algorithms have been used to find optimal or near-optimal solutions due to the computational cost of determining exact solutions. This work provides a hybridization of genetic algorithm and simulated annealing algorithm (HGASA) based multi-objective optimization algorithm for flow shop scheduling. HGASA could be a simple and proficient algorithm that is utilized to determine for every single and multi-objective problem in flow shop scheduling shop environment. This algorithm can works simply for realistic manufacturing system applications. The proposed hybrid algorithm searches the optimal solution for objectives by considering the makespan and total flow time. The performance of the proposed HGASA was tested on standard flow shop benchmark problems to calculate its performance. The test results show that the HGASA algorithm performed better in terms of searching quality and efficiency than other meta-heuristic algorithms.

Decoding methods for the flow shop scheduling with peak power consumption constraints

The permutation flow shop scheduling problem (PFSP) is of wide application backgrounds and plays an important role in the manufacturing systems. With the serious energy concerns in manufacturing enterprises, peak power consumption is considered one of the significant issues. For the PFSP with peak power consumption constraints (PFSPP), the real-time power consumption cannot exceed a given peak power at any time. Since the classical first-come first-serve scheduling method is not suitable for the PFSPP, this paper addresses the decoding methods to obtain feasible schedules based on the permutation encoding scheme. First, an earliest processing rule (EPR) is designed to determine the starting time of each operation, satisfying the power consumption constraints. Then, five decoding methods based on EPR are proposed to determine the suitable priority between the operations to yield feasible schedules with high quality. After analysing the complexity of the proposed decoding methods and comparing the performances via extensive numerical tests, some suggestions are provided for solving the PFSPP with different scales and power constraints.

Genetic algorithm-based hybrid approach for optimal instance selection of minimising makespan in permutation flowshop scheduling

Recently, the instance selection is getting more attention for the researchers to achieve enhanced performance of algorithms. A typical flowshop dataset can be represented in the form of a number of instances. The instances that are recorded during production process may not be a good example to learn useful knowledge. Therefore, the selection of high quality instances can be considered as a search problem and be solved by evolutionary algorithms. In this work, a genetic algorithm (GA) is proposed to select a sub-set of best instances. The selected instances are represented in the form of IF-Then else rules using a decision tree (DT) algorithm. The seed solution from DT is used as input to a scatter search (SS) algorithm for a few iterations, which acts as a local search to find the best value of the selected instances. The GA is used to select best instances in order to have a smaller tree size with good solution accuracy for minimizing makespan criterion in permutation flowshop scheduling. The computational experiments are performed with standard problems and compared against various existing literatures.

Genetic algorithm-based hybrid approach for optimal instance selection of minimising makespan in permutation flowshop scheduling

Recently, the instance selection is getting more attention for the researchers to achieve enhanced performance of algorithms. A typical flowshop dataset can be represented in the form of a number of instances. The instances that are recorded during production process may not be a good example to learn useful knowledge. Therefore, the selection of high quality instances can be considered as a search problem and be solved by evolutionary algorithms. In this work, a genetic algorithm (GA) is proposed to select a sub-set of best instances. The selected instances are represented in the form of IF-Then else rules using a decision tree (DT) algorithm. The seed solution from DT is used as input to a scatter search (SS) algorithm for a few iterations, which acts as a local search to find the best value of the selected instances. The GA is used to select best instances in order to have a smaller tree size with good solution accuracy for minimizing makespan criterion in permutation flowshop scheduling. The computational experiments are performed with standard problems and compared against various existing literatures.

A simheuristic for bi-objective stochastic permutation flow shop scheduling problem

A simheuristic for bi-objective stochastic permutation flow shop scheduling problem

Heuristic Algorithm for Permutation flow shop Scheduling

Heuristic Algorithm for Permutation flow shop Scheduling

An improvement heuristic for permutation flow shop scheduling

An improvement heuristic algorithm is proposed in this paper for solving flow shop scheduling problem (Fm / prmu / Cmax). To test its efficiency, firstly the performance of the proposed algorithm is done against the six heuristics existing in the literature including the best NEH heuristic on 120 Taillard benchmarks. Further, this set of 120 Taillard instances is increased to 266 benchmark problem instances which include Carlier's, some Reeves and some new hard VRF instances from Vallada et al. (2015). On these instances, the performance of the proposed algorithm is tested against the best NEH and the famous CDS heuristic with the best known upper bounds. Further, a brief analysis of the other heuristics and metaheuristics existing in literature is done on Taillard problem instances. The proposed heuristic outperforms all the heuristics reported in this paper.

A Multi-Objective Whale Swarm Algorithm for Energy-Efficient Distributed Permutation Flow shop Scheduling Problem with Sequence Dependent Setup Times

Abstract The distributed permutation flow shop scheduling problem with sequence dependent setup times (DPFSP_SDST) is a generalization of permutation flow shop scheduling problem with sequence dependent setup times (PFSP_SDST), where there exists a set of identical factories in a PFSP_SDST structure. It is concerned with first assignment of jobs to factories, and then scheduling jobs in each factory. In this paper, we try to find a trade-off between makespan and total energy consumption in a DPFSP_SDST environment, where machines are assumed to operate at varying speed levels. A multi-objective mixed integer linear programming model is presented based on (1) allocating jobs among factories, (2) determining velocity upon each machine, and (3) scheduling the jobs in each factory. Due to the NP-complete nature of the problem, a multi-objective whale swarm algorithm (MOWSA) is presented to solve this complex multi-objective DPFSP_SDST. We propose a problem specific encoding scheme, crossover and mutation operators as well as a very effective local search in MOWSA. The extensive experimental results show the effectiveness of MOWSA over NSGA-II, SPEA2 and PAES for approximating the Pareto front solution sets.

An improvement heuristic for permutation flow shop scheduling

An improvement heuristic algorithm is proposed in this paper for solving flow shop scheduling problem (Fm / prmu / Cmax). To test its efficiency, firstly the performance of the proposed algorithm is done against the six heuristics existing in the literature including the best NEH heuristic on 120 Taillard benchmarks. Further, this set of 120 Taillard instances is increased to 266 benchmark problem instances which include Carlier's, some Reeves and some new hard VRF instances from Vallada et al. (2015). On these instances, the performance of the proposed algorithm is tested against the best NEH and the famous CDS heuristic with the best known upper bounds. Further, a brief analysis of the other heuristics and metaheuristics existing in literature is done on Taillard problem instances. The proposed heuristic outperforms all the heuristics reported in this paper.

Permutation flow shop scheduling problem under non-renewable resources constraints

The majority of flow shop scheduling problems considers machines as the only resource. However, in most real-life manufacturing environments, jobs for their processing on machines may require additional non-renewable resources. Considering such resources, the scheduling problem is more realistic and much harder to solve. In this paper, we investigate the permutation flow shop scheduling problem subject to non-renewable resources constraints. The objective is to find a schedule that minimises the maximum completion time. An integer linear programming model is developed. Because of the computation time constraint, we propose an approximate resolution method based on genetic algorithm. To obtain better and more robust solutions, the Taguchi method is performed for tuning the parameters and operators of the algorithm. Furthermore, a local search is proposed to enhance the searching ability. Finally, computational experiments are conducted to evaluate the performance of both mathematical model and algorithm on different configurations of non-renewable resources availability.

A Discrete Artificial Bee Colony Algorithm for the Energy-Efficient No-Wait Flowshop Scheduling Problem

No-wait permutation flow shop scheduling problem (NWPFSP) is a variant of permutation flow shop scheduling problem (PFSP), where the processing of each job must be continuous from start to end without any interruption. That is, once a job starts its processing, it has to be processed until the last machine without any interruption. The aim of this study is to propose an energy-efficient NWPFSP for the determination of a trade-off between total flow time and total energy consumption by obtaining the Pareto optimal set that is the non-dominated solution set. A bi-objective mixed-integer programming model is developed where the machines can operate at different speed levels. Since the problem is NP-complete, an energy-efficient discrete artificial bee colony (DABC), and an energy-efficient genetic algorithm (MOGA), also a variant of this algorithm (MOGALS) are developed, as heuristic methods. First, the performance of these algorithms for comparison with the mathematical model is represented in small size instances in the scope of cardinality and quality of the non-dominated solutions, then it is shown that DABC performs better than two other algorithms in larger instances.

Permutation flow shop scheduling problem under non-renewable resources constraints

The majority of flow shop scheduling problems considers machines as the only resource. However, in most real-life manufacturing environments, jobs for their processing on machines may require additional non-renewable resources. Considering such resources, the scheduling problem is more realistic and much harder to solve. In this paper, we investigate the permutation flow shop scheduling problem subject to non-renewable resources constraints. The objective is to find a schedule that minimises the maximum completion time. An integer linear programming model is developed. Because of the computation time constraint, we propose an approximate resolution method based on genetic algorithm. To obtain better and more robust solutions, the Taguchi method is performed for tuning the parameters and operators of the algorithm. Furthermore, a local search is proposed to enhance the searching ability. Finally, computational experiments are conducted to evaluate the performance of both mathematical model and algorithm on different configurations of non-renewable resources availability.

A novel dynamic assignment rule for the distributed job shop scheduling problem using a hybrid ant-based algorithm

Distributed scheduling problems are among the most investigated research topics in the fields of Operational Research, and represents one of the greatest challenges faced by industrialists and researchers today. The Distributed Job shop Scheduling Problem (DJSP) deals with the assignment of jobs to factories and with determining the sequence of operations on each machine in distributed manufacturing environments. The objective is to minimize the global makespan over all the factories. Since the problem is NP-hard to solve, one option to cope with this intractability is to use an approximation algorithm that guarantees near-optimal solutions quickly. Ant based algorithm has proved to be very effective and efficient in numerous scheduling problems, such as permutation flow shop scheduling, flexible job shop scheduling problems and network scheduling, etc. This paper proposes a hybrid ant colony algorithm combined with local search to solve the Distributed Job shop Scheduling Problem. A novel dynamic assignment rule of jobs to factories is also proposed. Furthermore, the Taguchi method for robust design is adopted for finding the optimum combination of parameters of the ant-based algorithm. To validate the performance of the proposed algorithm, intensive experiments are carried out on 480 large instances derived from well-known classical job-shop scheduling benchmarks. Also, we show that our algorithm can process up to 10 factories. The results prove the efficiency of the proposed algorithm in comparison with others.

Permutation flowshop scheduling with simple linear deterioration

ABSTRACTThis article addresses permutation flowshop scheduling problems with simple linear deterioration. The objectives are to minimize logarithm of the makespan, total logarithm of the completion time, total weighted logarithm of the completion time, and the sum of the quadratic job logarithms of the completion times. Approximation algorithms and their worst-case bounds are presented and analysed. Branch-and-bound algorithms are also proposed to solve the problems optimally. Computational experiments are performed to illustrate the algorithms.

Constraint guided accelerated search for mixed blocking permutation flowshop scheduling

Mixed Blocking Permutation Flowshop Scheduling Problem (MBPFSP) with the objective of makespan minimisation is NP-Hard. It has important industrial applications that include the cider production industry. MBPFSP has made some progress in recent years. However, within practical time limits, existing incomplete algorithms still either find low quality solutions or struggle with large problems. One key reason behind this is the typical way of using generic heuristics or metaheuristics that usually lack problem specific structural knowledge. In MBPFSP, a machine could be blocked with the currently finished job until the subsequent machine is available to process the same job. These blocking constraints affect the makespan. So MBPFSP search should naturally take explicit steps to take the blocking constraints into account. Unfortunately, existing research on MBPFSP just uses only the makespan to compare generated solutions, but the search otherwise is not aware of the blocking constraints. Moreover, existing such methods use either an exhaustive or a random neighbourhood generation strategy. In this work, we aim to advance MBPFSP search by better exploiting the problem specific structural knowledge. We use the constraint and the objective functions to obtain such problem specific knowledge and we exploit such knowledge both in a constructive search method and in a local search method. In this paper, we also present an acceleration method to efficiently evaluate insertion-based neighbourhoods of MBPFSP. Our experimental results on three standard testbeds demonstrate that our proposed algorithms significantly improve over existing best-performing algorithms.

Ant colony optimisation algorithms for two-stage permutation flow shop with batch processing machines and nonidentical job sizes

This paper focuses on minimising the maximum completion time for the two-stage permutation flow shop scheduling problem with batch processing machines and nonidentical job sizes by considering blocking, arbitrary release times, and fixed setup and cleaning times. Two hybrid ant colony optimisation algorithms, one based on job sequencing (JHACO) and the other based on batch sequencing (BHACO), are proposed to solve this problem. First, max-min pheromone restriction rules and a local optimisation rule are embedded into JHACO and BHACO, respectively, to avoid trapping in local optima. Then, an effective lower bound is estimated to evaluate the performances of the different algorithms. Finally, the Taguchi method is adopted to investigate and optimise the parameters for JHACO and BHACO. The performances of the proposed algorithms are compared with that of CPLEX on small-scale instances and those of a hybrid genetic algorithm (HGA) and a hybrid discrete differential evolution (HDDE) algorithm on full-scale instances. The computational results demonstrate that BHACO outperforms JHACO, HDDE and HGA in terms of solution quality. Besides, JHACO strikes a balance between solution quality and run time.

Permutation Flow Shop Scheduling With Batch Delivery to Multiple Customers in Supply Chains

Rapid changes in production environments have motivated researchers and industrial manufacturers to coordinate the production and distribution in supply chain management. This paper aims to address the permutation flow shop scheduling problem with batch delivery to multiple customers. In this problem, products are first manufactured in a permutation flow shop, and subsequently delivered to multiple customers in batches. To optimize the tradeoff between customer service and distribution cost, the objective of this paper is to minimize the total cost of tardiness and batch delivery. To deal with such optimization problem, two simple heuristics and a novel meta-heuristic (GA-TVNS) are developed to determine integrated production and distribution schedules. GA-TVNS hybridizes genetic algorithm and variable neighborhood search (VNS) to provide better exploration and exploitation in the search space. Moreover, to improve the local search of VNS, two new learning-based neighborhood structures are designed based on the classical school learning process of teaching–learning-based optimization. Computation experiments on both small-sized and large-sized test problems indicate that GA-TVNS performs the best among all the compared scheduling algorithms.

A modified immune clone algorithm for energy-saving scheduling in permutation flow shop

For the permutation flow shop scheduling problem, an energy-saving scheduling model has been presented considering the energy consumption and idle time of deferment machines. The mathematical programming model was established to minimize the total energy consumption for idle time, and a modified immune clone algorithm was developed. Four mutation operators have been introduced to ensure its exploration ability. Meanwhile, a LCS-EDA neighbor search method was presented based on estimation of distribution algorithm, which aims to enhance the exploitation ability of MICA. Finally, the experiments were carried out based according to two standard testing collections. The results have validated the feasibility and effectiveness of the proposed energy-saving model and modified metaheuristic.

An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time

With the increasing attention on environment issues, green scheduling in manufacturing industry has been a hot research topic. As a typical scheduling problem, permutation flow shop scheduling has gained deep research, but the practical case that considers both setup and transportation times still has rare research. This paper addresses the energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time to minimise both makespan as economic objective and energy consumption as green objective. The mathematical model of the problem is formulated. To solve such a bi-objective problem effectively, an improved multi-objective evolutionary algorithm based on decomposition is proposed. With decomposition strategy, the problem is decomposed into several sub-problems. In each generation, a dynamic strategy is designed to mate the solutions corresponding to the sub-problems. After analysing the properties of the problem, two heuristics to generate new solutions with smaller total setup times are proposed for designing local intensification to improve exploitation ability. Computational tests are carried out by using the instances both from a real-world manufacturing enterprise and generated randomly with larger sizes. The comparisons show that dynamic mating strategy and local intensification are effective in improving performances and the proposed algorithm is more effective than the existing algorithms.

A TLBO and a Jaya heuristics for permutation flow shop scheduling to minimize the sum of inventory holding and batch delay costs

Abstract This paper deals with permutation flow shop scheduling problem in which an integrated cost model consisting of work-in-process inventory carrying cost and penalty cost due to batch delay is proposed. The objective is to obtain an optimum production schedule which minimizes the expected total cost per unit time of scheduling. To optimize the objective function, we apply two new metaheuristic optimization techniques namely TLBO (teaching-learning based optimization) and Jaya and two traditional algorithms: PSO (particle swarm optimization) and SA (simulated annealing). The problem is solved for several instances ranging from 8 jobs and 5 machines to 500 jobs and 20 machines. Computational results show that for small instances, all algorithms performed equally good when compared with the exact solution (total enumeration method). However, for medium and large size problems, enumeration method was unable to give the results in a reasonable computation time period. Therefore the results of all four algorithms are compared among themselves and found that Jaya outperforms all algorithms. However, for a few large instances, SA yields better results in less computation time as against other heuristics. The overall performance of all algorithms reveals that TLBO and Jaya have considerable potential to solve discrete combinatorial problems such as permutation flow-shop scheduling problems.