Classical Job Shop Scheduling Problem Research Articles

A generalized disjunctive graph model for a complex production problem

This work focuses on the modeling of the features of a real-world pharmaceutical production problem, where several limited resources must be gathered and scheduled in order to mix and process active substances. The problem can be modelled as a generalization of the job-shop scheduling problem, in which each job corresponds to an order. Besides the standard precedence and capacity constraints of a classical job-shop scheduling problem, release, no-wait and time interval production constraints are added. Furthermore, the processing of each job task must be assisted by an appropriate number of operators and performed by a specific machine, out of a set of feasible machines, that is temporarily installed in a compatible clean room. An innovative generalized disjunctive graph that models all the constraints and the resource conflicts is presented.

Solving Job-Shop Scheduling Problem Using Genetic Algorithm Approach

An effective job shop scheduling (JSS) in the manufacturing industry is helpful to meet the production demand and reduce the production cost, and to improve the ability to compete in the ever increasing volatile market demanding multiple products.In so many combinatorial optimization problems, job shop scheduling problems have earned a reputation for being difficult to solve. Job-shop scheduling is essentially an ordering problem. A new encoding scheme for a classic job-shop scheduling problem is presented. The aim is to find an allocation for each job and to define the sequence of jobs on each machine so that the resulting schedule has a minimal completion time.Genetic algorithm that has demonstrated considerable success in providing efficient solutions to many non polynomial-hard optimization problems is used to solve job-shop scheduling problem. The schedules given by genetic algorithms are constructed using a priority rule and under several constraints. After a schedule is obtained a checking operation is applied to ensure that the solution is feasible. The approach is tested on a set of instances. The results validate the effectiveness of the algorithm.

Metaheuristics for multiobjective optimization in energy-efficient job shops

Energy awareness is one of the most relevant research directions in scheduling problems. In this paper we consider the minimization of both the makespan and the energy consumption in the classical job shop scheduling problem. The energy model considered allows several possible states for the machines: off, stand-by, idle, setup and processing. To solve this multi-objective problem we propose an NSGA-II based evolutionary algorithm combined with local search and a heuristic procedure to improve the energy consumption of a given schedule. We also propose an advanced constraint programming (CP) approach as well as a Mixed-Integer Linear Programming (MILP) model, to the aim of comparing their performances against those obtained with the NSGA-II. The experimental study is performed against a benchmark set that extends by 41 instances of increasing size, the set tackled in the previous literature against the same problem. The experiments demonstrate the superiority of the NSGA-II algorithm over all other methods, despite the utilization of CP and MILP allows to draw interesting conclusions on the overall solution optimality, revealing that there is still room for further optimization.

A Novel Hybrid Whale Optimization Algorithm for Flexible Job-Shop Scheduling Problem

The flexible job shop scheduling problem (FJSP) is an extension of the classical job shop scheduling problem and one of the more well-known NP-hard problems. To get better global optima of the FJSP, a novel hybrid whale optimization algorithm (HWOA) is proposed for solving FJSP, in which minimizing the makespan is considered as the objective. Firstly, the uniformity and extensiveness of the initial population distribution are increased with a good point set (GPS). Secondly, a new nonlinear convergence factor (NCF) is proposed for coordinating the weight of global and local search. Then, a new multi-neighborhood structure (MNS) is proposed, within which a total of three new neighborhoods are used to search for the optimal solution from different directions. Finally, a population diversity reception mechanism (DRM), which ensures to some extent that the population diversity is preserved with iteration, is presented. Seven international benchmark functions are used to test the performance of HWOA, and the results show that HWOA is more efficient. Finally, the HWOA is applied to 73 FJSP and four Ra international instances of different scales and flexibility, and the results further verify the effectiveness and superiority of the HWOA.

Solving flexible job-shop scheduling problem using harmony search-based meerkat clan algorithm

The classical job shop scheduling (JSS) problem can be extended by allowing processing of an operation by any machine from a given set. This type of scheduling is known as flexible job shop scheduling (FJSS) problem. It incorporates all the difficulties and complexities of its predecessor classical problem. However, it is more complex as it is required to determine the assignment of operations to the machine. Swarm intelligence techniques proved their effectiveness in solving a wide range of complex NP-Hard real world problems. One of these techniques is the meerkat clan algorithm (MCA) that has been successfully applied to various optimization problems. This paper presents a modified MCA for solving the FJSS problem. The modification is based on using harmony search (HS). The introduction of HS provides more exploitation and intensification. HS generates various solutions, which are provided to the MCA. As a result, the exploitation of the local optimum is increased, which in turn increases the convergence rate. The experimental results show that the improved method achieves higher quality schedules. Additionally, the convergence rate is speeded up compared with the standalone algorithm. This gives the proposed method the superiority over the original algorithm.

A hybrid Jaya algorithm for solving flexible job shop scheduling problem considering multiple critical paths

As an extension of the classical job shop scheduling problem, flexible job shop scheduling problem (FJSP) is considered as a challenge in manufacturing systems for its complexity and flexibility. Meta-heuristic algorithms are shown effective in solving FJSP. However, the multiple critical paths issue, which has not been formally discussed in the existing literature, is discovered to be a primary obstacle for further optimization by meta-heuristics. In this paper, a hybrid Jaya algorithm integrated with Tabu search is proposed to solve FJSP for makespan minimization. Two Jaya operators are designed to improve solutions under a two-vector encoding scheme. During the local search phase, three approaches are proposed to deal with multiple critical paths and have been evaluated by experimental study and qualitative analyses. An incremental parameter setting strategy and a makespan estimation method are employed to speed up the searching process. The proposed algorithm is compared with several state-of-the-art algorithms on three well-known FJSP benchmark sets. Extensive experimental results suggest its superiority in both optimality and stability. Additionally, a real world scheduling problem, including six instances with different scales, is applied to further prove its ability in handling large-scale scheduling problems.

A Dynamic Opposite Learning Assisted Grasshopper Optimization Algorithm for the Flexible JobScheduling Problem

Job shop scheduling problem (JSP) is one of the most difficult optimization problems in manufacturing industry, and flexible job shop scheduling problem (FJSP) is an extension of the classical JSP, which further challenges the algorithm performance. In FJSP, a machine should be selected for each process from a given set, which introduces another decision element within the job path, making FJSP be more difficult than traditional JSP. In this paper, a variant of grasshopper optimization algorithm (GOA) named dynamic opposite learning assisted GOA (DOLGOA) is proposed to solve FJSP. The recently proposed dynamic opposite learning (DOL) strategy adopts the asymmetric search space to improve the exploitation ability of the algorithm and increase the possibility of finding the global optimum. Various popular benchmarks from CEC 2014 and FJSP are used to evaluate the performance of DOLGOA. Numerical results with comparisons of other classic algorithms show that DOLGOA gets obvious improvement for solving global optimization problems and is well-performed when solving FJSP.

A layered genetic algorithm with iterative diversification for optimization of flexible job shop scheduling problems

Flexible job shop scheduling problem (FJSSP) is a further expansion of the classical job shop scheduling problem (JSSP). FJSSP is known to be NP-hard with regards to optimization and hence poses a challenge in finding acceptable solutions. Genetic algorithm (GA) has successfully been applied in this regard since last two decades. This paper provides an insight into the actual complexity of selected benchmark problems through quantitative evaluation of the search space owing to their NP-hard nature. A four-layered genetic algorithm is then proposed and implemented with adaptive parameters of population initialization and operator probabilities to manage intensification and diversification intelligently. The concept of reinitialization is introduced whenever the algorithm is trapped in local minima till predefined number of generations. Results are then compared with various other standalone evolutionary algorithms for selected benchmark problems. It is found that the proposed GA finds better solutions with this technique as compared to solutions produced without this technique. Moreover, the technique helps to overcome the local minima trap. Further comparison and analysis indicate that the proposed algorithm produces comparative and improved solutions with respect to other analogous methodologies owing to the diversification technique.

Scheduling of Real-Time Tasks With Multiple Critical Sections in Multiprocessor Systems

The performance of multiprocessor synchronization and locking protocols is a key factor to utilize the computation power of multiprocessor systems under real-time constraints. While multiple protocols have been developed in the past decades, their performance highly depends on the task partition and prioritization. The recently proposed Dependency Graph Approach showed its advantages and attracted a lot of interest. It is, however, restricted to task sets where each task has at most one critical section. In this paper, we remove this restriction and demonstrate how to utilize algorithms for the classical job shop scheduling problem to construct a dependency graph for tasks with multiple critical sections. To show the applicability, we discuss the implementation in ${\rm Litmus^{RT}}$ and report the overheads. Moreover, we provide extensive numerical evaluations under different configurations, which in many situations show significant improvement compared to the state-of-the-art.

Integrated Search Method for Flexible Job Shop Scheduling Problem Using HHS–ALNS Algorithm

Classical job shop scheduling problems took many forms over decades out of which the prominent one is flexible job shop scheduling problem (FJSP), where any machine from a given set, rather than one specific machine can process each operation. To form a stronger search mechanism and better scheduling, an integrated search heuristic given as integrated HHS–ALNS, where the local search in hybrid harmony search (HHS) is replaced by adaptive large neighborhood search (ALNS), is proposed for the FJSP. In ALNS, a weight associated with every operation is adjusted during the end of search segments based on its previous behaviors and violation of capacity constraints. By using this proposed method, the performance is improved a lot in terms of makespan.

Comparative study of different heuristics algorithms in solving classical job shop scheduling problem

Abstract The job shop scheduling problem (JSSP) is one of the prominent optimization industrial problems. Distinctive optimization method consisting of Genetic algorithm (GA), Simulated Annealing (SA) etc., utilized in solving JSSP in many earlier works. In this work, a comparative study of three heuristics (Shifting Bottleneck, PSO (Particle swarm optimization), GA) is carried out to find the best solution of JSSP. The impact of the initial condition (such as the random generation of particles in PSO) on performance of the PSO algorithm is studied and makespan is found out. The convergence capability of the algorithms with different sizes problems was also studied

Metaheuristic for Solving Multi-Objective Job Shop Scheduling Problem in a Robotic Cell

This paper deals with the multi-objective job shop scheduling problem in a robotic cell (MOJRCSP). All the jobs are processed according to their operations order on workstations. Different from classical job shop scheduling problem, the studied problem considers that jobs' transportation is handled by a robot. Also, the jobs are expected to be finished in a time window, instead of a constant due date. A mixed Integer Programming (MIP) model is proposed to formulate this problem. Due to the special characteristics of the studied problem and its NP-hard computational complexity, a metaheuristic based on Teaching Learning Based Optimization (TLBO) algorithm has been proposed. The proposed algorithm determines simultaneously the operations' assignments on workstations, the robot assignments for transportation operations, and the robot moving sequence. The objective is to minimize the makespan and the total earliness and tardiness. Computational results further validated the effectiveness and robustness of our proposed algorithm.

Mathematical modeling and a hybridized bacterial foraging optimization algorithm for the flexible job-shop scheduling problem with sequencing flexibility

The flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem (JSP) in which operations can be performed by a set of candidate capable machines. An extended version of the FJSP, entitled sequencing flexibility, is studied in this work, which considers precedence between the operations in the form of a directed acyclic graph instead of a sequential order. In this work, a mixed integer linear programming (MILP) formulation is presented to minimize weighted tardiness for the FJSP with sequencing flexibility. Due to the NP-hardness of the problem, a novel biomimicry hybrid bacterial foraging optimization algorithm (HBFOA) is developed, which is inspired by the behavior of E. coli bacteria in its search for food. The developed HBFOA search method is hybridized with simulated annealing (SA). Additionally, the algorithm has been enhanced by a local search method based on the manipulation of critical operations. Classical dispatching rules have been employed to create the initial swarm of HBFOA, and a new dispatching rule named minimum number of operations has been devised. The developed approach has been packaged in the form of a decision support system (DSS) developed on top of Microsoft Excel—a tool most small and mid-range enterprises (SME) use heavily for planning. A case study with local industry is presented to validate the proposed HBFOA and MILP. Additional numerical experiments using literature benchmarks are further used for validation. The results demonstrate that the HBFOA outperformed the classical dispatching rules and the best integer solution of MILP when minimizing the weighted tardiness and offered comparable results for the makespan instances.

Solving the flexible job shop scheduling problem using an improved Jaya algorithm

The classical job shop scheduling problem (JSSP) has been a subject of extensive research for the past many years. Due to its high computational complexity, it is considered to be NP-hard (Non-deterministic polynomial time) in nature. The flexible job shop scheduling problem (FJSSP) which is a classification of basic JSSP further increases the complexity of the problem by considering a job to be processed on more than one machine. Hence a routing problem along with the sequencing problem needs to be considered. Considering the NP-hard nature of the problem the research has sailed through the extensive use of meta-heuristics to find near-optimal solutions. However, these meta-heuristics tend to get trapped in the local optimum and also contain algorithm-specific tuning parameters which need to be tuned to obtain an optimal solution. To overcome this, an improved Jaya algorithm is proposed in this work. To improve the solution quality and maintain diversity, an efficient initialization mechanism, a local search technique and acceptance criterion is incorporated into the algorithm. The performance of the improved Jaya algorithm is compared using makespan criteria with other well-known meta-heuristics on 203 benchmark instances. Results demonstrate the effectiveness of the proposed algorithm in solving the FJSSP.

Effective Neighborhood Generation Method in Search Algorithm for Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSSP) is an extension of the classical job shop scheduling problem (JSSP) that allocates jobs to resources while minimizing the maximum completion time of all the jobs. Machine assignment and job sequence are determined in the FJSSP. To efficiently solve the FJSSP, which is a non-deterministic polynomial-time hard problem, a heuristic method must be used. In previous studies, the FJSSP has been solved using neighborhood algorithms that employ various metaheuristic methods. These approaches constrain the neighborhood operation to jobs on a critical path and simultaneously change the machine assignment and job sequence. Branches on the critical path are easily generated in the FJSSP search processes; this branch structure can improve the efficiency of the FJSSP. This study investigates two neighborhood search algorithms used for changing the machine assignment and job sequence via a critical path. The first method changes the machine assignment and job sequence simultaneously, whereas the second method changes them independently. In this study, we propose an efficient neighborhood generating method using a branch block of critical path.

Efficient parallel tabu search for the blocking job shop scheduling problem

The Blocking Job Shop Scheduling (BJSS) is an NP-hard scheduling problem. It is obtained from the classical job shop scheduling problem by replacing the infinite buffer capacity constraint by a zero buffer capacity which introduces the blocking constraint. This constraint affects deeply the ability of meta-heuristics to find good solutions due to the low ratio of feasible to explored solutions. In this paper, we discuss the parallelization of the Tabu Search algorithm (TS) which represents one of the most widely used heuristics. Applying the classical TS neighborhood to the BJSS problem produces infeasible solutions in 98% of cases which leads to waste a valuable time in exploring infeasible solutions. For this reason, the use of a feasibility recovery strategy is unavoidable; however, the recovery step slows down considerably the TS algorithm. Therefore, incurring a huge time to explore a small area in the search space. To overcome this drawback and to accelerate the TS algorithm, we propose in this paper parallel multi-start TS approaches where several processes explore simultaneously the search space. Our parallelization exploits a cluster-based architecture with 512 CPU-cores. The obtained results show the positive impact of our proposed parallelization on the solution quality. Moreover, combining both the parallelism and the recovery strategy allowed us to improve the best result in the literature for a large number of known benchmarks.

An Effective Multi-Objective Artificial Bee Colony Algorithm for Energy Efficient Distributed Job Shop Scheduling

Distributed Job Shop Scheduling Problem (DJSSP) is a generalization of the classic job shop scheduling problem (JSSP), characterized by simultaneously assigning jobs to different factories/workshops and determining their processing sequence. Due to energy efficient and productivity significantly affect the profits of enterprises, two criteria (i.e., makespan and total energy consumption) are used to evaluate the DJSSP. In this paper, a mixed integer programming model is developed, and a multi-objective artificial bee colony algorithm (MOABC) is proposed to evaluate the trade-off between the two objectives. In the MOABC, a solution encoding is represented by three parts: a factory assignment vector, a job permutation vector and a machine speed selection matrix. Meanwhile, a solution decoding is designed to present the scheduling scheme. A numerical experiment is designed to verify the effectiveness of the proposed MOABC. The experimental result demonstrates that the proposed MOABC can generate better Pareto solutions than NSGA-II and SPEA2 for the DJSSP.

Metaheuristics for the job-shop scheduling problem with machine availability constraints

Abstract This paper addresses the job-shop scheduling problem in which the machines are not available during the whole planning horizon and with the objective of minimizing the makespan. The disjunctive graph model is used to represent job sequences and to adapt and extend known structural properties of the classical job-shop scheduling problem to the problem at hand. These results have been included in two metaheuristics (Simulated Annealing and Tabu Search) with specific neighborhood functions and diversification structures. Computational experiments on problem instances of the literature show that our Tabu Search approach outperforms Simulated Annealing and existing approaches.

An extended flexible job shop scheduling problem with parallel operations

Traditional planning and scheduling techniques still hold important roles in modern smart scheduling systems. Realistic features present in modern manufacturing systems need to be incorporated into these techniques. Flexible job-shop scheduling problem (FJSP) is one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical job shop scheduling problem where an operation can be processed by several different machines. In this paper, we consider the FJSP with parallel operations (EFJSP) and we propose and compare a discrete firefly algorithm (FA) and a genetic algorithm (GA) for the problem. Several FJSP and EFJSP instances were used to evaluate the performance of the proposed algorithms. Comparisons among our methods and state-of-the-art algorithms are also provided. The experimental results demonstrate that the FA and GA achieved improvements in terms of efficiency and efficacy. Solutions obtained by both algorithms are comparable to those obtained by algorithms with local search. In addition, based on our initial experiments, results show that the proposed discrete firefly algorithm is feasible, more effective and efficient than our proposed genetic algorithm for the considered problem.

Solving flexible job shop scheduling problems using a hybrid lion optimisation algorithm

This paper addresses the flexible job shop scheduling problem (FJSP) with makespan criterion. The FJSP has been proved to be strongly NP-hard. The FJSP is a generalisation and extension of the classical job shop scheduling problem (JSP). As the problem is NP-hard, exact solution techniques cannot be used to tackle the problem. Researchers have proposed several heuristics and meta-heuristics to solve the problem. The lion optimisation algorithm is one of the recently developed meta-heuristic algorithms. A hybrid lion optimisation algorithm (HLOA) is proposed in the present work to solve the FJSP. A heuristic is hybridised with the LOA to improve the solution quality. To the best of our knowledge this is the first reported application of the LOA to solve the scheduling problems. The performance of the proposed algorithm is tested with two different sets of benchmark problems addressed in the literature. Computational results substantiate the effectiveness of the proposed algorithm.