A modified shifting bottleneck heuristic for the reentrant job shop scheduling problem with makespan minimization

Lot streaming for product assembly in job shop environment

The job shop scheduling problem (JSSP) is one of the most difficult problems, as it is classified as an NP-complete one. In this paper, by integrating chaos mechanism and niche technique, a novel artificial immune algorithm based on the clonal selection principle and idiotypic immune network theory exhibited in biological immune system is proposed to solve classical job shop scheduling problem. Taking advantages of the ergodic and stochastic properties of chaotic variable, an adaptive chaos mutation operator is designed by the combination of prior knowledge of antibody and evolution iterations. The operator can avoid blind search and enhance the convergence speed effectively. Experimental results indicate that the proposed algorithm is highly competitive, being able to produce better solutions than GA and CLONALG in several cases, and is a viable alternative for solving efficiently job shop scheduling problem.

An ant colony optimization algorithm that accounts for the special requirements of Flexible Manufacturing Systems (FMS) is presented in this paper. The scheduling problem of FMS is conceived as a classical job shop scheduling problem (JSSP). The objective is to minimize the time taken for all jobs to finish execution (i.e. the makespan). The proposed algorithm accounts for the dynamicity of the FMS environment and automates the schedule update by incorporating newly arrived jobs to the existing schedule. The Ant Colony algorithm is applied to solve different discrete optimization problems by artificial ants, using indirect communication to make all routing decisions by reacting to their dynamically changing environment through cooperation between ants and updating their pheromone trails. The effectiveness of the algorithm proposed in this paper is investigated by examining numerical results, and the computational experiments have been executed based on the JSSP data benchmarks.

As an extension of the classical job shop scheduling problem, the flexible job shop scheduling problem (FJSP) plays an important role in real production systems. In FJSP, an operation is allowed to be processed on more than one alternative machine. It has been proven to be a strongly NP-hard problem. Ant colony optimization (ACO) has been proven to be an efficient approach for dealing with FJSP. However, the basic ACO has two main disadvantages including low computational efficiency and local optimum. In order to overcome these two disadvantages, an improved ant colony optimization (IACO) is proposed to optimize the makespan for FJSP. The following aspects are done on our improved ant colony optimization algorithm: select machine rule problems, initialize uniform distributed mechanism for ants, change pheromone’s guiding mechanism, select node method, and update pheromone’s mechanism. An actual production instance and two sets of well-known benchmark instances are tested and comparisons with some other approaches verify the effectiveness of the proposed IACO. The results reveal that our proposed IACO can provide better solution in a reasonable computational time.

With the growing emphasis on intelligent and sustainable manufacturing, the flexible job shop scheduling problem (FJSP) has emerged as a critical optimization challenge due to its capability to model complex and dynamic production environments. As an NP-hard problem, FJSP poses significantly greater complexity than the classical job shop scheduling problem, particularly in high-precision domains such as aerospace manufacturing, where traditional optimization methods often fall short. To overcome the limitations of the standard Whale Optimization Algorithm (WOA)–namely its continuous search paradigm and inadequate local search mechanisms–this paper proposes a genetic-operator-integrated whale optimization algorithm (GOI-WOA) tailored for discrete scheduling tasks. The GOI-WOA employs a two-layer discrete encoding strategy to represent operations and machine assignments, and introduces genetic operators, a critical-path-based neighborhood search, and a temporal-entropy-based local search to enhance solution diversity and local exploitation. Furthermore, an elite information-sharing mechanism is incorporated to facilitate the diffusion of high-quality solutions within the population. Comprehensive experiments conducted on standard benchmark instances demonstrate that GOI-WOA consistently outperforms baseline WOA and other state-of-the-art methods in terms of makespan minimization, convergence stability, and computational efficiency. These results validate the effectiveness and robustness of GOI-WOA as a competitive solution framework for complex manufacturing scheduling problems.

This paper addresses a problem related to the classical job shop scheduling problem with two jobs. The problem consists in concurrently determining the best subset of machines to be duplicated and the optimal scheduling of the operations in order to minimize completion time. Such a problem arises in the tool management for a class of flexible manufacturing cells. The job shop with two jobs is first reviewed, the application of the classical search algorithm A* to this problem is discussed and its performance compared with a previous approach. The complexity of the machine duplication problem is then analysed. The problem is proved to be in general NP‐hard in the strong sense, but in a class of special cases, relevant from the applications viewpoint, it can be solved in polynomial time by a dynamic programming algorithm. A heuristic based on such an algorithm and on A* is proposed for the general problem; the results are satisfactory in terms of both efficiency and quality of the solution.

Flexible job shop scheduling problem (FJSP) is an extended formulation of the classical job shop scheduling problem, endowing great significance in the modern manufacturing system. The FJSP defines an operation that can be processed by any machine from a given set, which is a strong constrained NP-hard problem and intractable to be solved. In this paper, three recent proposed meta-heuristic optimization algorithms have been employed in solving the FJSP aiming to minimize the makespan, including moth-flame optimization (MFO), teaching-learning-based optimization (TLBO) and Rao-2 algorithm. Two featured FJSP cases are carried out and compared to evaluate the effectiveness and efficiency of the three algorithms, also associated with other classical algorithm counterparts. Numerical studies results demonstrate that the three algorithms can achieve significant improvement for solving FJSP, and MFO method appears to be the most competitive solver for the given cases.

The classic job shop scheduling problem mainly focuses on one kind of manufacturing resources, such as machine tools, and etc. But the job shop scheduling in practical production activities always needs to consider the constraints of different manufacturing resources. In this paper, a double-resource flexible job shop scheduling problem (DFJSSP) is presented. Both machines and workers are considered in the process of job shop scheduling in this DFJSSP. And a genetic algorithm (GA) is used to solve this problem, in which a new well designed three-layer chromosome encoding method has been adopted and some effective crossover and mutation operators are designed. Finally, a case study is used to validate the method.

Ant colony optimization combined with taboo search for the job shop scheduling problem

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.

The Flexible Job Shop Scheduling Problem (FJSP) is an extension of the classical job shop scheduling problem, which is characterized by the fact that each process can be processed on multiple candidate machines, and needs to solve the two subproblems of machine allocation and process sequencing simultaneously. Since FJSP is an NP-hard problem, its complexity and multi-objective characteristics make the traditional exact methods inefficient. At the same time, the existing intelligent optimization algorithms are prone to falling into local optimums, which makes it difficult to balance global exploration and local exploitation capabilities. To this end, this study proposed a Levy flight-based Harmony Search algorithm (LHS), which effectively avoids premature convergence by dynamically and adaptively adjusting the Harmony Memory Considering Rate (HMCR), the probability of Pitch Adjusting Rate (PAR), and the arbitrary distance Bandwidth(BW), and by introducing a Levy flight mechanism to perturb the parameters to broaden the search space and enhance the diversity of the population. We validate the experiments using 8 × 8, 10 × 10, and 10 benchmark instances proposed by Brandimarte in the literature, and the experimental results show that the Harmony search algorithm based on Levy flight outperforms the other comparative algorithms in terms of the solution quality and the convergence speed, demonstrating the effectiveness of its solution for FJSP.

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 linguistic-based meta-heuristic modeling and solution approach for solving the flexible job shop scheduling problem (FJSSP) is presented in this study. FJSSP is an extension of the classical job-shop scheduling problem. The problem definition is to assign each operation to a machine out of a set of capable machines (the routing problem) and to order the operations on the machines (the sequencing problem), such that predefined performance measures are optimized. In this research, the scope of the problem is widened by taking into account the alternative process plans for each part (process plan selection problem). Probabilistic selection of alternative process plans and machines are also considered. The FJSSP is presented as a grammar and the productions in the grammar are defined as controls (Baykasoglu, 2002). Using these controls and Giffler and Thompson's (1960) priority rule-based heuristic along with the multiple objective tabu search algorithm of Baykasoglu et al. (1999) FJSSP is solved. This novel approach simplifies the modeling process of the FJSSP and enables usage of existing job shop scheduling algorithms for its fast solution. Instead of scheduling job shops with inflexible algorithms that cannot take into account the flexibility which is available in the job shop, the present algorithm is developed which can take into account the flexibility during scheduling. Such an approach will considerably increase the responsiveness of the job shops.

This thesis considers the scheduling challenges encountered at a particular facility in the nuclear industry. The scheduling problem is modelled as a variant of the job shop scheduling problem. Important aspects of the considered problem include the scheduling of jobs with both soft and hard due dates, and the integration of maintenance planning with job scheduling. Two variants of the scheduling problem are considered: The first variant makes the classic job shop assumption of infinite queueing capacity at each machine, while such queueing capacity is non-existent in the second variant. Without queueing capacity, the scheduling problem is a variant of the blocking job shop problem. For the non-blocking variant of the problem, it is shown that good solutions can be obtained quickly by hybridising a novel Ant Colony Optimisation method with a novel Branch and Bound method. For the blocking variant of the problem, it is shown that a novel Branch and Bound method can rapidly find optimal solutions. This Branch and Bound method is shown to provide good performance due to, amongst other things, a novel search strategy and a novel branching strategy.

As an extension of the classical job-shop scheduling problem, the flexible job-shop scheduling problem (FJSP) allows an operation to be performed by one machine out of a set of machines. To solve the problem in real job shops, this paper presents a method of the discrete neural network with transient chaos (TDNN). The method considers various constraints in a FJSP. Furthermore, a new computational energy function for FJSP is proposed. A production scheduling program is developed in this research for validation and implementation of the proposed method in practical engineering situations. The experimental results show that the method can converge to the global optimum or near to the global optimum in reasonable and finite time.