Flexible Job Shop Scheduling Problem Using an Improved Ant Colony Optimization

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 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.

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.

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.

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

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.

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.

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed 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.

Flexible Job Shop Scheduling (FJSS) problem has many real-world applications such as manufacturing and cloud computing, and thus is an important area of study. In real world, the environment is often dynamic, and unpredicted job orders can arrive in real time. Dynamic FJSS consists of challenges of both dynamic optimisation and the FJSS problem. In Dynamic FJSS, two kinds of decisions (so-called routing and sequencing decisions) are to be made in real time. Dispatching rules have been demonstrated to be effective for dynamic scheduling due to their low computational complexity and ability to make real-time decisions. However, it is time consuming and strenuous to design effective dispatching rules manually due to the complex interactions between job shop attributes. Genetic Programming Hyper-heuristic (GPHH) has shown success in automatically designing dispatching rules which are much better than the manually designed ones. Previous works only focused on standard job shop scheduling with only the sequencing decisions. For FJSS, the routing rule is set arbitrarily by intuition. In this paper, we explore the possibility of evolving both routing and sequencing rules together and propose a new GPHH algorithm with Cooperative Co-evolution. Our results show that co-evolving the two rules together can lead to much more promising results than evolving the sequencing rule only.

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.

The Flexible Job Shop scheduling Problem (FJSP) is a generalization of the classical Job Shop scheduling Problem (JSP) allowing to process operations on one machine out of a set of alternative machines. The FJSP is an NP-hard problem consisting of two sub-problems, which are the machine assignment and the operation scheduling problems. In this paper, we propose how to solve the FJSP by metaheuristics based on clustering in a holonic multiagent model. Firstly, a Neighborhood-based Genetic Algorithm (NGA) is applied by a scheduler agent for a global exploration of the search space. Secondly, a local search technique is used by a set of cluster agents to guide the research in promising regions of the search space and to improve the quality of the NGA final population. To evaluate our approach, numerical tests are made based on three sets of well known benchmark instances from the literature of the FJSP, which are Kacem, Brandimarte, Hurink. The experimental results show the efficiency of our approach in comparison to other approaches.

The ant colony optimization (ACO) algorithm is improved and further integrated with the immune algorithm (IA) to address its problems, such as slow convergence, local optimum, and premature convergence in the path planning. An algorithm integrating IA and improved ant colony optimization (IACO) is, therefore, put forward to realize the optimal planning of global path for an unmanned surface vehicle (USV). First, the ACO algorithm was improved in three aspects, that is, generation of initial pheromones, transition probability, and update of pheromones. The proposed IA-IACO algorithm combined the advantages of IA and IACO, sped up the convergence, and enhanced the optimization capability and operational efficiency. Second, the IA-IACO algorithm was designed and applied in the global path planning of an unmanned surface vehicle, achieving great global optimization and convergence. Finally, a path smoothing algorithm was devised to achieve the implementable, economic, and stable path while guaranteeing the safe navigation of the USV. A simulation test was carried out to prove the effectiveness and superiority of the designed global path planning algorithm in the practical engineering.

This paper researches on the flexible job shop scheduling problem (FJSP) with new job insertion. FJSP with new job insertion includes two phases: initializing schedules and rescheduling after new job(s) insertion. Initializing schedules is the standard FJSP problem while rescheduling is an FJSP with different job start time and different machine start time. The objective is to minimize maximum machine workload. A recently developed algorithm, so called Jaya, is employed to solve the FJSP with new job insertion and a discrete version of Jaya is proposed. Extensive computational experiments are carried out on eight real instances from remanufacturing enterprise. The discrete Jaya is compared to several existing heuristics and ensemble of them for FJSP with new job insertion. The results and comparisons verify that the discrete Jaya algorithm is superior over the existing methods. In future work, we will future improve the performance of discrete Jaya and compare it to more existing intelligent algorithms in literature.

Flexible job shop scheduling problem (FJSP) is very complex to be controlled, and it is a problem which inherits job shop scheduling problem (JSP) characteristics. FJSP has two sub-problems: routing sub-problem and scheduling sub-problem. In this paper, improved differential evolution (DE) algorithm is presented for multi-objective FJSP. Minimization of three objective functions includes maximum completion time, workload of the most loaded machine and total workload of all machines. The improved algorithm has a well-designed mutation and crossover operator, and uses a Pareto non-dominated sorting method. Computational simulations and comparisons demonstrate the effectiveness of the proposed improved DE algorithm.