Study on job shop scheduling with sequence-dependent setup times using biological immune algorithm

Large Language Models (LLMs) have emerged as a promising technology for solving combinatorial optimization problems. However, their direct application to scheduling problems remains limited due to the inherent complexity of these problems. This paper proposes an LLMs-based neighborhood search method that leverages LLMs to tackle the job shop scheduling problem (JSP) and its variants. The main contributions of this work are threefold. First, we introduce a novel LLMs-guided neighborhood evaluation strategy that guides local search by dynamically adjusting operation weights. Second, we develop a verification evolution (VeEvo) framework to mitigate the hallucination effects of LLMs, enabling the generation of high-quality heuristics for weight updates. Third, we integrate this framework with the weighted neighborhood evaluation strategy to effectively guide the search towards promising regions. Extensive experiments are conducted on 349 benchmark instances across three classical scheduling problems. The results demonstrate that our algorithm significantly outperforms existing state-of-the-art methods. For JSP, our algorithm reduces the average optimality gap from 10.46% to 1.35% on Taillard's instances compared to reinforced adaptive staircase curriculum learning. For flexible JSP (FJSP), it reduces the gap from 13.24% to 0.05% on Brandimarte's instances compared to deep reinforcement learning methods. Furthermore, for FJSP with sequence dependent setup time, our algorithm updates 9 upper bounds for benchmark instances.

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.

Job shop scheduling, as one of the classical scheduling problems, has been widely studied in literatures, and proved to be mostly NP-hard. Although it is extremely difficult to solve job shop scheduling with no-wait constraint to optimality, the two-machine no-wait job shop scheduling to minimise makespan could be solvable in polynomial time when each job has exactly two equal length operations (proportionate job shop). In the present paper, an extension is attempted by considering a proportionate flexible two-stage no-wait job shop scheduling problem with minimum makespan, and a set-covering formulation is put forward which contains a master problem and a pricing problem. To solve this problem, a column generation (CG)-based approach is implemented. In comparison, a mixed integer programming model is constructed and optimised by Cplex. A series of randomly generated numerical instances are calculated. And the testing result shows that the mixed integer model handled by Cplex can only solve small scale cases, while the proposed CG-based method can conquer larger size problems in acceptable time.

Genetic Programming based hyper-heuristics (GP-HH) for dynamic job shop scheduling (JSS) problems are approaches which aim to address the issue where heuristics are only effective for specific JSS problem domains, and that designing effective heuristics for JSS problems can be difficult. This paper is a preliminary investigation into improving the robustness of heuristics evolved by GP-HH by evolving ensembles of dispatching rules from a single population of GP individuals. The results show that the current approach does not evolve significantly better or more robust rules than a standard GP-HH approach of evolving single constituent rules.

The classical job-shop scheduling problem is one of the most difficult combinatorial optimization problems. Scheduling is defined as the art of assigning resources to tasks in order to insure the termination of these tasks in a reasonable amount of time. Job shop scheduling problems vary widely according to specific production tasks but most are NP-hard problems. Mathematical and heuristic methods are the two major methods for resolving JSP. Job shop Scheduling problems are usually solved using heuristics to get optimal or near optimal solutions. In this paper, a Hybrid algorithm combined artificial immune system and sheep flock heredity model algorithm is used for minimizing the total holding cost for different size benchmark problems. The results show that the proposed hybrid algorithm is an effective algorithm that gives better results than other hybrid algorithms compared in literature. The proposed hybrid algorithm is a good technique for scheduling problems.

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.

Production scheduling and reliability of machinery are prominent issues in flexible manufacturing systems that are led to decreasing of production costs and increasing of system efficiency. In this paper, multiobjective optimization of stochastic failure‐prone job shop scheduling problem is sought wherein that job processing time seems to be controllable. It endeavours to determine the best sequence of jobs, optimal production rate, and optimum preventive maintenance period for simultaneous optimization of three criteria of sum of earliness and tardiness, system reliability, and energy consumption. First, a new mixed integer programming model is proposed to formulate the problem. Then, by combining of simulation and NSGA‐II algorithm, a new algorithm is put forward for solving the problem. A set of Pareto optimal solutions is achieved through this algorithm. The stochastic failure‐prone job shop with controllable processing times has not been investigated in the earlier research, and for the first time, a new hedging point policy is presented. The computational results reveal that the proposed metaheuristic algorithm converges into optimal or near‐optimal solution. To end, results and managerial insights for the problem are presented.

In the just-in-time job-shop scheduling (JIT–JSS) problem every operation has a distinct due-date, and earliness and tardiness penalties. Any deviation from the due-date incurs penalties. The objective of JIT–JSS is to obtain a schedule, i.e., the completion time for performing the operations, with the smallest total (weighted) earliness and tardiness penalties. This paper presents a matheuristic algorithm for the JIT–JSS problem, which operates by decomposing the problem into smaller sub-problems, optimizing the sub-problems and delivering the optimal schedule for the problem. By solving a set of 72 benchmark instances ranging from 10 to 20 jobs and 20 to 200 operations we show that the proposed algorithm outperforms the state-of-the-art methods and the solver CPLEX, and obtains new best solutions for nearly 56% of the instances, including for 79% of the large instances with 20 jobs.

<p style='text-indent:20px;'>In today's competitive world, scheduling problems are one of the most important and vital issues. In this study, a bi-objective unrelated parallel machine scheduling problem with worker allocation, sequence dependent setup times, precedence constraints, and machine eligibility is presented. The objective functions are to minimize the costs of tardiness and hiring workers. In order to formulate the proposed problem, a mixed-integer quadratic programming model is presented. A strategy called repair is also proposed to implement the precedence constraints. Because the problem is NP-hard, two metaheuristic algorithms, a multi-objective tabu search (MOTS) and a multi-objective simulated annealing (MOSA), are presented to tackle the problem. Furthermore, a hybrid metaheuristic algorithm is also developed. Finally, computational experiments are carried out to evaluate different test problems, and analysis of variance is done to compare the performance of the proposed algorithms. The results show that MOTS is doing better in terms of objective values and mean ideal distance (MID) metric, while the proposed hybrid algorithm outperforms in most cases, considering other employed comparison metrics.</p>

A Petri net with controller is used to model discrete events in flexible job shop scheduling, the objective of scheduling problems is to minimize make-span, the scheduling results is obtained based on genetic and Tabu Search (TS) algorithm. It is proved capable of providing optimized schedule to the job-shop where the machine tool and manpower resources are both constrained. After crossover and mutation operations, an optimal or suboptimal scheduling plan can be found. The result of the test shows that this method is feasible and efficient. Job shop scheduling is the primary content and critical technology of the production management of CIMS, in the past during 30 years, a lot of researchers and results focus on it, but most of them deal with single objective and resource scheduling problems which are fixed processing route and constrained by machine, and production period is its optimal objective. Nevertheless, the production styles are variable and processing route is determined under the special condition. Moreover, job shop scheduling problem is the most difficult combined constraints optimal problem and typical NP hard problem which can't be solved in polynomial time by an effective algorithm. Up to date, there are some traditional algorithms to solve JSP problem (1-2). About paper (3), Petri net is used to construct JSP model and L1 which combines branch and bound algorithm with dynamic program is used to search its optimal solution. And paper (4), the job sequence is assigned by genetic code firstly, and then filtered beam search which based on breadth-first algorithm is adopted to search. In recent years, the Petri net as a discrete event dynamic system modeling and analysis tool(5), has been successfully applied to the flexible manufacturing system modeling, analysis and control. Some researchers put forward to be based on Petri network scheduling method, but only on the production line itself can not reflect the modeling, as in the production line of external control scheduling strategy influence. A hybrid algorithm is proposed to solve dual-resource scheduling problem in flexible production environment, and Petri net model with a controller, which can effectively model control. It combines the advantage of global search ability of GA with the self-adaptive merit of Tabu Search (TS) and improves its convergence. It is proved capable of global and part searching ability and efficient.

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes an improved immune clonal selection algorithm, called improved clonal selection algorithm for the JSSP. The new algorithm has the advantage of preventing from prematurity and fast convergence speed. Numerous well-studied benchmark examples in job-shop scheduling problems were utilized to evaluate the proposed approach. The computational results show that the proposed algorithm could obtain the high-quality solutions within reasonable computing times, and the results indicate the effectiveness and flexibility of the immune memory clonal selection algorithm.

The importance of job shop scheduling as a practical problem has attracted the attention of many researchers. However, most research has focused on special cases such as single machine, parallel machine, and flowshop environments due to the “hardness” of general job shop problems. In this paper, a hybrid algorithm based on an integration of a genetic algorithm and heuristic rules is proposed for a general job shop scheduling problem with sequence-dependent setups (Jm|sjk|Cmax ). An embedded simulator is employed to implement the heuristic rules, which greatly enhances the flexibility of the algorithm. Knowledge relevant to the problem is inherent in the heuristic rules making the genetic algorithm more efficient, while the optimization procedure provided by the genetic algorithm makes the heuristic rules more effective. Extensive numerical experiments have been conducted and the results have shown that the hybrid approach is superior when compared to recently published existing methods for the same problem.

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.

The issue in Lot Streaming is how to split lots into sublots in order to improve the makespan (or some other criterion). We present a model and an iterative procedure for a general job-shop environment. The procedure alternates between solving a lot-sizing problem with a given sequence of sublots on the machines, and a standard job-shop scheduling problem with fixed sublot sizes. We report the computational results on a significant sample of 120 job-shop and flow-shop scheduling problems (including the famous 10–10). In case of no setup, in a few iterations, the makespan approaches a lower bound using very few sublots, suggesting that the procedure yields a global optimum. As a by-product, this result somehow validates the capacitated lot-sizing models in which the detailed capacity constraints, induced by the sequencing of operations, are ignored.

For pt.I. see ibid., p.1006-15. This paper presents the application of parallel dynamic interaction (PDI) to three real problem domains: the flowshop scheduling problem, the job-shop scheduling problem and the vertex cover problem. Specific examples are provided as to how the general PDI framework, introduced in part I of this paper, can be applied to a particular problem. The results of an empirical study of 90 example instances of these problems indicate that PDI consistently out-performs previously published heuristics for the vertex cover problem, and can typically generate solutions within a few percent of optimal for flow-shop and job-shop problems. Out of the 76 examples for which the optimal solution could be determined, PDI was able to produce results averaging within 4% of optimal. In over 30% of the cases, PDI was able to find the optimal solution. In no case did the PDI solution deviate more than 15% from optimal. It is also seen that the time taken by PDI to arrive at these solutions is negligible compared to that taken by conventional search techniques. This provides strong empirical evidence that PDI is capable of generating high quality solutions to exponentially and super-exponentially hard problems in reasonably short periods of time. >