An improved genetic algorithm for the flexible job shop scheduling problem with multiple time constraints

https://doi.org/10.1016/j.swevo.2020.100664Get rights and content

Abstract

The flexible job shop scheduling problem is a very important problem in factory scheduling. Most of existing researches only consider the processing time of each operation, however, jobs often require transporting to another machine for the next operation while machines often require setup to process the next job. In addition, the times associated with these steps increase the complexity of this problem. In this paper, the flexible job scheduling problem is solved that incorporates not only processing time but setup time and transportation time as well. After presenting the problem, an improved genetic algorithm is proposed to solve the problem, with the aim of minimizing the makespan time, minimizing total setup time, and minimizing total transportation time. In the improved genetic algorithm, initial solutions are generated through three different methods to improve the quality and diversity of the initial population. Then, a crossover method with artificial pairing is adopted to preserve good solutions and improve poor solutions effectively. In addition, an adaptive weight mechanism is applied to alter mutation probability and search ranges dynamically for individuals in the population. By a series of experiments with standard datasets, we demonstrate the validity of our approach and its strong performance.

Introduction

The flexible job shop scheduling problem (FJSP) is a new scheduling problem that expands the traditional job shop scheduling problem (JSP). The traditional problem presumes that a job can be performed reasonably on a machine under specific objective constraints. These assumptions are as follows: each machine can be setup in zero time; only one job can be performed at the same time; a operation cannot be stopped; each job has a defined operation sequence on a known machine; and the processing time of each operation on each machine is known. The FSJP adds machine selection to the traditional JSP, that is, jobs can be processed on different machines. Solving the FJSP is equivalent to solving two sub-problems. The first is a machine selection problem for choosing suitable machines for different operations. The second is an operation sequencing problem for finding the optimal order for processing the jobs.

With the growing need to support custom manufacturing requests, small batch production is gradually becoming an important aspect of modern manufacturing enterprises, however, this kind of variable production for different types of increases the transportation time and setup time. In a steel furniture discrete production job shop, the actual production time and the planned time error caused by the scheduling scheme only considering the processing time state are large. The reason is that there is a lot of non-processing time in the production process, including transportation time and setup time. Therefore, the processing time, transportation time, and setup time are considered as independent time factors for FJSP in this paper. Also, an improved genetic algorithm is proposed to solve this problem. In order to speed up the convergence and improve the quality of the solution, we adopt three different ways to generate the initial solution, which not only improves the quality of the initial solution but also preserves its diversity. At the genetic operator stage, we design more effective crossover and mutation operators, the former one is to carry out the crossover by means of artificial crossover pairing, and the latter one is to acquire mutation probability and neighborhood search ranges by using an adaptive weight method.

Brucker and Schile [1] were the first to address this problem in 1990. Since then, many researchers have studied large-scale combinatorial optimization problems and proposed many methods in the research process. For example, Pezzella et al. [2] and Zhang et al. [3] applied genetic algorithm (GA) to solve the FJSP. Gao et al. [4] and Yazdani et al. [5] used variable neighborhood search (VNS) algorithm to solve the question. Xu et al. [6] used an ant colony algorithm (ACO) to solve FJSP. Li et al. [7] and Ho et al. [8] applied a cultural algorithm (CA) to solve FJSP. Karimi et al. [9] presented an efficient knowledge-based algorithm for solving FJSP.

Nonetheless, a single algorithm easily falls into a locally optimal solution or fails to converge completely when solving complex problems involving large-scale combinatorial optimization. Therefore, many scholars use hybrid algorithms to solve FJSP. Yuan et al. [10] proposed a novel hybrid harmony search (HHS) algorithm for solving FJSP. Yuan and Xu [11] proposed a hybrid differential evolution (HDE) algorithm for solving FJSP. Shao et al. [12] used discrete water wave optimization algorithm (IMMBO) for blocking flow-shop scheduling problem. Meng et al. [13] used migrating birds optimization to solve an integrated lot-streaming flow shop scheduling problem. Gao et al. [14] and Zhang et al. [15] combined a GA and a VNS. Li et al. [16] solved the FJSP using a GA and Tabu search (TS).

The problem can be divided into single or multiple objective problems, the optimization goal used to minimize the makespan. For instance, Teekeng et al. [17] used minimization of the total time as a single optimization objective. Ham et al. [18] considered the scheduling problem in parallel processing and took makespan as the optimization objective. Nevertheless, research on multi-objective problems has become more mainstream and valuable. The total completion time and resource consumption were regarded as multiple optimization objectives by Lu et al. [19]. Zhang et al. [20] combined total time, total machine workload, and total energy consumption as multiple objectives. Hu and Wang [21] minimized the overall completion time, total machine workload, and the greatest machine workload as the objective. Gao et al. [22,23] used the weighted combination of two minimization criteria, total completion time and the average time of early or late delivery as the optimization objective, he also used the makespan the mean of earliness and tardiness as two objectives to optimize.

Over time, researchers have taken more realistic factors into account when solving the FJSP. Karimi et al. [24] incorporated the time required for a job to move between machines. Zandieh et al. [25] taken condition-based maintenance (CBM) into account, recognizing that machines might be unavailable due to preventive maintenance, basic maintenance, or unforeseen breakdowns. Shen et al. [26] addressed the problem with sequence-dependent setup times. Wang et al. [27] regarded fuzzy processing time as a factor. Zhang et al. [28] regarded transportation time in flexible job shop scheduling problems.

The remainder of the paper is organized as follows. In Section 2, we describe the flexible job shop problem with multiple time constraints in detail and give an example. The improved genetic algorithm is described in Section 3, including encoding, decoding, generation of an initial solution and the chromosome genetic operator in detail. In Section 4, we present our experiments and results of our algorithm on standard dataset and compare them. Section 5 presents our conclusions and suggestions for future research.

Section snippets

Problem description

The flexible job shop scheduling problem is an NP-hard problem. Traditionally, researchers have only considered processing time. We consider not only the processing time of the job on different machines but also the time for transporting jobs between machines and the time for setting up machines before processing a job in the actual scheduling process.

The problem is described as follows. N jobs need to be processed on M machines, and each job can contain one or more operations. Each operation

Chromosome coding

Coding is a method of transforming the feasible solutions of a given problem from the solution space to a search space that the algorithm can handle. Effective coding expresses the relationship between the individual and the feasible solution without producing illegal solutions. The FJSP contains two sub-problems: machine selection and sequencing. We use the machine selection sub-problem to identify which machine to perform each operation of the job. We use the operation sequencing sub-problem

Experimental studies

The proposed algorithm was implemented in MATLAB on a computer with an Intel Core i3-8100 CPU at 3.6 ​GHz with 8 ​GB of RAM. In order to make the calculation results more meaningful, we ran each test question 10 times continuously when the algorithm was running. All the algorithm parameters are designed by orthogonal experiment to make the proposed algorithm more effective and obtain better solution. The parameters are shown in Table 3.

Our first set of experiments uses test data from Kacem

Conclusion and avenues for future research

In this paper, we have proposed an improved genetic algorithm for solving the flexible job shop scheduling model with multiple time constraints. In order to improve the quality of the initial solution, three different methods were proposed to generate the initial solution. To preserve good solutions and improve poor solutions quickly, we use a manual matching method to improve crossover operation. We apply an adaptive weight method to make different mutation probabilities of different

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This paper presents work funded by the National Natural Science Foundation of China (U1904167, 51705472, 71871204), Excellent Youth Foundation of Science & Technology Innovation of Henan Province (184100510001, 184100510004), Humanities and Social Sciences of Ministry of Education Planning Fund (18YJAZH125), Science and Technology Research Project of Henan Province (202102210131), Key Research Project in Universities of Henan Province (17A520030), and Postgraduate Education Innovation Program

References (34)

Cited by (135)

View all citing articles on Scopus
View full text