A competitive and cooperative Migrating Birds Optimization algorithm for vary-sized batch splitting scheduling problem of flexible Job-Shop with setup time
Introduction
Flexible Job-Shop Scheduling Problem (FJSP) is a classic combinational optimization problem that is an extension of tradition Job-Shop Scheduling Problem (JSP). It is common in modern manufacturing industries where several processing machines should be allocated reasonably and operation orders of the jobs order should be sorted properly to improve production efficiency. Its main feature involves several machines with identical function but different operation time, which amounts to the term flexibility.
Batch production is widely used in mass-producing manufacturing. Batch Splitting Scheduling Problem of Flexible Job-Shop (BS-FJSP) is an extension of FJSP in which machines process a whole batch at a time and batch splitting technique is applied to further enhance the production efficiency. Due to its NP-hard nature, it is usually solved by using heuristic algorithms. With more constraints and more complex structure, it is a more complicated problem than normal FJSP which requires higher algorithm capabilities. Therefore, it is necessary to improve the algorithm for this problem.
Migrating Birds Optimization (MBO) is a new swarm based heuristic algorithms that simulates the behavior of migratory birds flying in a V-shaped formation. It has been successfully applied in different researching fields with satisfying results due to its strong local search ability and simple structure. In this paper, MBO is modified to fit the need of BS-FJSP and applied to solve this complicated problem. In this paper, a Competitive and Cooperative Migrating Birds Optimization (CCMBO) algorithm is proposed, which consists of three main stages with different functions.
The remainder of the paper is organized as follows. Related Works on Batch Splitting Scheduling Problems and the MBO algorithm are shown in Section 2. The problem under study in this paper is described in Section 3. The MBO and CCMBO for the problem are introduced in Section 4. Experiments on CCMBO are reported in Section 5 and the conclusions are summarized in the final section.
Section snippets
On batch splitting scheduling problem
The number of studies on the Batch Splitting Scheduling Problem is very limited. Most of the studies solve this problem using heuristic algorithms which have been widely used in many fields such as function optimization [1,2,3,4], classification [5], production scheduling [6,7], electrical scheduling [8], route scheduling [9], cloud computing [10], data replication [11] and so forth. These algorithms are time efficient and can find acceptable suboptimal solutions in a relatively short time. For
Introduction to BS-FJSP
In the batch production environment, every batch contains several identical jobs. Different batches contain different types of jobs. Generally speaking, all the machines operate a whole batch at a time. All the jobs in the same batch have to wait until the last job in the batch is operated. The batch would be transferred to another machine as a whole, after which all the jobs in the batch can start their next operation. Sometimes the batch size, which equals to the product sum of the number of
Basic MBO
Migrating Birds Optimization (MBO) algorithm is one of the swarm based heuristic algorithms proposed by Duman et al. [20]. It simulates the behavior of migratory birds flying in a V-shaped formation. When a bird is flying, due to the structural characteristics of its wings, the wingtips will produce swirling airflow, which is able to provide lifting force for the follower birds. Thus flying in a V-shaped formation can save the total energy of the whole bird population. It can also prevent
Experiment results and comparisons
In order to test the performance of CCMBO, experiments are carried out. Two sets of test cases are used in this paper. All test cases are BS-FJSP with consistent sub-batches and detached setup. The experiment objective is to minimize makespan. All the programs are coded with Python 3.6 and run on a computer with 3.20 GHz processor, 16.0 GB RAM. The parameters of MBO are selected same as those in literature[20] which were discussed and verified they were best. namely, , , , ,
Conclusion
This paper mainly studied the BS-FJSP problem, which is a complicated NP-hard problem, and proposed a novel algorithm named CCMBO for this problem. First, the decoding scheme based on Flexibility Index was proposed to make the algorithm feasible to be applied in BS-FJSP problem. Then the procedure of CCMBO, which consisted of three main stages with different functions, was introduced. The improved V-shaped flying stage was able to avoid the neighborhood of the follower birds being wholly
Acknowledgements
This work is supported by Guangzhou Municipal Science and Technology Project (Grant No. 201707010437), Science and Technology Planning Project of Guangdong Province (Grant No. 2017B090910005) and National Natural Science Foundation of Guangdong Province (Grant No. 2016A030313465). Science and Technology Planning Project of Guangdong Province (Grant No. 2017A040405025).
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2022, Computers and Industrial EngineeringCitation Excerpt :Iterated greedy algorithm (IG) from (Riahi et al., 2020) performed well in no-idle flow line scheduling problems. Particle swarm optimization (PSO) from (Kato et al., 2018), Migrating birds optimization (MBO) from (M. Zhang et al., 2020) and Grey wolf optimizer (GWO) from (Zhu & Zhou, 2020) were effective for flexible job-shop scheduling problems. To investigate the statistical significance, a non-parametric Friedman test (L. Li et al., 2016) is conducted.