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Top1. Introduction
The body shop and paint shop for the transport producers are adaptable stream shops. The processing flow is isolated into numerous stages, and there are numerous parallel machines to handle occupations in each stage. Due to the huge volume of the buses and the long generation cycle, as it were buffers with a limited number of spaces can be conveyed within the generation line. At the same time, the transport isn't equipped with a chassis for beginning the motor within the installation workshop, and they can as it were be carried on the skids. In this manner, there's ordinarily a buffer between the body shop and paint shop, and the buffer is usually isolated into different paths for the ease of planning and operation (Ahmad et al., 2019). Each path has an equal number of spaces for the transport bodies. The transport enters the path from one side and exits the path from the other side. The flexible flow-shop scheduling problem (FFSP) is a kind of classical NP-hard problem (Khamseh, Jolai & Babaei, 2015). The limited buffer flexible flow shop scheduling problem (LBFFSP) is a kind of derivative problem of the FFSP and it has stimulated the focus of a huge number of researchers. Gerstl, Mosheiov & Sarig (2014) assumed the buffer between the stages is infinite in the classical FFSP. However, confined by the equipment, space capacity of the buffer and other factors, the middle buffer is usually limited and even doesn’t exist in lots of actual production processes in iron, chemical and pharmaceutical industries. For this reason, the study of LBFFSP has important theoretical and practical value. Wardono & Fathi (2004) used heuristic algorithm to solve the FFSP of multi-process parallel machine constrained by buffer, but this solution can only be used to solve the problem of smaller scale. Smutnicki (1998) adopted a branch-and-bound method to work out the FFSP with buffer constraints. However, the coding methods of these algorithms are not perfect, and they can only solve small-scale scheduling problems.
Last several years, increasingly new intelligent algorithms were put forward by different researchers to resolve FFSP with buffer. Gupta (1988) designed a hybrid differential evolution algorithm to figure out the FFSP with buffer constraints. In order to work out FFSP with buffer constraints a hybrid bat algorithm has adopted. Wang, Zhang & Zheng, (2006) used hybrid genetic algorithm (HGA) in dealing with this problem. To better demonstrate the effectiveness of swarm intelligence algorithm, this paper will introduce imperialist competitive algorithm (ICA) to deal with LBFFSP. The ICA algorithm is a new type of algorithm put forward by Atashpaz & Lucas, (2007) which is come from the simulation of colonial competition in human society. The ICA is highly efficient, whose biggest advantage is simple and time-saving. Recently, the ICA has been broadly utilized in numerous diverse areas. For instance, Xu, Wang & Huang (2014) used ICA algorithm in dealing with traveling salesman problem. Forouharfard & Zandieh (2010) used ICA to solve logistics programs of transfer storage. Ghasemia et al., (2014) applied ICA to multi-objective energy flow optimization problems; Zhao et al., (2020) came up with a modified imperialist competitive algorithm to evaluate the harmonic emissions in electric field systems; Chen, Li & Liu (2018) combined the ICA algorithm and the firefly algorithm (FA) and proposed an ICA-FA algorithm for solving the multi-period portfolio determination issue beneath questionable investment environment; In above studies, ICA algorithm exhibits eminent characteristics in terms of speed and getting optimal solution to the problem, so it has better optimization effect. At present, the application of ICA in scheduling optimization is still relatively small. Therefore, this paper uses the improved ICA to solve the LBFFSP and proves the superiority of the algorithm.