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Algorithms 2016, 9(4), 71; https://doi.org/10.3390/a9040071

# A Variable Block Insertion Heuristic for the Blocking Flowshop Scheduling Problem with Total Flowtime Criterion

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International Logistics Management Department, Yasar University, Izmir 35100, Turkey
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Department of Industrial and Manufacturing System Engineering, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Industrial Engineering Department, Yasar University, Izmir 35100, Turkey
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School of Electrical and Electronics, Nanyang Technological University, Singapore 639798, Singapore
*
Author to whom correspondence should be addressed.
Academic Editor: Javier Del Ser Lorente
Received: 30 June 2016 / Revised: 1 October 2016 / Accepted: 8 October 2016 / Published: 20 October 2016
(This article belongs to the Special Issue Metaheuristic Algorithms in Optimization and Applications)

# Abstract

In this paper, we present a variable block insertion heuristic (VBIH) algorithm to solve the blocking flowshop scheduling problem with the total flowtime criterion. In the VBIH algorithm, we define a minimum and a maximum block size. After constructing the initial sequence, the VBIH algorithm starts with a minimum block size being equal to one. It removes the block from the current sequence and inserts it into the partial sequence sequentially with a predetermined move size. The sequence, which is obtained after several block moves, goes under a variable local search (VLS), which is based on traditional insertion and swap neighborhood structures. If the new sequence obtained after the VLS local search is better than the current sequence, it replaces the current sequence. As long as it improves, it keeps the same block size. However, if it does not improve, the block size is incremented by one and a simulated annealing-type of acceptance criterion is used to accept the current sequence. This process is repeated until the block size reaches at the maximum block size. Furthermore, we present a novel constructive heuristic, which is based on the profile fitting heuristic from the literature. The proposed constructive heuristic is able to further improve the best known solutions for some larger instances in a few seconds. Parameters of the constructive heuristic and the VBIH algorithm are determined through a design of experiment approach. Extensive computational results on the Taillard’s well-known benchmark suite show that the proposed VBIH algorithm outperforms the discrete artificial bee colony algorithm, which is one of the most efficient algorithms recently in the literature. Ultimately, 52 out of the 150 best known solutions are further improved with substantial margins. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

# Supplementary material

MDPI and ACS Style

Tasgetiren, M.F.; Pan, Q.-K.; Kizilay, D.; Gao, K. A Variable Block Insertion Heuristic for the Blocking Flowshop Scheduling Problem with Total Flowtime Criterion. Algorithms 2016, 9, 71.

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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