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A Variable Block Insertion Heuristic for Solving Permutation Flow Shop Scheduling Problem with Makespan Criterion

1
Department of Industrial Engineering, Yasar University, Izmir 35100, Turkey
2
Department of Industrial and System Engineering, Istinye University, Istanbul 34010, Turkey
3
Department of Industrial and Manufacturing System Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
4
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(5), 100; https://doi.org/10.3390/a12050100
Received: 8 April 2019 / Revised: 3 May 2019 / Accepted: 6 May 2019 / Published: 9 May 2019
(This article belongs to the Special Issue Metaheuristic Algorithms in Optimization and Applications (volume 2))
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Abstract

In this paper, we propose a variable block insertion heuristic (VBIH) algorithm to solve the permutation flow shop scheduling problem (PFSP). The VBIH algorithm removes a block of jobs from the current solution. It applies an insertion local search to the partial solution. Then, it inserts the block into all possible positions in the partial solution sequentially. It chooses the best one amongst those solutions from block insertion moves. Finally, again an insertion local search is applied to the complete solution. If the new solution obtained is better than the current solution, it replaces the current solution with the new one. As long as it improves, it retains the same block size. Otherwise, the block size is incremented by one and a simulated annealing-based acceptance criterion is employed to accept the new solution in order to escape from local minima. This process is repeated until the block size reaches its maximum size. To verify the computational results, mixed integer programming (MIP) and constraint programming (CP) models are developed and solved using very recent small VRF benchmark suite. Optimal solutions are found for 108 out of 240 instances. Extensive computational results on the VRF large benchmark suite show that the proposed algorithm outperforms two variants of the iterated greedy algorithm. 236 out of 240 instances of large VRF benchmark suite are further improved for the first time in this paper. Ultimately, we run Taillard’s benchmark suite and compare the algorithms. In addition to the above, three instances of Taillard’s benchmark suite are also further improved for the first time in this paper since 1993. View Full-Text
Keywords: heuristic optimization; block insertion heuristic; flow shop scheduling; iterated greedy algorithm; constraint programming; mixed integer programming heuristic optimization; block insertion heuristic; flow shop scheduling; iterated greedy algorithm; constraint programming; mixed integer programming
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Kizilay, D.; Tasgetiren, M.F.; Pan, Q.-K.; Gao, L. A Variable Block Insertion Heuristic for Solving Permutation Flow Shop Scheduling Problem with Makespan Criterion. Algorithms 2019, 12, 100.

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