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Mathematical Problems in Engineering
Volume 2016, Article ID 1257060, 11 pages
Research Article

A Pareto-Based Adaptive Variable Neighborhood Search for Biobjective Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup Time

1School of Electrical Engineering & Automation, Tianjin Polytechnic University, Tianjin, China
2School of Management, Tianjin Polytechnic University, Tianjin, China
3Guangxi Colleges and University Key Laboratory of Minerals Engineering, Guangxi University, Guangxi, China

Received 29 December 2015; Revised 7 September 2016; Accepted 12 October 2016

Academic Editor: Yan-Jun Liu

Copyright © 2016 Huixin Tian et al. 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.


Different from most researches focused on the single objective hybrid flowshop scheduling (HFS) problem, this paper investigates a biobjective HFS problem with sequence dependent setup time. The two objectives are the minimization of total weighted tardiness and the total setup time. To efficiently solve this problem, a Pareto-based adaptive biobjective variable neighborhood search (PABOVNS) is developed. In the proposed PABOVNS, a solution is denoted as a sequence of all jobs and a decoding procedure is presented to obtain the corresponding complete schedule. In addition, the proposed PABOVNS has three major features that can guarantee a good balance of exploration and exploitation. First, an adaptive selection strategy of neighborhoods is proposed to automatically select the most promising neighborhood instead of the sequential selection strategy of canonical VNS. Second, a two phase multiobjective local search based on neighborhood search and path relinking is designed for each selected neighborhood. Third, an external archive with diversity maintenance is adopted to store the nondominated solutions and at the same time provide initial solutions for the local search. Computational results based on randomly generated instances show that the PABOVNS is efficient and even superior to some other powerful multiobjective algorithms in the literature.