A modified teaching–learning-based optimisation algorithm for bi-objective re-entrant hybrid flowshop scheduling

Abstract

In this paper, a modified teaching–learning-based optimisation (mTLBO) algorithm is proposed to solve the re-entrant hybrid flowshop scheduling problem (RHFSP) with the makespan and the total tardiness criteria. Based on the simple job-based representation, a novel decoding method named equivalent due date-based permutation schedule is proposed to transfer an individual to a feasible schedule. At each generation, a number of superior individuals are selected as the teachers by the Pareto-based ranking phase. To enhance the exploitation ability in the promising area, the insertion-based local search is embedded in the search framework as the training phase for the TLBO. Due to the characteristics of the permutation-based discrete optimisation, the linear order crossover operator and the swap operator are adopted to imitate the interactions among the individuals in both the teaching phase and the learning phase. To store the non-dominated solutions explored during the search process, an external archive is used and updated when necessary. The influence of the parameter setting on the mTLBO in solving the RHFSP is investigated, and numerical tests with some benchmarking instances are carried out. The comparative results show that the proposed mTLBO outperforms the existing algorithms significantly.

Keywords:

• re-entrant hybrid flowshop scheduling
• bi-objective
• teaching–learning-based optimisation
• decoding method

Acknowledgements

The authors would like to thank Professor Cho HM and Professor Ying KC for providing us the benchmarking instances.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by National Science Fund for Distinguished Young Scholars of China [grant number 61525304]; the National Science Foundation of China [grant number 61174189]; the Doctoral Program Foundation of Institutions of Higher Education of China [20130002110057].