Bi-objective mathematical model and improved algorithm for optimisation of welding shop scheduling problem

Abstract

This paper addresses a bi-objective welding shop scheduling problem (BWSSP) aiming to minimise the total tardiness and the machine interaction effect. The BWSSP is a special flow-shop scheduling problem (FSP) which is characterised by the fact that more than one machine can process on one job at a certain stage. This study analyses the operation of a structural metal manufacturing plant, and includes various aspects such as job sequence, machine-number-dependent processing time, lifting up time, lifting down time and different delivery time. A novel mixed-integer programming model (MIPM) is established, which can be used to minimise the delayed delivery time and the total machine interaction effect. One machine interaction effect formula is given in this paper. In order to solve this BWSSP, an appropriate non-dominated sorting Genetic Algorithm III (NSGAIII), embedded with a restarted strategy (RNSGAIII), is proposed. The restarted strategy, which can increase the diversity of the solutions, will be triggered with a restart probability. Following the iterative process, an effective strategy is applied to reduce the interaction effect penalty, on the premise that the makespan will remain unchanged. Total five algorithms, namely NSGAII, NSGAIII, harmony search algorithm (HSA), strength Pareto evolutionary algorithm (SPEA2), and RNSGAIII are utilised to solve this engineering problem. Numerical simulations show that the improved RNSGAIII outperforms the other methods, and the Pareto solution distribution and diversity, in particular, are significantly improved.

Keywords:

• welding flow-shop scheduling problem
• non-dominated sorting Genetic Algorithm III
• total tardiness
• machine interaction effect
• setup time

Acknowledgements

In addition, this paper follows the GWO algorithm developed in the paper (Meng, Rao, and Luo 2019), which is the related work of our research team. We gratefully acknowledge all supports that have been provided for this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed at https://doi.org/10.1080/00207543.2019.1656837.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 51675206]; the open fund project of the Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance [grant number 2017KJX10]; and the new intelligent manufacturing models for rail transit shield machine funded by Ministry of Industry and Information Technology of China.