# Metaheuristics for solving a multi-objective flow shop scheduling problem with sequence-dependent setup times

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## Abstract

Industries such as textiles, paints, chemicals, paper, drugs and pharmaceuticals operate as flow shops with sequence-dependent setup times (SDST). The sequence-dependent setup environment is characterised by the dependence of the setup time on the current job and also on the previous job processed on that machine. To further complicate the problem, in most real-life scenarios, decision-makers have to optimise more than one performance measure while scheduling jobs on machines. This work considers such a multi-objective SDST flow shop environment. The objectives considered in the present study are minimisation of makespan and minimisation of mean tardiness. Four metaheuristics, viz. non-dominated sorting genetic algorithm (NSGA) II, hybrid NSGA II, discrete particle swarm optimisation and hybrid discrete particle swarm optimisation, belonging to the category of intelligent optimisation techniques, are developed to obtain a set of Pareto-optimal solutions. The proposed metaheuristics are applied on benchmark SDST flow shop problems and their performance compared using different measures. Analysis of the results reveals that hybrid NSGA II outperforms the other three algorithms for all problem sizes considered in the present research. The results also indicate that hybridisation of the metaheuristics with variable neighbourhood search improves their performance.

## Keywords

Permutation flow shop Sequence-dependent setup time NSGA II Discrete particle swarm optimisation Variable neighbourhood search## Notes

### Acknowledgements

The authors are most grateful to the reviewers, the associated editor and the editor-in-chief for their supportive and constructive comments.

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