# Development and Analysis of a Discrete Particle Swarm Optimisation for Bi-criteria Scheduling of a Flow Shop with Sequence-Dependent Setup Time

## Abstract

Most studies in flow shop scheduling neglect the setup times or consider the setup times along with the processing times. However, in industries that manufacture paint, textiles, ceramic tiles, etc., the setup times are significant and are sequence dependent. This paper addresses the problem of scheduling a flow shop operating in a sequence-dependent setup time (SDST) environment considering the objectives, namely minimisation of makespan and mean tardiness. The evolutionary method of discrete particle swarm optimisation (DPSO) based on weighted approach is developed and applied to SDST benchmark problems of flow shop scheduling. The efficacy of the metaheuristic is compared with that of a hybrid genetic algorithm, and it is observed that on an average, the proposed DPSO provides an improvement of 7.8, 22.3 and 11.3% in the values of mean ideal distance, computational time and diversification matrix, respectively. For most problems, the proposed DPSO performs superior to the hybrid genetic algorithm.

## Keywords

Permutation flow shop Sequence-dependent setup time Discrete particle swarm optimisation Hybrid genetic algorithm## Notes

### Acknowledgements

The authors express their sincere thanks to the reviewers for their suggestions which helped in improving the initial version of the paper.

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