# Mathematical models and migrating birds optimization for robotic U-shaped assembly line balancing problem

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## Abstract

Modern assembly line systems utilize robotics to replace human resources to achieve higher level of automation and flexibility. This work studies the task assignment and robot allocation in a robotic U-shaped assembly line. Two new mixed-integer programming linear models are developed to minimize the cycle time when the number of workstations is fixed. Recently developed migrating birds optimization algorithm is employed and improved to solve large-sized problems. Problem-specific improvements are also developed to enhance the proposed algorithm including modified consecutive assignment procedure for robot allocation, iterative mechanism for cycle time update, new population update mechanism and diversity controlling mechanism. An extensive comparative study is carried out to test the performance of the proposed algorithm, where seven high-performing algorithms recently reported in the literature are re-implemented to tackle the considered problem. The computational results demonstrate that the developed models are capable to achieve the optimal solutions for small-sized problems, and the proposed algorithm with these proposed improvements achieves excellent performance and outperforms the compared ones.

## Keywords

Robotic U-shaped assembly line Integer programming Migrating birds optimization Artificial intelligence## Notes

### Acknowledgements

The first author acknowledges the financial support from the National Natural Science Foundation of China under Grant 61803287 and China Postdoctoral Science Foundation under grant 2018M642928.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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