Multi-objective simulated annealing algorithm for robotic mixed-model two-sided assembly line balancing with setup times and multiple constraints

Robotic mixed-model two-sided assembly lines (RMTALs) have become increasingly prevalent in manufacturing industries for productivity enhancement. However, only limited attention has been paid to the RMTAL balancing problems that contain both setup times and multiple constraints such as positional constraints, zoning constraints, and synchronism constraints. Given the coexistence of these aspects in real-world scenarios, this study aims to address the RMTAL balancing problem with setup times and the mentioned constraints. To formulate the problem, a mixed integer programming model is proposed to optimize cycle time and total energy consumption. To handle multiple constraints and setup times, a new method based on four-vector encoding is introduced. This method addresses the three constraints during the encoding phase using four intervals and five rules, while setup times are processed during the decoding phase. To solve the problem, a Pareto entropy-based two-mode multi-objective simulated annealing algorithm is developed. The algorithm employs variable neighborhood descent algorithm with switchable objectives to generate the initial Pareto archive. Subsequently, it selects the initial solution with minimal potential in the Pareto archive, alternating between two search modes of exploration and exploitation based on the entropy difference of Pareto solutions. Comparative experiments with four state-of-the-art algorithms on benchmark instances of varying scales demonstrate that the proposed algorithm outperforms the others in over 93% of instances for the hypervolume ratio and inverted generational distance metrics.