Mathematical model and bee algorithms for mixed-model assembly line balancing problem with physical human–robot collaboration

The collaboration of human workers and robots draws increasing attention from the manufacturing enterprises to embrace the Industry 4.0 paradigm in a competitive way. Motivated by the requirements of collaboration between human workers and robots in assembly lines, this study investigates the mixed-model assembly line balancing (MMALB) problem with the collaboration between human workers and robots. A mixed-integer linear programming (MILP) model is formulated to tackle the small-size problems optimally to minimize the sum of cycle times of models. Also, bee algorithm (BA) and artificial bee colony (ABC) algorithm are implemented and improved to solve the large-size problems due to the NP-hardness of this problem. The proposed BA algorithm utilizes a new employed bee phase to accelerate the evolution of the swarm and new scout phase to escape from being trapped into local optima and produce a high-quality and diverse population. The developed ABC proposes a new onlooker phase to accelerate the evolution of the whole swarm by removing the poor-quality solutions, new scout phase to achieve high-quality solutions while preserving the diversity of the swarm, and local search to enhance exploitation capacity. Computational study on a set of generated instances indicates that the improvements enhance the BA and ABC algorithm by a significant margin, and the proposed BA and ABC algorithm achieve competing performance in comparison with nine other algorithms, including the late acceptance hill-climbing algorithm, simulated annealing algorithm, genetic algorithm, particle swarm optimization algorithm, discrete cuckoo search algorithm, the original bee algorithm, and three artificial bee colony algorithms.