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

Abstract

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.