Mathematical model and grey wolf optimization for low-carbon and low-noise U-shaped robotic assembly line balancing problem

Abstract

Since the industrial robots are incrementally utilized in U-shaped assembly lines to replace operators, the focus of these lines is not only on productivity improvement, but also more on the carbon and noise emissions. Hence, this paper proposes a novel multi-objective mixed integer non-linear model to minimize carbon emission, noise emission and cycle time concurrently. In this model, quantifying carbon emission and noise emission is achieved respectively via presentations connected with processing time of tasks and robots. Existing general constraints of precedence relationship are readjusted into a novel integrated formula so as to remove worthless equations and improve computational efficiency. Besides, Hybrid Pareto Grey Wolf Optimization (HPGWO) is designed to solve the multi-objective balancing problems. This algorithm proposes a novel code to initialize the wolves and designs two new searching methods to update the position of wolf. Simultaneously, two crossover operators are designed to enhance the communication between the low-grade wolves. Finally, the proposed algorithm is compared with five other well-known multi-objective algorithms and the results indicate that the proposed algorithm outperforms these compared algorithms in the evaluation metrics of the inverse generation convergence (IGD), maximum spread (MS) and hypervolume ratio (HVR). That is, our proposed algorithm can achieve the trade-off in reducing carbon and noise emission and minimizing cycle time.