Energy-efficient multi-objective scheduling algorithm for hybrid flow shop with fuzzy processing time

Increasing costs of energy and environmental pollution is prompting scholars to pay close attention to energy-efficient scheduling. This study constructs a multi-objective model for the hybrid flow shop scheduling problem with fuzzy processing time to minimize total weighted delivery penalty and total energy consumption simultaneously. Setup times are considered as sequence-dependent, and in-stage parallel machines are unrelated in this model, meticulously reflecting the actual energy consumption of the system. First, an energy-efficient bi-objective differential evolution algorithm is developed to solve this mixed integer programming model effectively. Then, we utilize an Nawaz-Enscore-Ham-based hybrid method to generate high-quality initial solutions. Neighborhoods are thoroughly exploited with a leader solution challenge mechanism, and global exploration is highly improved with opposition-based learning and a chaotic search strategy. Finally, problems in various scales evaluate the performance of this green scheduling algorithm. Computational experiments illustrate the effectiveness of the algorithm for the proposed model within acceptable computational time.