A hybrid memetic algorithm for an energy-aware distributed blocking hybrid flowshop scheduling problem with transportation time

Abstract This study examines the energy-aware distributed blocking hybrid flowshop scheduling problem (DBHFSP-E) considering transportation time. A mathematical programming model is formulated to simultaneously minimize makespan and total energy consumption, and its validity is verified through the Gurobi solver. To effectively solve this complex problem, a hybrid memetic algorithm (HMA) is developed. The proposed algorithm adopts a three-layer encoding framework and integrates two complementary initialization strategies to improve population diversity and search efficiency. During the evolutionary process, several adaptive local search operators are incorporated to strengthen solution refinement. Moreover, a problem-specific energy-saving neighborhood strategy is introduced to eliminate redundant energy consumption. Computational experiments conducted on 100 benchmark instances with varying numbers of jobs, machines, and factories indicate that the proposed approach achieves competitive solution quality compared with existing state-of-the-art algorithms.