Research on low-carbon scheduling method for high-dimensional multi-objective flexible job shop improved by NSGA-III

Aiming at the flexible job shop scheduling problem considering low-carbon indicators, a high-dimensional multi-objective flexible job shop low-carbon scheduling (MaOFJLCSP) mathematical model with carbon emissions, machine energy consumption, completion time, and machine load as optimization objectives was established. In view of the problems that NSGA-III has poor initial solution quality and is easy to fall into local optimality when solving the above model, an improved NSGA-III (NSGA-III-HD) is proposed. Firstly, a real number encoding mechanism based on chaos mapping is proposed, and on this basis, cubic chaos mapping is introduced to initialize the population and improve the quality of the initial population. Secondly, a selection strategy for multi-population elite storage is designed to avoid the algorithm falling into the local optimum also enriches the diversity of the population. Finally, the analytic hierarchy process and the approximate ideal solution method (AHP-TOPSIS) are integrated to select a more comprehensive and accurate scheduling plan. The improved algorithm was verified and compared through the benchmark test case Brandimarte data set and instance data. The results show that NSGA-III-HD has high superiority in solving MaOFJLCSP.