Minimizing the energy consumption and the total weighted tardiness for the flexible flowshop using NSGA-II and NRGA

This paper presents a bi-objective MIP model for the flexible flow shop scheduling  problem (FFSP) in which the total weighted tardiness and the energy consumption are minimized simultaneously. In addition to considering unrelated machines at each stage, the set-up times are supposed to be sequence- and machine-dependent, and it is assumed that jobs have different release times. Two Taguchi-based-tuned algorithms: (i) non-dominated sorting genetic algorithm II (NSGA-II), and (ii) non-dominated ranked genetic algorithm (NRGA) are applied to solve themodel. Six numerical examples with different sizes (small, medium, and large) are used to demonstrate the applicability and to exhibit the efficacy of the algorithms. The results show that the NRGA outperforms significantly the NSGA-II in the performance metrics for all six numerical examples.