A Multi-objective Immune System for a New Bi-objective Permutation Flowshop Problem with Sequence-dependent Setup Times

We present a new mathematical model for a permutation flowshop scheduling problem with sequence-dependent setup times considering minimization of two objectives, namely makespan and weighted mean total earliness/tardiness. Only small-sized problems with up to 20 jobs can be solved by the proposed integer programming approach. Thus, an effective multi-objective immune system (MOIS) is specially proposed to solve the given problem. Finally, the computational results are reported showing that the proposed MOIS is effective in finding solutions of large-sized problems.