A genetic algorithm approach for problem

In this paper, a genetic algorithm is presented for an identical parallel-machine scheduling problem with family setup time that minimizes the total weighted flow time ( ). No set-up is necessary between jobs belonging to the same family. A set-up must be scheduled when switching from the processing of family i jobs to those of another family j, i  j, the duration of this set-up being the sequence-independent set-up time sj for family j. This problem is shown to be NP-hard in the strong sense and obtaining an optimal solution for the large-sized problems in reasonable computational time is extremely difficult. Further, it is computationally evaluated the performance of the proposed genetic algorithm solutions obtained using a mixed integer programming (MIP) with the Lingo 8.0 software.