This book contains some aspects of flow shop scheduling problems including sequence dependent set up time with minimization of multi-criteria fitness function.There are different criteria's which have to be optimized for the customer and industrial requirement. The present work dealt with multi-criteria fitness function which includes weighted sum of total weighted squared tardiness, Makespan, Total weighted earliness and number of tardy jobs.Multi-criteria fitness function is very difficult to be optimised as there is tradeoff between different criteria. Metaheuristic like genetic algorithm and simulated annealing is a powerful techniques for the solution of such type of scheduling problems. Hybridization of different metaheuristic such as Genetic algorithm and simulated annealing has also been proposed for such type of scheduling problems. These metaheuristics tested proves to be powerful methods for solution to these type of NP hard problems in a reasonable time.