The permutation flowshop sequencing problem (PFSP) is a well-known scheduling problem that can be described as follows: a set J of k-independent jobs has to be processed on a set M of machine m-independent machines. Each job j ∈ J requires a given fixed processing time math Pij ≥ 0 on each. Iterated Local Search Method :

• Starts from a locally optimum.
• Perturbs the solution to escape local optima.
• Uses a Local Search method to find the new local optima.
• Accepts non improving solutions along the process. The stopping criterion can be reaching a maximum number of iterations is achieved, or a maximum CPU time is reached, or a maximum number of non-improvements is reached. in our case we choose the number of iterations.

(1) Generate an Initial Solution => (2) Apply a Local Search on that Solution => (3) Perturbe that solution => (4) Apply for the second time Local Search => Test the solution.