A Multiobjective Optimization Approach to Solve a Parallel Machines Scheduling Problem

Algorithm 1

Structure of the NSGA-II algorithm [25].

(1) Generate the initial population 𝑃_𝑡 of size 𝑛𝑠

(2) Evaluate these solutions

(3) Sort these solutions by non domination and crowding distance

(4) Creation of the offspring population 𝑄_𝑡 with the operators of selection, crossover and mutation

(5) Evaluate all solutions

(6) Sort the solutions of two populations: 𝑃_𝑡 and 𝑄_𝑡

(7) Choose the best solutions for the new population 𝑃_𝑡 with the remaining steps (ranking into non

 dominated front, crowding distance)

(8) If the stopping criteria is satisfied then the algorithm is stopped, the obtained results are all the

 solutions in the first non dominated front; repeat steps (4) to (7) otherwise