A Multiobjective Optimization Approach to Solve a Parallel Machines Scheduling Problem

Algorithm 2

Structure of the SPEA-II algorithm [26].

(1) Generate an initial population 𝑃_𝑡 and an empty Pareto archive 𝑄_𝑡, set 𝑡 to 0

(2) Evaluate all the solutions in 𝑃_𝑡 and 𝑄_𝑡

(3) Find the non dominated solutions between 𝑃_𝑡 and 𝑄_𝑡. If there are too many non dominated

 solutions for the archive, calculate the distance σ of the solutions, we only kept the best solutions

 with a decreasing order of distance 𝜎. In contrary, if there are not enough non dominated solutions in

 the archive, the best dominated solutions must be filled in the archive till this archive is full

(4) If the stopping criteria is satisfied, then stop the algorithm and export the non dominated

 solutions in the Pareto archive as the result

(5) The operators of selection, crossover and mutation are applied for the new population 𝑃_𝑡+1, and

 then return to step (2)