A Novel MOEA/D for Multiobjective Scheduling of Flexible Manufacturing Systems

Algorithm 1

Algorithm DMOEA/D.

Input

: the number of sub-problems used in DMOEA/D;

: the set of uniform spread weight vectors;

H: the size of neighborhood of each weight vector;

Initialize

Set , initialize population ;

Set , , initialize , where ;

Compute the Euclidean distances between any two weight vectors and figure out the H closest ones of each weight vector;

Set , where are the H closest weight vectors to .

While(the stopping criterion is not met)

 For   

  Randomly select three different neighbors x^a, x^b, and x^c from E(j);

  Generate the mutated solution x^v from x^a, x^b, and x^c;

  Generate the trial solution x^u from x^j and x^v; Amend x^u;

  For

   If

    Set ;

   // End For

  For (each index )

   If()

    Set ; ;

   // End For

  Remove all the vectors dominated by F(x^u) from EP;

  If(there is no vector dominates F(x^u) and F(x^u) do not exist in EP)

   Add F(x^u) into EP;

  // End For

// End While

Output EP