Research Article

Morphing Wing Structural Optimization Using Opposite-Based Population-Based Incremental Learning and Multigrid Ground Elements

Algorithm 3

Procedure for OMPBIL.
Initialization Probability matrix , opposite probability matrix , external Pareto archive Pareto = .
(1) Generate a binary population from .
(2) Decode the binary population to be and find the objective values .
(3) Update Pareto by replacing it with the non-dominated solutions of a union set Pareto    .
(4) If the number of members in Pareto exceeds the predefined archive size , remove some of them by using an archiving
technique.
(5) If the termination criterion is fulfilled, stop the procedure. Otherwise, go to step 6:
(6) Update and create a binary population
(6.1) Set a binary population .
(6.2) For = 1 to .
   (6.2.1) Select binary solutions from Pareto randomly.
   (6.2.2) Find using (4).
   (6.2.3) Update the th row of by using (3).
   (6.2.4) Compute and generate the th row of the opposite probability matrix using (9).
   (6.2.5) Generate rand a uniform random number.
   (6.2.6) If rand < the predefined mutation probability, update the th row of and using (5).
   (6.2.7) Generate binary subpopulations and from the th row of and respectively.
   (6.2.8) Set
(6.3) Next .
(7) Go to step 2.