Research Article

Biological Flower Pollination Algorithm with Orthogonal Learning Strategy and Catfish Effect Mechanism for Global Optimization Problems

Algorithm 1

OL strategy.
Input
 Number of factors ( = ) and number of levels ( = 3).
 Three individuals: , , .
 Objective function (solution) of minimization or maximization problems.
 Number of fitness evaluations FEs = 0.
Output
 OL result.
Begin
% Construct the OA based on and .
 Compute the minimum integer that satisfies ()/() = , then .
 Construct an OA based on [24].
% Compute the value of each level at each dimension by using (10).
For
   = = ; = .
End for
 Generate solutions based on .
 The solution vectors are formulated as Equation (11).
 % Evaluate the solutions with objective function.
 The results are: .
% Accumulate the number of fitness evaluations.
 FEs = FEs + .
 % Choose the best solution .
=   or  .
 % Compute the average effect of each level at each dimension  .
For
 % Find the row index that having the same level at dimension d based on OA.
 % Compute the mean value of fitness results according to the index vector.
  Index_1 = find (OA(:, ) == 1), = mean((Index_1));
  Index_2 = find (OA(:, ) == 2), = mean((Index_2));
  Index_3 = find (OA(:, ) == 3), = mean((Index_3));
  Compare , , , select the most beneficial level at dimension .
End for
 Construct by combining all the most beneficial level values .
 Compare and , and choose the best one as the OL result.
End