Efficient Conical Area Differential Evolution with Biased Decomposition and Dual Populations for Constrained Optimization

Algorithm 1

The framework of CADE.

  Input:  : the size of feasible sub-population P1; : the size of conical sub-population P2;

       : the maximum number of function evaluations;

       : the adaptive parameter to choose the operation to generate a child;

       : the parameter control the individuals of P2 to generate an offspring.

  Output:   :the best solution in the final population.

1  ; ;

2  ; ;

3 Create initial solutions by uniformly randomly sampling from the decision space ;

4  where , ;

5   ;

6  Rank the rest individuals through the tolerance-based sorting to form P1;

7  Group P1 into levels in sequence;

8  while    do

9      ;

10    Update ;

11    if is successfully updated and   then

12      Group the individuals in P1 through the tolerance-based sorting;

13    end

14    ;

15    ;

16     if   mod   then

17        Update and ;

18       if    then

19       Update ;

20      end

21      end

22  end

23  return