Kriging-Based Space Exploration Global Optimization Method in Aerodynamic Design
Algorithm 1
The encoding type of KSE.
The KSE for Global Optimization
Input: (1) original design space ;
(2) global exploration iteration number ;
(3) cluster number , cluster radius ;
(4) maximum iteration number ;
(5) : EI function;
(6) threshold of RMSE:
Output: the best solution as global optima ;
Begin
Choose an initial set of sample points by LHS sampling method.
Evaluate to obtain the corresponding response , and store them in the database .
While
for
Employ EGO algorithm with ;
Store the optimized solution and its function response value in the database ;
;
end
Select clusters from database , and identify the cluster center , other sample points within the distance , would be classified into the corresponding cluster . The distance between sample points with cluster center was computed by Euclidean distance.
for
Sort all sample points of in terms of their function response value in ascending order;
Use Cross-validation to obtain the predicted value of all sample points;
;
if
Store into fully explored local minima dataset ;
else
Store into partially explored local minima dataset ;
end
end
if
for
Define local space centered at by the ETRM algorithm;
Employ EGO algorithm with in ;
Store the optimized solution and its function response value in the database ;
