Optimization of load of structure in order to obtain desired shape of letter T (formulation for maximization) 

Optimization of testing example (formulation for maximization) 




1  Create_initial_neurons(); 
2  while (stopping criteria) { 
3  Create_network(); 
4  GRADE(); 
5  Update_network(); } 
1  void Create_network(void) { 
2  y = y  Linear_regression_part; 
3  dmax = sqrt(n_dimension); 
4  r = (dmax*(n_dimension*n_neurons)^(1/n_dimension))^2; 
5  for ( i=0; i<n_neurons; i++ ) { 
6  for ( j=0; j<n_neurons; j++ ) { 
7  basis_functions(i,j) = exp( (sum((points(i)points(j)).^2)) / r) }}; 
8  y = basis_function*weights; } 
parameter  description  default value 

nstep  number of RBFN improvements  300 
lambda  regularization factor  0.0000001 
GRBFN  GRBFN regpoly0  GRBFN regpoly1  
Function  Dim  Optimum  Precission  SR  ANFC  SR  ANFC  SR  ANFC 
F1  1  1.12323  0.011232  100  23  100  28  100  28 
F3  1  12.0312  0.120312  100  43  100  45  100  46 
Branin  2  0.39789  0.003979  100  51  100  24  100  62 
Camelback  2  1.03163  0.010316  100  61  100  50  100  54 
Goldprice  2  3  0.03  100  217  100  397  53  725 
PShubert1  2  186.731  1.867309  78  573  96  547  78  579 
PShubert2  2  186.731  1.867309  98  540  0    0   
Quartic  2  0.35239  0.003524  56  83  100  103  100  88 
Shubert  2  186.731  1.867309  100  499  100  500  100  513 
Hartman1  3  3.86278  0.038678  100  34  100  38  100  45 
Shekel1  4  10.1532  0.101532  0    0    0   
Shekel2  4  10.4029  0.104029  0    0    0   
Shekel3  4  10.5364  0.105364  0    0    0   
Hartman2  6  3.32237  0.033224  100  130  0    0   
Hosc45  10  1  0.01             
Brown1  20  2  0.02             
Brown3  20  0  0.1             
F5n  20  0  0.1             
F10n  20  0  0.1             
F15n  20  0  0.1             
[1] 
BlackBox Function Optimization using Radial Basis Function Networks,
Proceedings of the Eighth International Conference on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering,
2005 PDF (375kB) 
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[2] 
Identification of nonlinear mechanical model parameters based on softcomputing methods,
Ph.D. thesis, Ecole Normale Supérieure de Cachan, Laboratoire de Mécanique et Technologie,
2007, PDF (5.03MB), prezentation (4.55MB), BiBTeX entry 
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[3] 
Novel anisotropic continuumdiscrete damage model capable of representing localized failure of massive structures. Part II: identification from tests under heterogeneous stress field.
Engineering Computations.
(2009), accepted for publication, eprint: arXiv:0902.1665 
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