Methods and guidelines for effective model calibration

Alternative Optimization Algorithm
Presently used alternative algorithms for the minimization of the least-squared objective 
function with respect to parameter values include adjoint-state methods (as used by, for example, 
Carrera and Neuman, 1986; Xiang and others, 1992; Tarantola, 1994), and global optimization 
methods such as simulated annealing, genetic algorithms (Wagner, 1995), and tabu search (Zheng 
and Wang, 1996). In adjoint-state methods, the derivative of the objective function with respect to 
the parameter values is calculated and can be used instead of the composite scaled sensitivities. 
There are no replacements for the one-percent and dimensionless scaled sensitivities and the pa-
rameter correlations in the adjoint-state method. It is not uncommon, however, for adjoint-state al-
gorithms also to be programmed to calculate the sensitivities and variance-covariance matrix on 
the parameters as discussed above, in which case the guidelines apply directly.
Global optimization methods are most useful for problems with very irregular objective 
function surfaces that are not amenable to the much more numerically efficient gradient search 
methods, such as modified Gauss-Newton or adjoint states. For problems with such irregular ob-
jective functions, scaled sensitivities, composite scaled sensitivities, and parameter correlation co-
efficients are likely to change values so dramatically as parameter values change that they would 
be worthless. Other aspects of the guidelines, however, would still be applicable.
Alternative Objective Functions
The primary alternative to the least-squares objective function is the sum of the absolute 
values of weighted residuals. Minimizing this objective function requires methods that do not use 
sensitivities or derivatives of the objective function, so that there are no scaled sensitivities, com-
posite scaled sensitivities, or parameter correlation coefficients. As with adjoint states, however, 
the algorithms developed for this objective function also have been programmed to calculate sen-
sitivities, so that, again, the guidelines would apply directly.