The functions ϕ C (x C ) can be regarded as penalization factors that decrease the joint probability of a hypothesized state if it involves an unexpected relations among targets.
And it is found that the existing qp-relaxation stress interpolation scheme to resolve the singularity issue in TO just shows the local optima issue in reinforcement TO design with different penalization factors in Solid Isotropic Material with Penalization (SIMP).
This variability is thought to be caused by inadequacies of the individual distance measures (Pettitt et al., 2005), but it may also reflect subtle dependencies between a scoring function and the particular distance measure used (such as similar penalization factors for incomplete models).
While models of this complexity are reasonable given the large sample size, in order to obtain more stable and smoother estimates, we used a ridge-regression penalization approach with the penalty factor chosen to optimize the 'corrected Akaike Information Criterion' (Harrell, 2001).
Our method can therefore overcome those computational complexity issues, and identify complex interactions (between two or more factors) that contribute to the response model, at varying degrees of sparsity (controlled by the penalization component).
We used L2 penalization (penalizing the squared norm of the parameter vector).
