search_better: implement an adjustable cooling parameter in the generator [big work]

[huizezhang-sherry]

The cooling parameter would ideally be adjustable based on the difference of two consecutive index_val. When the difference is large, we don't want the alpha to be adjusted by cooling by much (maybe not adjust by it at all). When the difference is small, we want a small cooling para that shrinks alpha quickly.

An initial idea about the range of the index_val is necessary so that one can determine the magnitude of the difference. Fitting distribution would be helpful to estimate the max and min of the index_val.

• Simulate basis and compute index_val via search_better()
• plot the histogram of the index_val and fit into the extreme value distributions
• calculate the index_val for the, say, n = 1,000,000 to estimate the max