The Metropolis choice is to maximize the \( A \) values, that is $$ A_{j \rightarrow i} = \min \left ( 1, \frac{p_iT_{i\rightarrow j}}{ p_jT_{j\rightarrow i}}\right ). $$ Other choices are possible, but they all correspond to multilplying \( A_{i\rightarrow j} \) and \( A_{j\rightarrow i} \) by the same constant smaller than unity.\footnote{The penalty function method uses just such a factor to compensate for \( p_i \) that are evaluated stochastically and are therefore noisy.}