sufficiently large to allow moves will result in configurations where the constraints are poorly satisfied.

We overcome this difficulty by regarding $T^*$ as a parameter (taking the place of $\lambda$) and by adiabatically varying $T^*$ from zero (where the constraints are satisfied but MTS is ineffective at making moves) to a finite value (where the constraints are relaxed and MTS becomes effective) and back to zero again (to reimpose the constraints). During the course of changing $T^*$, we make $n$ $E_\mathrm h$ moves (each with the instantaneous value of $T^*$). The effect of these $n$ moves will be an $E_\mathrm h$ move with $T^* = 0$, i.e., a move which satisfies the $E_\mathrm h$ constraint.

It remains to give a recipe for varying $T^*$. As we vary $T^*$, we would naturally adjust the step size for the moves in such a way that the number of steps needed to equilibrate the system is a constant, suggesting that we vary $T^*$ exponentially. We therefore pick $$T^*_i = \left\{
\begin{array}{l@{\hspace{1em}}l}
T^*_A \exp(\alpha (i - 1)), & \mbox{for $0 < i \le m$},\\
T^*_A \exp(\alpha (n - i)), & \mbox{for $m < i \le n$},
\end{array}\right.$$ where we have taken $n = 2m 