  We propose a new implementation of the replica-exchange method (REM) in which
replicas follow a pre-planned route in temperature space instead of a random
walk. Our method satisfies the detailed balance condition in the proposed
route. The method forces tunneling events between the highest and lowest
temperatures to happen with an almost constant period. The number of tunneling
counts is proportional to that of the random-walk REM multiplied by the square
root of moving distance in temperature space. We applied this new
implementation to two kinds of REM and compared the results with those of the
conventional random-walk REM. The test system was a two-dimensional Ising
model, and our new method reproduced the results of the conventional
random-walk REM and improved the tunneling counts by three times or more than
that of the random-walk REM.
