Consider again the scales balancing problem
described in Section .
I.e., we are given a set of n weights,
,
which are to be placed on a pair of scales in the way that
minimizes the difference between the total weight in each pan.
Feasible solution to the problem all have the form
,
where
To solve this problem using simulated annealing, we need a strategy for generating random moves. The move generator should make small, random changes to the current solution and it must ensure that all possible solutions can be reached. A simple approach is to use the formula
where is the initial solution,
is a new solution,
is a sequence of zeroes and ones
generated randomly,
and
denotes elementwise addition modulo two.