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.