  We introduce a weighed-loop algorithm that is applicable to any weighed graph
network. It is designed to prefer a route of energetically unfavourable bonds
in the lattice that can then be flipped without changing the structure inside
and outside the enclosed loop. Due to this property there are effectively no
energy barriers thus making this algorithm very suitable for finding low energy
states in very rough energy landscapes. We apply this algorithm to the random
bond Ising model with domain walls and show that the weighed-loop algorithm can
outperform Niedermayer's algorithm for low enough temperatures and high enough
disorder. We consolidate the high-temperature behaviour of the roughness of a
domain-wall with a low-temperature expansion presented in this paper and show
agreement with results from our simulations. The effects of temperature,
disorder, and system size on the roughness of domain-walls is also
investigated.
