The main dividing word here is "solve". The harmony search method will probably never be able to compete at all with modern divide-and-conquer methods (like branch-and-cut and the like), but may be able to find near-optimal solutions in some cases (while not being able to prove whether it is a near-optimal one or not.) One bug with these is that there is almost never a measure of non-optimality - which typically the theoretically solid B&B methods will give you (through, for example local lower bounds), and that is a very important point that often is neglected in the heuristic fora.
This particular algorithm has been strongly criticised by other researchers (alongside many other so called "nature-inspired algorithms").
The first paper I linked to proposes some convincing arguments that harmony search is a special case of evolutionary strategy. The second is a general criticism of metaphor based metaheuristics.
Article A critical analysis of the harmony search algorithm—How not ...