In practice, the simplex algorithm is quite efficient and can be guaranteed to find the global optimum if certain precautions against "cycling" are taken.
Although this technique is computationally expensive, its guarantee of a global optimum solution is useful in cases where only a few sequences need to be aligned accurately.
With ligands having up to 15-20 degrees of freedom (freely rotatable bonds) and complex nature of energy surface, global optimum search represents generally unsolved scientific task.