On the practical importance of asymptotic optimality in certain heuristic algorithms

This article presents an informal discussion of the issue of asymptotic optimality of heuristics from the viewpoint of the operations research practitioner. It is suggested that certain heuristics belonging to the above class are likely to perform questionably in practice, with regard both t o relative error and t o computational tractability. Possible explanations of this phenomenon are offered and suggestions for further research toward a better understanding of this problem are presented.