How to decide upon stopping a heuristic algorithm in facility-location problems?

Abstract

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. In this paper we compare the methods proposed previous literate of estimating minimum, and propose some thought of it.