An empirical investigation of the effectiveness of a vertex substitution heuristic

Many problems require the identification of a subset of points to minimize (or maximize) some function. A vertex substitution heuristic (VSH) employs a strategy of one-by-one replacement to approximate, or perhaps find, the optimal set. The Teitz and Bart heuristic is the archetype of this procedure and is the heuristic most frequently used for the solution of the <i>p</i>-median problem. One study of the performance of this heuristic with increasing numbers of facilities (<i>p</i>) in problems with a very small number of demand nodes (<i>n</i>) has been published. However, no study satisfactorily indicates the relative effectiveness of this heuristic method with increasing values of <i>n </i>or <i>p</i>. In this paper we compare optimal and heuristic solutions for ninety problems varying the values of <i>n </i>and <i>p </i>systematically. The results indicate that there is a definite reduction in the effectiveness of the heuristic with increasing values of <i>n </i>or <i>p</i>.