Heuristic Concentration: Its Care and Feeding

Abstract

Rosing (1997) has demonstrated, specifically in the case of the Teitz and Bart (1968) heuristic applied to the p-median problem, that the quality of the solution provided by an interchange heuristic deteriorates as either the number of basic individuals (termed demand nodes and symbolised as n) and/or the number of medians to be located (termed facilities and symbolised by p) increases. The deterioration is shown to involve both the probability of finding the optimal solution and, judged by functional value, the closeness of a typical solution to the optimal. Applications of combinatorial analysis in GIS, in facility location, in studies of aggregation error and in many other fields involve extremely large values for the number of basic individuals, n, and the number of medians to be chosen from the basic individuals or the number of groups, p. If the trends identified by Rosing (1997) are indeed general to interchange heuristics and if they hold for problems outside the domain studied (n # 300, p # 50) it is an extremely serious situation since optimal methods are unavailable for these larger problems.