The Subtour Centre Problem

Abstract

The subtour centre problemis the problem of finding a closed trail S of bounded length on a connected simple graph G that minimises the maximum distance from S to any vertex of G. It is a central location problem related to the cycle centre and cycle median problems (Foulds et al., 2004; Labbé et al., 2005) and the covering tour problem (Current and Schilling, 1989). Two related heuristics and an integer linear programme are formulated for it. These are compared numerically using a range of problems derived from tsplib (Reinelt, 1995). The heuristics usually perform substantially better then the integer linear programme and there is some evidence that the simpler heuristics perform better on the less dense graphs that may be more typical of applications.

Keywords: Location, Combinatorial optimization, Heuristics, Linear programming