1. ¹University of Kent, Canterbury, UK
2. ²King Saud University, Riyadh, Saudi Arabia

Correspondence: S Salhi, Centre for Heuristic Optimisation (CHO), Kent Business School, University of Kent, Canterbury, Kent, CT2 7PE, UK. E-mail: s.salhi@kent.ac.uk

Received January 2008; Accepted May 2009; Published online 28 October 2009.

Abstract

We solve the vertex p-centre problem optimally using an exact method that considers both upper and lower bounds as part of its search engine. Tight upper bounds are generated quickly via an efficient three-level heuristic, which are then used to derive potential 'lower bounds' accordingly. These two pieces of information when used together make our chosen exact method more efficient at obtaining optimal solutions relatively quickly. The proposed implementation produced excellent results when tested on the OR Library data set. This integrated approach can be adopted for those exact methods that consider both upper and lower bounds within their search engine and hence provide a wider spectrum of applicability in other hard combinatorial problems.