Neighbourhood Reduction in Global and Combinatorial Optimization: The Case of the p-Centre Problem

Neighbourhood reductions for a class of location problems known as the vertex (or discrete) and planar (or continuous) p-centre problems are presented. A brief review of these two forms of the p-centre problem is first provided followed by those respective reduction schemes that have shown to be promising. These reduction schemes have the power of transforming optimal or near optimal methods such as metaheuristics or relaxation-based procedures, which were considered relatively slow, into efficient and exciting ones that are now able to find optimal solutions or tight lower/upper bounds for larger instances. Research highlights of neighbourhood reduction for global and combinatorial optimisation problems in general and for related location problems in particular are also given.