Solving large \(p\)-median problems by a multistage hybrid approach using demand points aggregation and variable neighbourhood search
A hybridisation of a clustering-based technique and of a variable neighbourhood search (VNS) is designed to solve large-scale \(p\)-median problems. The approach is based on a multi-stage methodology where learning from previous stages is taken into account when tackling the next stage. Each stage is made up of several subproblems that are solved by a fast procedure to produce good feasible solutions. Within each stage, the solutions returned are put together to make up a new promising subset of potential facilities. This augmented \(p\)-median problem is then solved by VNS. As these problems used aggregation, a cost evaluation based on the original demand points instead of aggregation is computed for each of the aggregation-based solution. The one yielding the least cost is then selected and its chosen facilities included into the next stages. This multi-stage process is repeated several times until a certain criterion is met. This approach is enhanced by an efficient way to aggregate the data and a neighbourhood reduction scheme when allocating demand points to their nearest facilities. The proposed approach is tested, using various values of \(p\), on the largest data sets from the literature with up to 89,600 demand points with encouraging results.
\(p\)-median aggregation variable neighbourhood search location problem