Node based compact formulations for the Hamiltonian <i>p</i>‐median problem

In this paper, we introduce, study and analyze several classes of compact formulations for the symmetric Hamiltonian p $$ -median problem (H MP). Given a positive integer weighted complete undirected graph G = ( V , E ) G=\left(V,E\right) with weights on edges, H MP is to find minimum weight set elementary cycles partitioning vertices . The advantage developing that they can be readily used in combination off-the-shelf optimization software, unlike other types possibly involving use exponentially sized sets variables or constraints. main part paper focuses eliminating solutions less than cycles. Such are well known studied which prevent more proposed based common motivation, is, contain assign labels nodes, by stating different depots must have nodes same cycle label. We introduce aggregated (which consider represent label node) disaggregated binary each node given label). models new. not, although all them new enhancements been included make competitive models. two conclusions are: (i) context formulations, it worth looking at variables, smaller size. Despite their weaker LP relaxation bounds, fewer constraints lead faster resolution, especially when solving instances 50 nodes; (ii) best our exhibit performance that, overall, comparable methods (including branch-and-cut algorithms), optimality up 226 within 1 h. This corroborates message knowledge inequalities preventing much understood.