The Hamiltonian p-median problem: Polyhedral results and branch-and-cut algorithms
研究了在边赋权图中寻找p个顶点不交的圈覆盖所有顶点且总权重最小的哈密顿p-中位问题，提出了两类有效不等式并设计了分支切割算法，在多达400个顶点的实例上验证了算法性能。
In this paper we study the Hamiltonian p-median problem, in which we are given an edge-weighted graph and we are asked to determine p vertex-disjoint cycles spanning all vertices of the graph and having minimum total weight. We introduce two new families of valid inequalities for a formulation of the problem in the space of edge variables. Each one of the families forbids solutions to the 2-factor relaxation of the problem that have less than p cycles. The inequalities in one of the families are associated with large cycles of the underlying graph and generalize known inequalities associated with Hamiltonian cycles. The other family involves inequalities for the case with p=n/3, associated with edge cuts and multi-cuts whose shores have specific cardinalities. We identify inequalities from both families that define facets of the polytope associated with the problem. We design branch-and-cut algorithms based on these families of inequalities and on inequalities associated with 2-opt moves removing sub-optimal solutions. Computational experiments on benchmark instances show that the proposed algorithms exhibit a comparable performance with respect to existing exact methods from the literature. Moreover the algorithms solve to optimality new instances with up to 400 vertices.