Given an undirected graph with weights associated with its nodes, the Steiner tree problem consists in nding a minimum weight subgraph spanning a given subset of nodes (terminals) of the original graph. In this paper, we describe an improved tabu search algorithm for the Steiner problem in graphs, based on a neighborhood deened by insertions and… (More)
A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. Given an undirected graph with weights associated with its nodes, the Steiner tree problem consists in nding a minimum weight subgraph spanning a given subset of (terminal) nodes of the original graph. In this paper, we describe a parallel GRASP for the… (More)
We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in… (More)
Given an undirected graph with weights associated with its edges, the degree-constrained minimum spanning tree problem consists in nding a minimum spanning tree of the given graph, subject to constraints on node degrees. We propose a variable neighborhood search heuristic for the degree-constrained minimum spanning tree problem, based on a dynamic… (More)
Given an undirected graph G = (V, E) and a function d : V → N , the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem is to find a minimum cost spanning tree T of G where each node i ∈ V has minimum degree d(i) or is a leaf node. This problem is closely related with the well-known Degree Constrained Minimum Spanning Tree (d-MST) problem, where… (More)
We consider here a multicommodity flow network optimization problem with non-convex but piecewise convex arc cost functions. We derive complete optimality conditions for local minima based on negative-cost cycles associated with each commodity. These conditions do not extend to the convex non-smooth case.