Formulations and algorithms for the optimum communication spanning tree problem

The Optimum Communication Spanning Tree problem (OCT) has applications in many fields of study such as logistics, telecommunications and bioinformatics. This problem receives as input an undirected graph with weighted edges and requirement value for each pair of nodes, and seeks for a spanning tree that minimizes the communication cost, given by the sum of requirement of each pair of nodes times the distance separating them in the tree. In this work we design a new integer formulation for OCT as well as four different strategies of evolutionary algorithms and a combined strategy with simulated annealing. We give public access to our implementations. We test our approaches on instances from the literature and from real-world data sets. The experiments show that our best strategies were able to obtain very accurate solutions, getting close to the best known value for all tested instances, improving the results of previous metaheuristics from the literature.O problema da árvore geradora de comunicação ótima possui aplicação em diversos campos de estudo como logística, telecomunicações e bioinformática. Esse problema recebe como entrada um grafo com pesos nas arestas e um valor de requerimento entre cada par de nodos do grafo, e procura por uma árvore geradora que minimiza o custo de comunicação que é calculado pela soma dos requerimentos de cada par de nodos vezes a distância que os separa na árvore. Neste trabalho propomos uma nova formulação inteira para o problema e desenvolvemos quatro estratégias diferentes de algoritmos evolutivos e uma combinada com o método simulated annealing, dando acesso público às nossas implementações. Testamos nossos algoritmos com instâncias da literatura e com outras baseadas em conjuntos de dados do mundo real. Os experimentos mostram que nossas melhores estratégias foram capazes de obter soluções muito precisas para todas as instâncias testadas, melhorando os resultados de metaheurísticas anteriores da literatura

A Polynomial Time Approximation Scheme for Optimal Product-Requirement Communication Spanning Trees

[[abstract]]Given an undirected graph with nonnegative edge lengths and nonnegative vertex weights, the routing requirement of a pair of vertices is assumed to be the product of their weights. The routing cost for a pair of vertices on a given spanning tree is defined as the length of the path between them multiplied by their routing requirement. The optimal product-requirement communication spanning tree is the spanning tree with minimum total routing cost summed over all pairs of vertices. This problem arises in network design and computational biology. For the special case that all vertex weights are identical, it has been shown that the problem is NP-hard and that there is a polynomial time approximation scheme for it. In this paper we show that the generalized problem also admits a polynomial time approximation scheme.[[fileno]]2030209010005[[department]]資訊工程學

The Optimum Communication Spanning Tree Problem : properties, models and algorithms

For a given cost matrix and a given communication requirement matrix, the OCSTP is defined as finding a spanning tree that minimizes the operational cost of the network. OCST can be used to design of more efficient communication and transportation networks, but appear also, as a subproblem, in hub location and sequence alignment problems. This thesis studies several mixed integer linear optimization formulations of the OCSTP and proposes a new one. Then, an efficient Branch & Cut algorithm derived from the Benders decomposition of one of such formulations is used to successfully solve medium-sized instances of the OCSTP. Additionally, two new combinatorial lower bounds, two new heuristic algorithms and a new family of spanning tree neighborhoods based on the Dandelion Code are presented and tested.Postprint (published version