Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

A strategy for searching with different access costs

AbstractLet us consider an ordered set of keys A={a1<⋯<an}, where the probability of searching ai is 1/n, for i=1,…,n. If the cost of testing each key is similar, then the standard binary search is the strategy with minimum expected access cost. However, if the cost of testing ai is ci, for i=1,…,n, then the standard binary search is not necessarily the best strategy.In this paper, we prove that the expected access cost of an optimal search strategy is bounded above by 4Cln(n+1)/n, where C=∑i=1nci. Furthermore, we show that this upper bound is asymptotically tight up to constant factors. The proof of this upper bound is constructive and generates a 4ln(n+1)-approximated algorithm for constructing near-optimal search strategies. This algorithm runs in O(n2) time and requires O(n) space, which can be useful for practical cases, since the best known exact algorithm for this problem runs in O(n3) time and requires O(n2) space

O primeiro contato com educandos do 9º Ano de uma Escola particular de Natal/RN: analisando uma cena e refletindo sobre concepções de música e cultura no contexto de Ensino e Aprendizagem

Este trabalho foi desenvolvido a partir das primeiras interações entre mim e os educandos de uma turma de 9º ano de uma escola particular de Natal (RN). Inspirado em alguns trabalhos da área da Educação Musical que analisam cenas verídicas com vistas a discutir questões concernentes à relação com a música na vida e nas escolas, apresentei uma cena que sugere aspectos que norteiam a visão dos alunos acerca de cultura e música. A partir da análise da cena, demonstrei que o imaginário em torno do termo "cultura" esteve atrelado a algo necessariamente "de qualidade", de um determinado valor estético, autêntico e/ou intelectual. Neste contexto, apontei a escola como entidade difusora dessa revitalização de regionalismos e etnicismos, que acabam enquadrando o termo “cultura” a práticas exóticas, vinculadas ao folclore e como essências da cultura nacional. Também conectei os repertórios musicais atacados pelos jovens como parte do mainstream da música popular e os repertórios exaltados e respeitados como parte do underground da música popular, destacando o estabelecimento de relações etnocêntricas entre estas categorias. O trabalho demonstra o quanto o primeiro contato com educandos pode ser valioso, em função da possibilidade de traçar sob qual ótica eles compreendem o mundo. A partir daí, podem ser (re)pensadas estratégias e abordagens pedagógicas que sejam significativas e condizentes com as necessidades do contexto em questão. De acordo com o diagnóstico constatado, aplicarei propostas educacionais que abarquem diferentes universos musicais, para que os educandos tenham sua experiência musical expandida e compreendam melhor sua própria prática musical

Improved Branch-Cut-and-Price algorithm for the Heterogeneous Vehicle Routing Problem

National audienc

Avaliação do mapeamento de suscetibilidade de deslizamento de terra em uma Bacia Amazônica via Lógica Fuzzy

The landslide phenomena cause great social and economic damages worldwide each year and are conditioned by several factors such as: climate, lithology and rock structures, pedology, morphology, anthropic action and others. Preventive actions such as the effective warning system and the establishment of areas susceptible to these processes are important because they can minimize the losses and damages caused by these disasters. Thus, the objective of this research was to elaborate a susceptibility map of landslides using the Fuzzy Logic that, in a qualitative way, provides a prediction of susceptibility and critical thresholds of alert scenarios for the Trombetas watershed using assistance from the Geographic Information System (GIS). The area of study is of low urban density, but of great economic interest, mainly in relation to mineral exploration and natural resources. In this study, seven input parameters characterizing the topographic, pedological and environmental conditions were included in the Mamdani type Fuzzy Inference System (FIS). The results showed the existence of areas classified as very low (14.11%), low (47.23%), moderate (35.08%), high (20%) and very high. (3.39%) susceptibility to slippage.Os fenômenos de deslizamentos de terra causam grandes prejuízos sociais, econômicos em todo o mundo a cada ano e são condicionados por diversos fatores como: clima, litologia e estruturas de rochas, pedologia, morfologia, ação antrópica e outros. Ações preventivas como o efetivo sistema de alerta e o estabelecimento de áreas suscetíveis a esses processos são importantes, pois podem minimizar as perdas e danos causados por esses desastres. Assim, o objetivo desta pesquisa foi elaborar um mapa de suscetibilidade de escorregamentos de terra por intermédio de Lógica Fuzzy que, de forma qualitativa, forneça uma previsão de suscetibilidade e limiares críticos de cenários de alerta para a bacia hidrográfica do Rio Trombetas com auxílio do Sistema de Informações Geográficas (SIG). A área de estudo é de baixa densidade urbana, porém de grande interesse econômico, principalmente em relação à exploração mineral e recursos naturais. Neste estudo, sete parâmetros de entrada caracterizando as condições topográficas, pedológicas e ambientais foram incluídos no Sistema de Inferência Fuzzy (FIS) do tipo Mamdani. Observou-se pelos resultados a existência de áreas classificadas como muito baixas (14,11%), baixas (47,23%), moderadas (35,08%), altas, (20%) e muito altas. (3,39%) susceptibilidade de deslizamento

A Bucket Graph Based Labelling Algorithm for Vehicle Routing

International audienceWe consider the Shortest Path Problem with Resource Constraints (SPPRC) arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to the so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance checks and the running time of the algorithm. We also show how the forward/backward route symmetry can be exploited and how to eliminate arcs from the bucket graph using reduced costs. The proposed algorithm can be especially beneficial for vehicle routing instances with large vehicle capacity and/or with time window constraints. Computational experiments were performed on instances from the distance constrained vehicle routing problem, including multi-depot and site-dependent variants, on the vehicle routing problem with time windows, and on the "nightmare" instances of the heterogeneous fleet vehicle routing problem. Significant improvements over the best algorithms in the literature were achieved and many instances could be solved for the first time

Solving Bin Packing Problems Using VRPSolver Models

International audienceWe propose branch-cut-and-price algorithms for the classic bin packing problem and also for the following related problems: vector packing, variable sized bin packing and variable sized bin packing with optional items. The algorithms are defined as models for VRPSolver, a generic solver for vehicle routing problems. In that way, a simple parameterization enables the use of several branch-cut-and-price advanced elements: automatic stabilization by smoothing, limited-memory rank-1 cuts, enumeration, hierarchical strong branching and limited discrepancy search diving heuristics. As an original theoretical contribution, we prove that the branching over accumulated resource consumption (Gélinas et al. 1995), that does not increase the difficulty of the pricing subproblem, is sufficient for those bin packing models. Extensive computational results on instances from the literature show that the VRPSolver models have a performance that is very robust over all those problems, being often superior to the existing exact algorithms on the hardest instances. Several instances could be solved to optimality for the first time