The Team Orienteering Problem: Formulations and Branch-Cut and Price

The Team Orienteering Problem is a routing problem on a graph with durations associated to the arcs and profits assigned to visiting the vertices. A fixed number of identical vehicles, with a limited total duration for their routes, is given. The total profit gathered by all routes is to be maximized. We devise an extended formulation where edges are indexed by the time they are placed in the route. A new class of inequalities, min cut, and the triangle clique cuts of Pessoa et. al., 2007 are added. The resulting formulation is solved by column generation. Branching is done following the work of Boussier et al. 2007, to which the branch-cut-and-price algorithm here proposed is compared. A few new upper bounds were obtained. Overall the presented approach has shown to be very competitive

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;

Distance Transformation for Network Design Problems

International audienceWe propose a new generic way to construct extended formulations for a large class of network design problems with given connectivity requirements. The approach is based on a graph transformation that maps any graph into a layered graph according to a given distance function. The original connectivity requirements are in turn transformed into equivalent connectivity requirements in the layered graph. The mapping is extended to the graphs induced by fractional vectors through an extended linear integer programming formulation. While graphs induced by binary vectors are mapped to isomorphic layered graphs, those induced by fractional vectors are mapped to a set of graphs having worse connectivity properties. Hence, the connectivity requirements in the layered graph may cut off fractional vectors that were feasible for the problem formulated in the original graph. Experiments over instances of the Steiner Forest and Hop-constrained Survivable Network Design problems show that significant gap reductions over the state-of-the art formulations can be obtained

A reexamination of the effective fine structure constant of graphene, as measured in graphite

We present a refined and improved study of the influence of screening on the effective fine structure constant of graphene, $\alpha^*$, as measured in graphite using inelastic x-ray scattering. This follow-up to our previous study [J. P. Reed, et al., Science 330, 805 (2010)] was carried out with two times better energy resolution, five times better momentum resolution, and improved experimental setup with lower background. We compare our results to RPA calculations and evaluate the relative importance of interlayer hopping, excitonic corrections, and screening from high energy excitations involving the $\sigma$ bands. We find that the static, limiting value of $\alpha^*$ falls in the range 0.25 to 0.35, which is higher than our previous result of 0.14, but still below the value expected from RPA. We show the reduced value is not a consequence of interlayer hopping effects, which were ignored in our previous analysis, but of a combination of excitonic effects in the $\pi \rightarrow \pi^*$ particle-hole continuum, and background screening from the $\sigma$-bonded electrons. We find that $\sigma$-band screening is extremely strong at distances of the order of a few nm, and should be highly effective at screening out short-distance, Hubbard-like interactions in graphene, as well as other carbon allotropes.Comment: 23 pages, 5 figure

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

National audienc

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

Quantification of basal digital blood flow and after cold stimulus by laser doppler imaging in patients with systemic sclerosis

OBJECTIVES: The objective of this study was to investigate the dynamic behavior of the blood flow of the microvascular circulation of the fingertips before and after two cold stimuli (CS), using Laser Doppler Imaging with different intensities in patients with systemic sclerosis (SSc) and in healthy individuals. PATIENTS AND METHODS: Fourteen SSc patients (51.2 ± 5.5 years) with Raynaud's phenomenon and 12 healthy controls (44.8 ± 9.0 years) were included in this study. Two CS protocols (submersion of the hands in water at 10 ºC or 15 ºC for 1 minute) were performed on the same day. Mean fingertip blood flow (FBF) of four digits of the left hand was measured using LDI (Moor LDI-VR, Moor Instruments) at baseline and at 1, 4, 10, 25, and 40 minutes after CS. RESULTS: Baseline blood flow was significantly lower in both CS protocols in SSc patients when compared to controls (312.9 ± 102.7 vs 465.4 ± 135.4 PU, P = 0.006 at 15 ºC; 305.2 ± 121.0 vs 437.9 ± 119.8 PU; P = 0.01 at 10 ºC). In the control group, a significant decrease in FBF after CS, when compared to baseline, was observed 1 minute (P = 0.001) after CS at 15 ºC and at 1 (P = 0.005) and 25 minutes (P = 0.001) after CS at 10 ºC. In SSc patients, a significant decrease in FBF was observed in both CS protocols at 1, 4, and 10 minutes (P < 0.000; P = 0.002; P = 0.014, after CS at 15 ºC; P < 0.000; P = 0.004; P = 0.001, after CS at 10 ºC). CONCLUSIONS: Laser Doppler Imaging showed lower baseline fingertip perfusion and further reduction after CS in SSc patients compared to controls. Quantification of fingertip blood flow by LDI may be useful in the longitudinal monitoring of the disease status and therapeutic interventions in SSc.OBJETIVO: Determinar o comportamento dinâmico do fluxo sanguíneo da microcirculação digital, antes e após dois estímulos frios (EF) de diferentes intensidades, utilizando o método do Laser Doppler Imaging (LDI) em pacientes com esclerose sistêmica (ES) e controles saudáveis. MÉTODOS: Foram incluídos 14 pacientes com ES (51,2 ± 5,5 anos de idade) e 12 controles saudáveis (44,8 ± 9,9 anos). Foram realizados dois protocolos alternativos de EF (submersão das mãos em água a 10 ºC ou 15 ºC, durante 1 minuto). O fluxo médio das quatro polpas digitais da mão esquerda (FPD) foi mensurado com a utilização do LDI (Moor LDI-VR), em condições basais, nos períodos de 1, 4, 10, 25 e 40 minutos após EF. RESULTADOS: O fluxo basal foi significativamente menor em ambos os protocolos em pacientes com ES comparados a controles (312,9 ± 102,7 versus 465,4 ± 135,4 PU, P = 0,006, no protocolo a 15 ºC; 305,2 ± 121,0 versus 437,9 ± 119,8 PU, P = 0,01, no protocolo a 10 ºC). Nos controles houve declínio significativo do FPD após EF, em comparação aos valores basais apenas no tempo de um minuto após EF a 15 ºC (P = 0,001) e nos tempos de 1 e 25 minutos após EF a 10 ºC (P = 0,005; P = 0,001, respectivamente). Nos pacientes com ES, houve declínio significativo do FPD nos tempos de 1, 4 e 10 minutos após ambos EFs (P < 0,000; P = 0,002; P = 0,014, EF a 15 ºC; P < 0,000; P = 0,004; P = 0,001, EF a 10 ºC, respectivamente). CONCLUSÃO: LDI demonstrou baixa perfusão em polpa digital em condições basais e elevado declínio de perfusão com retardo na recuperação após EF na ES. A quantificação do fluxo sanguíneo pelo LDI pode ser útil para o seguimento longitudinal da doença e para a monitoração de intervenções terapêuticas na ES.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)UNIFESP disciplina de reumatologiaUNIFESP disciplina de reumatologia ambulatório de Esclerose SistêmicaUNIFESP, disciplina de reumatologiaUNIFESP, disciplina de reumatologia ambulatório de Esclerose SistêmicaSciEL

Oral N-acetylcysteine in the treatment of Raynaud's phenomenon secondary to systemic sclerosis: A randomized, double-blind, placebo-controlled clinical trial

Objective To evaluate the safety and efficacy of oral N-acetylcysteine (NAC) on digital microcirculation blood flow in patients with Raynaud's phenomenon (RP) secondary to systemic sclerosis (SSc). Methods This was a randomized, double-blind, placebo-controlled trial in which 42 patients with SSc received oral NAC at a dose of 600mg tid (21 patients, mean age 45.6±9.5 years) or placebo (21 patients, mean age 45.0±12.7 years) for four weeks. The primary endpoint was the change in cutaneous microcirculation blood flow before and after cold stimulation measured by laser Doppler imaging (LDI) at weeks 0 and 4. The frequency and severity of RP and the number of digital ulcers were also measured at weeks 0 and 4. The adverse events were recorded in the fourth week. Results There was no significant change in digital blood flow assessed by LDI before or after cold stimulus after four weeks of NAC or placebo. Both groups showed significant improvement in the frequency and severity of RP attacks, with no difference between the two groups. At the end of the study, the placebo group had three digital ulcers, while the NAC group showed no ulcers. NAC was well tolerated and no patient discontinued the treatment. Conclusions NAC orally at a dose of 1800mg/day showed no vasodilator effect on hands’ microcirculation after four weeks of treatment in patients with RP secondary to SSc.Objetivo Avaliar a segurança e a eficácia da N-acetilcisteína (NAC) por via oral sobre o fluxo sanguíneo da microcirculação digital em pacientes com fenômeno de Raynaud (FRy) secundário à esclerose sistêmica (ES). Métodos Este foi um estudo randomizado, duplo-cego e placebo-controlado, no qual 42 pacientes com ES receberam NAC oral na dose de 600 mg, três vezes ao dia (21 pacientes, idade média 45,6±9,5 anos) ou placebo (21 pacientes, idade média 45,0±12,7 anos) durante quatro semanas. O desfecho primário do estudo foi: melhora no fluxo sanguíneo da microcirculação cutânea antes e após estímulo frio avaliado pelo laser Doppler imaging (LDI) nas semanas 0 e 4. A frequência e a gravidade do FRy e o número de úlceras digitais também foram avaliados nas semanas 0 e 4. Os efeitos adversos foram registrados na quarta semana. Resultados Não houve mudança significativa no fluxo sanguíneo digital avaliado pelo LDI antes ou depois do estímulo frio após quatro semanas de NAC ou placebo. Ambos os grupos apresentaram melhora significativa na frequência e gravidade dos ataques de FRy, sem diferença entre os dois. O grupo placebo apresentou três úlceras digitais enquanto o grupo NAC não apresentou úlceras ao final do estudo. NAC foi bem tolerada e nenhum paciente descontinuou o tratamento. Conclusões NAC por via oral na dose de 1.800mg/dia não demonstrou efeito vasodilatador sobre a microcirculação das mãos após quatro semanas de tratamento em pacientes com FRy secundário à ES.Universidade Federal de São Paulo (UNIFESP)UNIFESPSciEL

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