New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem

[EN] The min-max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch-and-cut algorithm that produced some promising computational results was implemented. In this article, we present further results for this problem. We describe several new facet-inducing inequalities obtained from the WRPP, as well as some inequalities that have to be satisfied by any optimal solution. We present an enhanced branch-and-cut algorithm that takes advantage of both these new inequalities and high quality min-max K-WRPP feasible solutions obtained by a metaheuristic. Computational results on a large set of instances are also reported. © 2011 Wiley Periodicals, Inc.Contract grant sponsor: Ministerio de Ciencia e Innovacion of Spain; Contract grant numbers: MTM2006-14961-C05-02, MTM2009-14039-C06-02Benavent López, E.; Corberán, A.; Plana, I.; Sanchís Llopis, JM. (2011). New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem. Networks. 58(4):255-272. https://doi.org/10.1002/net.20469S255272584D. Ahr Contributions to multiple postmen problems 2004Ahr, D., & Reinelt, G. (2002). New Heuristics and Lower Bounds for the Min-Max k-Chinese Postman Problem. Lecture Notes in Computer Science, 64-74. doi:10.1007/3-540-45749-6_10Ahr, D., & Reinelt, G. (2006). A tabu search algorithm for the min–max k-Chinese postman problem. Computers & Operations Research, 33(12), 3403-3422. doi:10.1016/j.cor.2005.02.011D. Applegate R. E. Bixby V. Chvátal W. Cook Finding cuts in the TSP 1995Benavent, E., Carrotta, A., Corberán, A., Sanchis, J. M., & Vigo, D. (2007). Lower bounds and heuristics for the Windy Rural Postman Problem. European Journal of Operational Research, 176(2), 855-869. doi:10.1016/j.ejor.2005.09.021Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2009). Min-Max K -vehicles windy rural postman problem. Networks, 54(4), 216-226. doi:10.1002/net.20334Benavent, E., Corberán, Á., & Sanchis, J. M. (2009). A metaheuristic for the min–max windy rural postman problem with K vehicles. Computational Management Science, 7(3), 269-287. doi:10.1007/s10287-009-0119-2Corberáan, A., Letchford, A. N., & Sanchis, J. M. (2001). A cutting plane algorithm for the General Routing Problem. Mathematical Programming, 90(2), 291-316. doi:10.1007/pl00011426Corberán, A., Plana, I., & Sanchis, J. M. (2007). A branch & cut algorithm for the windy general routing problem and special cases. Networks, 49(4), 245-257. doi:10.1002/net.20176Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Frederickson, G. N., Hecht, M. S., & Kim, C. E. (1978). Approximation Algorithms for Some Routing Problems. SIAM Journal on Computing, 7(2), 178-193. doi:10.1137/0207017Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-6I. Plana The windy general routing problem 200

Joint Cuts and Matching of Partitions in One Graph

As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives few attention. In this paper, we first formalize the problem of simultaneously cutting a graph into two partitions i.e. graph cuts and establishing their correspondence i.e. graph matching. Then we develop an optimization algorithm by updating matching and cutting alternatively, provided with theoretical analysis. The efficacy of our algorithm is verified on both synthetic dataset and real-world images containing similar regions or structures

Enhancing quantum entropy in vacuum-based quantum random number generator

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator. At the same time, it directly determine the extraction ratio of true randomness from the raw data, in other words, it affects quantum random numbers generating rate obviously. In this work, considering the effects of classical noise, the best way to enhance quantum entropy in the vacuum-based quantum random number generator is explored in the optimum dynamical analog-digital converter (ADC) range scenario. The influence of classical noise excursion, which may be intrinsic to a system or deliberately induced by an eavesdropper, on the quantum entropy is derived. We propose enhancing local oscillator intensity rather than electrical gain for noise-independent amplification of quadrature fluctuation of vacuum state. Abundant quantum entropy is extractable from the raw data even when classical noise excursion is large. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the local oscillator power when classical noise excursions of the raw data is obvious.Comment: 12 pages,8 figure

Tumor and circulating biomarkers in patients with second-line hepatocellular carcinoma from the randomized phase II study with tivantinib

ARQ 197-215 was a randomized placebo-controlled phase II study testing the MET inhibitor tivantinib in second-line hepatocellular carcinoma (HCC) patients. It identified tumor MET as a key biomarker in HCC. Aim of this research was to study the prognostic and predictive value of tumor (MET, the receptor tyrosine kinase encoded by the homonymous MNNG-HOS transforming gene) and circulating (MET, hepatocyte growth factor [HGF], alpha-fetoprotein [AFP], vascular endothelial growth factor [VEGF]) biomarkers in second-line HCC. Tumor MET-High status was centrally assessed by immunohistochemistry. Circulating biomarkers were centrally analyzed on serum samples collected at baseline and every 4-8 weeks, using medians as cut-off to determine High/Low status. Tumor MET, tested in 77 patients, was more frequently High after (82%) versus before (40%) sorafenib. A significant interaction (p = 0.04) between tivantinib and baseline tumor MET in terms of survival was observed. Baseline circulating MET and HGF (102 patients) High status correlated with shorter survival (HR 0.61, p = 0.03, and HR 0.60, p = 0.02, respectively), while the association between AFP (104 patients) or VEGF (103 patients) status and survival was non-significant. Conclusions: Tumor MET levels were higher in patients treated with sorafenib. Circulating biomarkers such as MET and HGF may be prognostic in second-line HCC. These results need to be confirmed in larger randomized clinical trials

Cluster observations of the midaltitude cusp under strong northward interplanetary magnetic field

We report on a multispacecraft cusp observation lasting more than 100 min. We determine the cusp boundary motion and reveal the effect on the cusp size of the interplanetary magnetic field (IMF) changing from southward to northward. The cusp shrinks at the beginning of the IMF rotation and it reexpands at the rate of 0.40° invariant latitude per hour under stable northward IMF. On the basis of plasma signatures inside the cusp, such as counterstreaming electrons with balanced fluxes, we propose that pulsed dual lobe reconnection operates during the time of interest. SC1 and SC4 observations suggest a long-term regular periodicity of the pulsed dual reconnection, which we estimate to be ~1–5 min. Further, the distances from the spacecraft to the reconnection site are estimated on the basis of observations from three satellites. The distance determined using SC1 and SC4 observations is ~15 RE and that determined from SC3 data is ~8 RE. The large-scale speed of the reconnection site sunward motion is ~16 km s-1. We observe also a fast motion of the reconnection site by SC1, which provides new information about the transitional phase after the IMF rotation. Finally, a statistical study of the dependency of plasma convection inside the cusp on the IMF clock angle is performed. The relationship between the cusp stagnation, the dual lobe reconnection process, and the IMF clock angle is discussed