Edge Elimination in TSP Instances

The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that has been solved optimally has 85,900 vertices. Its solution required more than 136 years of total CPU time using the branch-and-cut based Concorde TSP code [1]. In this paper we present graph theoretic results that allow to prove that some edges of a TSP instance cannot occur in any optimum TSP tour. Based on these results we propose a combinatorial algorithm to identify such edges. The runtime of the main part of our algorithm is $O(n^2 \log n)$ for an n-vertex TSP instance. By combining our approach with the Concorde TSP solver we are able to solve a large TSPLIB instance more than 11 times faster than Concorde alone

Collaborative Delivery with Energy-Constrained Mobile Robots

We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the message, each agent handing over the message to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before. We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the 23rd International Colloquium on Structural Information and Communication Complexity 2016, SIROCCO'1

Branching on multi-aggregated variables

open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic

Accounting for the mortality benefit of drug-eluting stents in percutaneous coronary intervention: a comparison of methods in a retrospective cohort study

<p>Abstract</p> <p>Background</p> <p>Drug-eluting stents (DES) reduce rates of restenosis compared with bare metal stents (BMS). A number of observational studies have also found lower rates of mortality and non-fatal myocardial infarction with DES compared with BMS, findings not observed in randomized clinical trials. In order to explore reasons for this discrepancy, we compared outcomes after percutaneous coronary intervention (PCI) with DES or BMS by multiple statistical methods.</p> <p>Methods</p> <p>We compared short-term rates of all-cause mortality and myocardial infarction for patients undergoing PCI with DES or BMS using propensity-score adjustment, propensity-score matching, and a stent-era comparison in a large, integrated health system between 1998 and 2007. For the propensity-score adjustment and stent era comparisons, we used multivariable logistic regression to assess the association of stent type with outcomes. We used McNemar's Chi-square test to compare outcomes for propensity-score matching.</p> <p>Results</p> <p>Between 1998 and 2007, 35,438 PCIs with stenting were performed among health plan members (53.9% DES and 46.1% BMS). After propensity-score adjustment, DES was associated with significantly lower rates of death at 30 days (OR 0.49, 95% CI 0.39 - 0.63, <it>P </it>< 0.001) and one year (OR 0.58, 95% CI 0.49 - 0.68, <it>P </it>< 0.001), and a lower rate of myocardial infarction at one year (OR 0.72, 95% CI 0.59 - 0.87, <it>P </it>< 0.001). Thirty day and one year mortality were also lower with DES after propensity-score matching. However, a stent era comparison, which eliminates potential confounding by indication, showed no difference in death or myocardial infarction for DES and BMS, similar to results from randomized trials.</p> <p>Conclusions</p> <p>Although propensity-score methods suggested a mortality benefit with DES, consistent with prior observational studies, a stent era comparison failed to support this conclusion. Unobserved factors influencing stent selection in observational studies likely account for the observed mortality benefit of DES not seen in randomized clinical trials.</p

Verifying integer programming results

Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates

Haiku - a Scala combinator toolkit for semi-automated composition of metaheuristics

There is an emerging trend towards the automated design of metaheuristics at the software component level. In principle, metaheuristics have a relatively clean decomposition, where well-known frameworks such as ILS and EA are parametrised by variant components for acceptance, perturbation etc. Automated generation of these frameworks is not so simple in practice, since the coupling between components may be implementation specific. Compositionality is the ability to freely express a space of designs ‘bottom up’ in terms of elementary components: previous work in this area has used combinators, a modular and functional approach to componentisation arising from foundational Computer Science. In this article, we describeHaiku, a combinator tool-kit written in the Scala language, which builds upon previous work to further automate the process by automatically composing the external dependencies of components. We provide examples of use and give a case study in which a programatically-generated heuristic is applied to the Travelling Salesman Problem within an Evolutionary Strategies framework

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Landscape Encodings Enhance Optimization

Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states. In addition, smooth landscapes may be established on encoded state spaces to guide local search dynamics towards the ground state

Highly Pathogenic Avian Influenza Virus H5N1 Infection in a Long-Distance Migrant Shorebird under Migratory and Non-Migratory States

Corticosterone regulates physiological changes preparing wild birds for migration. It also modulates the immune system and may lead to increased susceptibility to infection, with implications for the spread of pathogens, including highly pathogenic avian influenza virus (HPAIV) H5N1. The red knot (Calidris canutus islandica) displays migratory changes in captivity and was used as a model to assess the effect of high plasma concentration of corticosterone on HPAIV H5N1 infection. We inoculated knots during pre-migration (N = 6), fueling (N = 5), migration (N = 9) and post-migration periods (N = 6). Knots from all groups shed similar viral titers for up to 5 days post-inoculation (dpi), peaking at 1 to 3 dpi. Lesions of acute encephalitis, associated with virus replication in neurons, were seen in 1 to 2 knots per group, leading to neurological disease and death at 5 to 11 dpi. Therefore, the risk of HPAIV H5N1 infection in wild birds and of potential transmission between wild birds and poultry may be similar at different times of the year, irrespective of wild birds' migratory status. However, in knots inoculated during the migration period, viral shedding levels positively correlated with pre-inoculation plasma concentration of corticosterone. Of these, knots that did not become productively infected had lower plasma concentration of corticosterone. Conversely, elevated plasma concentration of corticosterone did not result in an increased probability to develop clinical disease. These results suggest that birds with elevated plasma concentration of corticosterone at the time of migration (ready to migrate) may be more susceptible to acquisition of infection and shed higher viral titers—before the onset of clinical disease—than birds with low concentration of corticosterone (not ready for take-off). Yet, they may not be more prone to the development of clinical disease. Therefore, assuming no effect of sub-clinical infection on the likelihood of migratory take-off, this may favor the spread of HPAIV H5N1 by migratory birds over long distances