Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Reactions of Imidazolio-Phosphides with Organotin Chlorides : Surprisingly Diverse

Reactions of primary imidazolio-phosphides ("imidazolylidene-phosphinidenes") with R2SnCl2 yield as main products spectroscopically detectable Lewis pairs which undergo base-induced dehydrochlorination in the presence of excess dichlorostannane to afford zwitterionic chloride adducts of distannylated imidazolio-phosphines. In contrast, reactions with R3SnCl proceed under dismutation to furnish mixtures containing imidazolium salts and stannylated (oligo)phosphines P(SnR3)(3) and P-7(SnR3)(3), respectively. DFT studies were used to rationalize the divergent behavior based on the presumption that the reactions proceed under thermodynamic control and the products observed represent the most stable species under the specific reaction conditions. Computational simulation of selected reaction steps provides a model mechanism for Lewis-acid promoted creation of PP-bonds, which is a prerequisite for oligophosphine formation. The computational studies further highlight parallels between reactions of imidazolio-phosphides with Lewis and Bronsted acids, and allow also to extrapolate the behavior of the P-nucleophiles towards other electrophiles than organotin chlorides.Peer reviewe

Mixed uncertainty sets for robust combinatorial optimization

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a “true” model of uncertainty. We consider theoretical aspects of this approach and show that it is as easy to model as the classic setting. In an extensive computational study using a shortest path problem based on real-world data, we auto-tune uncertainty sets to the available data, and show that with regard to out-of-sample performance, the combination of multiple sets can give better results than each set on its own

Reading Articles Online

We study the online problem of reading articles that are listed in an aggregated form in a dynamic stream, e.g., in news feeds, as abbreviated social media posts, or in the daily update of new articles on arXiv. In such a context, the brief information on an article in the listing only hints at its content. We consider readers who want to maximize their information gain within a limited time budget, hence either discarding an article right away based on the hint or accessing it for reading. The reader can decide at any point whether to continue with the current article or skip the remaining part irrevocably. In this regard, Reading Articles Online, RAO, does differ substantially from the Online Knapsack Problem, but also has its similarities. Under mild assumptions, we show that any $\alpha$-competitive algorithm for the Online Knapsack Problem in the random order model can be used as a black box to obtain an $(\mathrm{e} + \alpha)C$-competitive algorithm for RAO, where $C$ measures the accuracy of the hints with respect to the information profiles of the articles. Specifically, with the current best algorithm for Online Knapsack, which is $6.65<2.45\mathrm{e}$-competitive, we obtain an upper bound of $3.45\mathrm{e} C$ on the competitive ratio of RAO. Furthermore, we study a natural algorithm that decides whether or not to read an article based on a single threshold value, which can serve as a model of human readers. We show that this algorithmic technique is $O(C)$-competitive. Hence, our algorithms are constant-competitive whenever the accuracy $C$ is a constant.Comment: Manuscript of COCOA 2020 pape

From chaos to order: Chain-length dependence of the free energy of formation of meso-tetraalkylporphyrin self-assembled monolayer polymorphs

© 2016 American Chemical Society. We demonstrate that systematic errors can be reduced and physical insight gained through investigation of the dependence of free energies for meso-tetraalkylporphyrin self-assembled monolayers (SAMs) polymorphism on the alkyl chain length m. These SAMs form on highly ordered pyrolytic graphite (HOPG) from organic solution, displaying manifold densities and atomic structures. SAMs with m = 11-19 are investigated experimentally while those with m = 6-28 are simulated using density-functional theory (DFT). It is shown that, for m = 15 or more, the alkyl chains crystallize to dominate SAM structure. Meso-tetraalkylporphyrin SAMs of length less than 11 have never been observed, a presumed effect of inadequate surface attraction. Instead, we show that free energies of SAM formation actually enhance as the chain length decreases. The inability to image regular SAMs stems from the appearance of many polymorphic forms of similar free energy, preventing SAM ordering. We also demonstrate a significant odd/even effect in SAM structure arising from packing anomalies. Comparison of the chain-length dependence of formation free energies allows the critical dispersion interactions between molecules, solvent, and substrate to be directly examined. Interpretation of the STM data combined with measured enthalpies indicates that Grimme's D3 explicit-dispersion correction and the implicit solvent correction of Floris, Tomasi and Pascual Ahuir are both quantitatively accurate and very well balanced to each other

Genetic evidence for multiple invasions of subterranean termites into Canada

Modern quantum chemical electronic structure methods typically applied to localized chemical bonding are developed to predict atomic structures and free energies for meso-Tetraalkylporphyrin self-Assembled monolayer (SAM) polymorph formation from organic solution on highly ordered pyrolytic graphite surfaces. Large polymorphdependent dispersion-induced substrate-molecule interactions (e.g., -100 kcal mol-1 to -150 kcal mol-1 for tetratrisdecylporphyrin) are found to drive SAM formation, opposed nearly completely by large polymorph-dependent dispersion-induced solvent interactions (70- 110 kcal mol-1) and entropy effects (25-40 kcal mol-1 at 298 K) favoring dissolution. Dielectric continuum models of the solvent are used, facilitating consideration of many possible SAM polymorphs, along with quantum mechanical/molecular mechanical and dispersion- corrected density functional theory calculations. These predict and interpret newly measured and existing high-resolution scanning tunnelling microscopy images of SAM structure, rationalizing polymorph formation conditions. A wide range of molecular condensed matter properties at room temperature now appear suitable for prediction and analysis using electronic structure calculations

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Accurate quantum chemical energies for tetrapeptide conformations: why MP2 data with an insufficient basis set should be handled with caution

This article discusses potential problems if the widely-applied MP2 approach is used in such situations with basis sets of insufficient size