Cut sharing for multistage stochastic linear programs with interstage dependency

Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms. Research leading to this work was partially supported by the Department of Energy Contract DE-FG03-92ER25116-A002; the Office of Naval Research Contract N00014-89-J-1659; the National Science Foundation Grants ECS-8906260, DMS-8913089; and the Electric Power Research Institute Contract RP 8010-09, CSA-4O05335. This author's work was supported in part by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.     

A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.     

A genetic algorithm for the structural optimization of Morse clusters

This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches. Received: 27 October 1999 / Accepted: 7 December 1999 / Published online: 19 April 2000     

MM3 parametrization of four‐ and five‐coordinated rhenium complexes by a genetic algorithm—Which factors influence the optimization performance?

Genetic algorithms (GA) were used to solve one of the multidimensional problems in computational chemistry, the optimization of force field parameters. The correlation between the composition of the GA, its parameters (p(c), p(m)) and the quality of the results were investigated. The composition was studied for all combinations of a Simple GA/Steady State GA with a Roulette Wheel/Tournament Selector using different values each for crossover (0.5, 0.7, 0.9) and mutation rates (0.01, 0.02, 0.05, 0.10, 0.20). The results show that the performance is strongly dependent on the GA scheme, where the Simple GA/Tournament Selector yields the best results. Two new MM3 parameters were introduced for rhenium compounds with coordination number four (204) and coordination number five (205), the formal oxidation states of rhenium ranging from +V to +VII. A manifold of parameters (Re-C, N, O, S) was obtained by using a diverse set of CSD structures. The advantage of the GA vs. UFF calculations is shown by comparison of several examples. The GA optimized parameters were able to reproduce the geometrical data of the X-ray structures.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

The de novo design of median molecules within a property range of interest

Summary In this paper an application is presented of the median molecule workflow to the de novo design of novel molecular entities with a property profile of interest. Median molecules are structures that are optimised to be similar to a set of existing molecules of interest as an approach for lead exploration and hopping. An overview of this workflow is provided together with an example of an instance using the similarity to camphor and menthol as objectives. The methodology of the experiments is defined and the workflow is applied to designing novel molecules for two physical property datasets: mean molecular polarisability and aqueous solubility. This paper concludes with a discussion of the characteristics of this method.     

Rivality index neighbourhood algorithm with density and distances weighted schemes for the building of robust QSAR classification models with high reliable applicability domain

The rivality index (RI) is a normalized distance measurement between a molecule and their first nearest neighbours providing a robust prediction of the activity of a molecule based on the known activity of their nearest neighbours. Negative values of the RI describe molecules that would be correctly classified by a statistic algorithm and, vice versa, positive values of this index describe those molecules detected as outliers by the classification algorithms. In this paper, we have described a classification algorithm based on the RI and we have proposed four weighted schemes (kernels) for its calculation based on the measuring of different characteristics of the neighbourhood of molecules for each molecule of the dataset at established values of the threshold of neighbours. The results obtained have demonstrated that the proposed classification algorithm, based on the RI, generates more reliable and robust classification models than many of the more used and well-known machine learning algorithms. These results have been validated and corroborated by using 20 balanced and unbalanced benchmark datasets of different sizes and modelability. The classification models generated provide valuable information about the molecules of the dataset, the applicability domain of the models and the reliability of the predictions.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

Clustering Algorithms to Analyze Molecular Dynamics Simulation Trajectories for Complex Chemical and Biological Systems?

Molecular dynamics (MD) simulation has become a powerful tool to investigate the structurefunction relationship of proteins and other biological macromolecules at atomic resolution and biologically relevant timescales. MD simulations often produce massive datasets containing millions of snapshots describing proteins in motion. Therefore, clustering algorithms have been in high demand to be developed and applied to classify these MD snapshots and gain biological insights. There mainly exist two categories of clustering algorithms that aim to group protein conformations into clusters based on the similarity of their shape (geometric clustering) and kinetics (kinetic clustering). In this paper, we review a series of frequently used clustering algorithms applied in MD simulations, including divisive algorithms, agglomerative algorithms (single-linkage, complete-linkage, average-linkage, centroid-linkage and ward-linkage), center-based algorithms (K-Means, K-Medoids, K-Centers, and APM), density-based algorithms (neighbor-based, DBSCAN, density-peaks, and Robust-DB), and spectral-based algorithms (PCCA and PCCA+). In particular, differences between geometric and kinetic clustering metrics will be discussed along with the performances of different clustering algorithms. We note that there does not exist a one-size-fits-all algorithm in the classification of MD datasets. For a specific application, the right choice of clustering algorithm should be based on the purpose of clustering, and the intrinsic properties of the MD conformational ensembles. Therefore, a main focus of our review is to describe the merits and limitations of each clustering algorithm. We expect that this review would be helpful to guide researchers to choose appropriate clustering algorithms for their own MD datasets.