The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

An alternative method for the evaluation of docking performance: RSR vs RMSD

A new assessment criterion for docking poses is proposed in which experimental electron density is taken into account when evaluating the ability of docking programs to reproduce experimentally observed binding modes. Three docking programs (Gold, Glide, and Fred) were used to generate poses for a set of 88 protein-ligand complexes for which the crystal structure is known. The new criterion is based on the real space R-factor (RSR), which measures how well a group of atoms-in our case the ligand-fits the experimental electron density by comparing that density to the expected density, calculated from the model (i.e., the predicted ligand pose). The RSR-based measure is compared to the traditional criterion, the root-mean-square distance (RMSD) between the docking pose and the binding configuration in the crystallographic model. The results highlight several shortcomings of the RMSD criterion that do not affect the RSR-based measure. Examples illustrate that the RSR-derived approach allows a more meaningful a posteriori assessment of docking methods and results. Practical implications for docking evaluations and for methodological development work in this field are discussed.     

Data-driven optimization in management

Computational Management Science -     

Energy spectra for decaying 2D turbulence in a bounded domain

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.     

Application and limitations of X-ray crystallographic data in structure-based ligand and drug design

Structure-based design usually focuses upon the optimization of ligand affinity. However, successful drug design also requires the optimization of many other properties. The primary source of structural information for protein-ligand complexes is X-ray crystallography. The uncertainties introduced during the derivation of an atomic model from the experimentally observed electron density data are not always appreciated. Uncertainties in the atomic model can have significant consequences when this model is subsequently used as the basis of manual design, docking, scoring, and virtual screening efforts. Docking and scoring algorithms are currently imperfect. A good correlation between observed and calculated binding affinities is usually only observed only when very large ranges of affinity are considered. Errors in the correlation often exceed the range of affinities commonly encountered during lead optimization. Some structure-based design approaches now involve screening libraries by using technologies based on NMR spectroscopy and X-ray crystallography to discover small polar templates, which are used for further optimization. Such compounds are defined as leadlike and are also sought by more traditional high-throughput screening technologies. Structure-based design and HTS technologies show important complementarity and a degree of convergence.     

The Protein Data Bank archive as an open data resource

The Protein Data Bank archive was established in 1971, and recently celebrated its 40th anniversary (Berman et al. in Structure 20:391, 2012). An analysis of interrelationships of the science, technology and community leads to further insights into how this resource evolved into one of the oldest and most widely used open-access data resources in biology.     

The active site of cellobiohydrolase Cel6A from Trichoderma reesei: the roles of aspartic acids D221 and D175

Trichoderma reesei cellobiohydrolase Cel6A is an inverting glycosidase. Structural studies have established that the tunnel-shaped active site of Cel6A contains two aspartic acids, D221 and D175, that are close to the glycosidic oxygen of the scissile bond and at hydrogen-bonding distance from each other. Here, site-directed mutagenesis, X-ray crystallography, and enzyme kinetic studies have been used to confirm the role of residue D221 as the catalytic acid. D175 is shown to affect protonation of D221 and to contribute to the electrostatic stabilization of the partial positive charge in the transition state. Structural and modeling studies suggest that the single-displacement mechanism of Cel6A may not directly involve a catalytic base. The value of (D2O)(V) of 1.16 +/- 0.14 for hydrolysis of cellotriose suggests that the large direct effect expected for proton transfer from the nucleophilic water through a water chain (Grotthus mechanism) is offset by an inverse effect arising from reversibly breaking the short, tight hydrogen bond between D221 and D175 before catalysis.     

Newsvendor-type models with decision-dependent uncertainty

Models for decision-making under uncertainty use probability distributions to represent variables whose values are unknown when the decisions are to be made. Often the distributions are estimated with observed data. Sometimes these variables depend on the decisions but the dependence is ignored in the decision maker??s model, that is, the decision maker models these variables as having an exogenous probability distribution independent of the decisions, whereas the probability distribution of the variables actually depend on the decisions. It has been shown in the context of revenue management problems that such modeling error can lead to systematic deterioration of decisions as the decision maker attempts to refine the estimates with observed data. Many questions remain to be addressed. Motivated by the revenue management, newsvendor, and a number of other problems, we consider a setting in which the optimal decision for the decision maker??s model is given by a particular quantile of the estimated distribution, and the empirical distribution is used as estimator. We give conditions under which the estimation and control process converges, and show that although in the limit the decision maker??s model appears to be consistent with the observed data, the modeling error can cause the limit decisions to be arbitrarily bad.