Quantile-Based Optimization of Noisy Computer Experiments with Tunable Precision

This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: first, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical expected improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Second, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety. This article has supplementary material available online. The proposed criterion is available in the R package DiceOptim.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Analyzing diffuse scattering with supercomputers

Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341–359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super- or grid computer. The faulted layer stacking in single crystals of trigonal three-pointedstar- shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

X-ray image calibration and its application to clinical orthopedics.

X-ray imaging is one of the most commonly used medical imaging modality. Albeit X-ray radiographs provide important clinical information for diagnosis, planning and post-operative follow-up, the challenging interpretation due to its 2D projection characteristics and the unknown magnification factor constrain the full benefit of X-ray imaging. In order to overcome these drawbacks, we proposed here an easy-to-use X-ray calibration object and developed an optimization method to robustly find correspondences between the 3D fiducials of the calibration object and their 2D projections. In this work we present all the details of this outlined concept. Moreover, we demonstrate the potential of using such a method to precisely extract information from calibrated X-ray radiographs for two different orthopedic applications: post-operative acetabular cup implant orientation measurement and 3D vertebral body displacement measurement during preoperative traction tests. In the first application, we have achieved a clinically acceptable accuracy of below 1° for both anteversion and inclination angles, where in the second application an average displacement of 8.06±3.71 mm was measured. The results of both applications indicate the importance of using X-ray calibration in the clinical routine.

Optimization of TRPV6 Calcium Channel Inhibitors Using a 3D Ligand-Based Virtual Screening Method

Herein, we report the discovery of the first potent and selective inhibitor of TRPV6, a calcium channel overexpressed in breast and prostate cancer, and its use to test the effect of blocking TRPV6-mediated Ca2+-influx on cell growth. The inhibitor was discovered through a computational method, xLOS, a 3D-shape and pharmacophore similarity algorithm, a type of ligand-based virtual screening (LBVS) method described briefly here. Starting with a single weakly active seed molecule, two successive rounds of LBVS followed by optimization by chemical synthesis led to a selective molecule with 0.3 μM inhibition of TRPV6. The ability of xLOS to identify different scaffolds early in LBVS was essential to success. The xLOS method may be generally useful to develop tool compounds for poorly characterized targets.

Evidence Based Development of a Novel Lateral Fibula Plate (VariAx Fibula) Using a Real CT Bone Data Based Optimization Process During Device Development

Development of novel implants in orthopaedic trauma surgery is based on limited datasets of cadaver trials or artificial bone models. A method has been developed whereby implants can be constructed in an evidence based method founded on a large anatomic database consisting of more than 2.000 datasets of bones extracted from CT scans. The aim of this study was the development and clinical application of an anatomically pre-contoured plate for the treatment of distal fibular fractures based on the anatomical database. 48 Caucasian and Asian bone models (left and right) from the database were used for the preliminary optimization process and validation of the fibula plate. The implant was constructed to fit bilaterally in a lateral position of the fibula. Then a biomechanical comparison of the designed implant to the current gold standard in the treatment of distal fibular fractures (locking 1/3 tubular plate) was conducted. Finally, a clinical surveillance study to evaluate the grade of implant fit achieved was performed. The results showed that with a virtual anatomic database it was possible to design a fibula plate with an optimized fit for a large proportion of the population. Biomechanical testing showed the novel fibula plate to be superior to 1/3 tubular plates in 4-point bending tests. The clinical application showed a very high degree of primary implant fit. Only in a small minority of cases further intra-operative implant bending was necessary. Therefore, the goal to develop an implant for the treatment of distal fibular fractures based on the evidence of a large anatomical database could be attained. Biomechanical testing showed good results regarding the stability and the clinical application confirmed the high grade of anatomical fit.

A benchmark of kriging-based infill criteria for noisy optimization

Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.

An application of combinatorial optimization in the printing industry

Offset printing is a common method to produce large amounts of printed matter. We consider a real-world offset printing process that is used to imprint customer-specific designs on napkin pouches. The print- ing technology used yields a number of specific constraints. The planning problem consists of allocating designs to printing-plate slots such that the given customer demand for each design is fulfilled, all technologi- cal and organizational constraints are met and the total overproduction and setup costs are minimized. We formulate this planning problem as a mixed-binary linear program, and we develop a multi-pass matching-based savings heuristic. We report computational results for a set of problem instances devised from real-world data.

Patient-specific spinal stiffness in AIS: a preoperative and noninvasive method.

INTRODUCTION The clinical tests currently used to assess spinal biomechanics preoperatively are unable to assess true mechanical spinal stiffness. They rely on spinal displacement without considering the force required to deform a patient's spine. We propose a preoperative method for noninvasively quantifying the three-dimensional patient-specific stiffness of the spines of adolescent idiopathic scoliosis patients. METHODS The technique combines a novel clinical test with numerical optimization of a finite element model of the patient's spine. RESULTS A pilot study conducted on five patients showed that the model was able to provide accurate 3D reconstruction of the spine's midline and predict the spine's stiffness for each patient in flexion, bending, and rotation. Statistically significant variation of spinal stiffness was observed between the patients. CONCLUSION This result confirms that spinal biomechanics is patient-specific, which should be taken into consideration to individualize surgical treatment.

Rapid method to express and purify human membrane protein using the Xenopus oocyte system for functional and low-resolution structural analysis.

Progress toward elucidating the 3D structures of eukaryotic membrane proteins has been hampered by the lack of appropriate expression systems. Recent work using the Xenopus oocyte as a novel expression system for structural analysis demonstrates the capability of providing not only the significant amount of protein yields required for structural work but also the expression of eukaryotic membrane proteins in a more native and functional conformation. There is a long history using the oocyte expression system as an efficient tool for membrane transporter and channel expression in direct functional analysis, but improvements in robotic injection systems and protein yield optimization allow the rapid scalability of expressed proteins to be purified and characterized in physiologically relevant structural states. Traditional overexpression systems (yeast, bacteria, and insect cells) by comparison require chaotropic conditions over several steps for extraction, solubilization, and purification. By contrast, overexpressing within the oocyte system for subsequent negative-staining transmission electron microscopy studies provides a single system that can functionally assess and purify eukaryotic membrane proteins in fewer steps maintaining the physiological properties of the membrane protein.

Optimization of Schwinger pair production in colliding laser pulses

Recent studies of Schwinger pair production have demonstrated that the asymptotic particle spectrum is extremely sensitive to the applied field profile. We extend the idea of the dynamically assisted Schwinger effect from single pulse profiles to more realistic field configurations to be generated in an all-optical experiment searching for pair creation. We use the quantum kinetic approach to study the particle production and employ a multi-start method, combined with optimal control theory, to determine a set of parameters for which the particle yield in the forward direction in momentum space is maximized. We argue that this strategy can be used to enhance the signal of pair production on a given detector in an experimental setup.

Global Optimization with Sparse and Local Gaussian Process Models

We present a novel surrogate model-based global optimization framework allowing a large number of function evaluations. The method, called SpLEGO, is based on a multi-scale expected improvement (EI) framework relying on both sparse and local Gaussian process (GP) models. First, a bi-objective approach relying on a global sparse GP model is used to determine potential next sampling regions. Local GP models are then constructed within each selected region. The method subsequently employs the standard expected improvement criterion to deal with the exploration-exploitation trade-off within selected local models, leading to a decision on where to perform the next function evaluation(s). The potential of our approach is demonstrated using the so-called Sparse Pseudo-input GP as a global model. The algorithm is tested on four benchmark problems, whose number of starting points ranges from 102 to 104. Our results show that SpLEGO is effective and capable of solving problems with large number of starting points, and it even provides significant advantages when compared with state-of-the-art EI algorithms.

Optimized on-line enantioselective capillary electrophoretic method for kinetic and inhibition studies of drug metabolism mediated by cytochrome P450 enzymes.

Pharmacokinetic and pharmacodynamic properties of a chiral drug can significantly differ between application of the racemate and single enantiomers. During drug development, the characteristics of candidate compounds have to be assessed prior to clinical testing. Since biotransformation significantly influences drug actions in an organism, metabolism studies represent a crucial part of such tests. Hence, an optimized and economical capillary electrophoretic method for on-line studies of the enantioselective drug metabolism mediated by cytochrome P450 enzymes was developed. It comprises a diffusion-based procedure, which enables mixing of the enzyme with virtually any compound inside the nanoliter-scale capillary reactor and without the need of additional optimization of mixing conditions. For CYP3A4, ketamine as probe substrate and highly sulfated γ-cyclodextrin as chiral selector, improved separation conditions for ketamine and norketamine enantiomers compared to a previously published electrophoretically mediated microanalysis method were elucidated. The new approach was thoroughly validated for the CYP3A4-mediated N-demethylation pathway of ketamine and applied to the determination of its kinetic parameters and the inhibition characteristics in presence of ketoconazole and dexmedetomidine. The determined parameters were found to be comparable to literature data obtained with different techniques. The presented method constitutes a miniaturized and cost-effective tool, which should be suitable for the assessment of the stereoselective aspects of kinetic and inhibition studies of cytochrome P450-mediated metabolic steps within early stages of the development of a new drug.