Global Optimization Procedure Research Articles

Proteome-Wide Modeling of Transmembrane Alpha-Helical Homodimers by TMDOCK

A novel energy-based method, TMDOCK, has been developed for ab initio modeling of 3D structures of parallel homodimers in membranes. Instead of exploring the entire conformational space, the method employs a fast template-driven global energy optimization procedure that combines the knowledge of geometrically feasible packing arrangements and local energy minimization with a novel force field. Ranking and selection of optimal dimerization modes is based on the calculated free energy of α-helix association (ΔGassoc) which includes van der Waals, hydrogen bonding and dipole-dipole interactions between helices, side chain conformational entropy, and solvation energy in the anisotropic lipid environment. The fast version of the TMDOCK method is available through the web server (http://membranome.org/tm_server.php).TMDOCK successfully reproduced 26 experimental dimeric structures formed by transmembrane (TM) α-helices of 21 single-pass membrane proteins (including 4 mutants) with Cα atom r.m.s.d. from 1.0 to 3.3 A. Additional testing demonstrated consistency of calculated dimer structures with published TOXCAT, mutagenesis, or other experimental data for more than 80 bitopic proteins. Subsequent application of the method to 6041 bitopic proteins from six proteomes included in the Membranome database (membranome.org) shows that ∼70% of the proteins tend to form stable dimers with ΔGassoc<-3 kcal/mol. Results of modeling indicate three different types of dimerization behavior of TM α-helices. A unique dimerization mode is usually observed for TM domains carrying a single GxxxG-like motif, interhelical disulfide bridges, or polar residues in the middle of a helix. Proteins with several GxxxG-like motifs usually have a few dimerization modes with similar energies. Proteins with Phe-rich sequences often show multiple helix association modes. The preferred modes of dimerization are frequently evolutionarily conserved (e.g. in cadherin, HLA histocompatibility antigen, receptor tyrosine kinase, and cytochrome P450 families), but they can also change even after a single mutation.

Calibration of an agricultural-hydrological model (RZWQM2) using surrogate global optimization

Robust calibration of an agricultural-hydrological model is critical for simulating crop yield and water quality and making reasonable agricultural management. However, calibration of the agricultural-hydrological system models is challenging because of model complexity, the existence of strong parameter correlation, and significant computational requirements. Therefore, only a limited number of simulations can be allowed in any attempt to find a near-optimal solution within an affordable time, which greatly restricts the successful application of the model. The goal of this study is to locate the optimal solution of the Root Zone Water Quality Model (RZWQM2) given a limited simulation time, so as to improve the model simulation and help make rational and effective agricultural-hydrological decisions. To this end, we propose a computationally efficient global optimization procedure using sparse-grid based surrogates. We first used advanced sparse grid (SG) interpolation to construct a surrogate system of the actual RZWQM2, and then we calibrate the surrogate model using the global optimization algorithm, Quantum-behaved Particle Swarm Optimization (QPSO). As the surrogate model is a polynomial with fast evaluation, it can be efficiently evaluated with a sufficiently large number of times during the optimization, which facilitates the global search. We calibrate seven model parameters against five years of yield, drain flow, and NO3-N loss data from a subsurface-drained corn-soybean field in Iowa. Results indicate that an accurate surrogate model can be created for the RZWQM2 with a relatively small number of SG points (i.e., RZWQM2 runs). Compared to the conventional QPSO algorithm, our surrogate-based optimization method can achieve a smaller objective function value and better calibration performance using a fewer number of expensive RZWQM2 executions, which greatly improves computational efficiency.

Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017

NO EVIDENCE FOR ACTIVITY CORRELATIONS IN THE RADIAL VELOCITIES OF KAPTEYN’S STAR

ABSTRACT Stellar activity may induce Doppler variability at the level of a few m s−1 which can then be confused by the Doppler signal of an exoplanet orbiting the star. To first order, linear correlations between radial velocity measurements and activity indices have been proposed to account for any such correlation. The likely presence of two super-Earths orbiting Kapteyn’s star was reported in Anglada-Escudé et al., but this claim was recently challenged by Robertson et al., who argued for evidence of a rotation period (143 days) at three times the orbital period of one of the proposed planets (Kapteyn’s b, P = 48.6 days) and the existence of strong linear correlations between its Doppler signal and activity data. By re-analyzing the data using global statistics and model comparison, we show that such a claim is incorrect given that (1) the choice of a rotation period at 143 days is unjustified, and (2) the presence of linear correlations is not supported by the data. We conclude that the radial velocity signals of Kapteyn’s star remain more simply explained by the presence of two super-Earth candidates orbiting it. We note that analysis of time series of activity indices must be executed with the same care as Doppler time series. We also advocate for the use of global optimization procedures and objective arguments, instead of claims based on residual analyses which are prone to biases and incorrect interpretations.

Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling

Characterizing the mechanical properties of white matter is important to understand and model brain development and injury. With embedded aligned axonal fibers, white matter is typically modeled as a transversely isotropic material. However, most studies characterize the white matter tissue using models with a single anisotropic invariant or in a small-strain regime. In this study, we combined a single experimental procedure – asymmetric indentation – with inverse finite element (FE) modeling to estimate the nearly incompressible transversely isotropic material parameters of white matter. A minimal form comprising three parameters was employed to simulate indentation responses in the large-strain regime. The parameters were estimated using a global optimization procedure based on a genetic algorithm (GA). Experimental data from two indentation configurations of porcine white matter, parallel and perpendicular to the axonal fiber direction, were utilized to estimate model parameters. Results in this study confirmed a strong mechanical anisotropy of white matter in large strain. Further, our results suggested that both indentation configurations are needed to estimate the parameters with sufficient accuracy, and that the indenter-sample friction is important. Finally, we also showed that the estimated parameters were consistent with those previously obtained via a trial-and-error forward FE method in the small-strain regime. These findings are useful in modeling and parameterization of white matter, especially under large deformation, and demonstrate the potential of the proposed asymmetric indentation technique to characterize other soft biological tissues with transversely isotropic properties.

A general method to select representative models for decision making and optimization under uncertainty

The optimization of subsurface flow processes under geological uncertainty technically requires flow simulation to be performed over a large set of geological realizations for each function evaluation at every iteration of the optimizer. Because flow simulation over many permeability realizations (only permeability is considered to be uncertain in this study) may entail excessive computation, simulations are often performed for only a subset of ‘representative' realizations. It is however challenging to identify a representative subset that provides flow statistics in close agreement with those from the full set, especially when the decision parameters (e.g., time-varying well pressures, well locations) are unknown a priori, as they are in optimization problems. In this work, we introduce a general framework, based on clustering, for selecting a representative subset of realizations for use in simulations involving ‘new’ sets of decision parameters. Prior to clustering, each realization is represented by a low-dimensional feature vector that contains a combination of permeability-based and flow-based quantities. Calculation of flow-based features requires the specification of a (base) flow problem and simulation over the full set of realizations. Permeability information is captured concisely through use of principal component analysis. By computing the difference between the flow response for the subset and the full set, we quantify the performance of various realization-selection methods. The impact of different weightings for flow and permeability information in the cluster-based selection procedure is assessed for a range of examples involving different types of decision parameters. These decision parameters are generated either randomly, in a manner that is consistent with the solutions proposed in global stochastic optimization procedures such as GA and PSO, or through perturbation around a base case, consistent with the solutions considered in pattern search optimization. We find that flow-based clustering is preferable for problems involving new well settings (e.g., time-varying well bottom-hole pressures) or small changes in well configuration, while both permeability-based and flow-based clustering provide similar results for (new) random multiwell configurations. We also investigate the use of efficient tracer-type simulations for obtaining flow-based features and demonstrate that this treatment performs nearly as well as full-physics simulations for the cases considered. The various procedures are applied to select realizations for use in production optimization under uncertainty, which greatly accelerates the optimization computations. Optimization performance is shown to be consistent with the realization-selection results for cases involving new decision parameters.

Genetic algorithms for dipole location of fetal magnetocardiography.

In this paper, we explore the use of Maximum Likelihood (ML) method with Genetic Algorithms (GA) as global optimization procedure for source reconstruction in fetal magnetocardiography (fMCG) data. A multiple equivalent current dipole (ECD) model was used for sources active in different time samples. Inverse solutions across time were obtained for a single-dipole approximation to estimate the trajectory of the dipole position. We compared the GA and SIMPLEX methods in a simulation environment under noise conditions. Methods are applied on a real fMCG data. Results show robust estimators of the cardiac sources when GA is used as optimization technique.

MEMS mirrors using sub-wavelength High- Contrast-Gratings with asymmetric unit cells

High-contrast gratings (HCG) are ultra-thin elements operating in sub-wavelength regime with the period of the grating smaller than the wavelength and with the high-index grating material fully surrounded by low-index material. Design of MEMS mirrors made from HCG with specific reflectivity response is of great practical interest in integrated optoelectronics. We theoretically investigate design of the spectral response for HCGs with the complex unit cells. We show that the spectral response can be tailored via the unit cell perturbations and with the asymmetric unit cell perturbations may introduce completely new spectral response. Our results can serve as guidance for the design of the complex HCGs and help with the choice of the efficient initial grating topology prior to global optimization procedure.

Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization

Geometric and information frameworks for constructing global optimization algorithms are considered, and several new ideas to speed up the search are proposed. The accelerated global optimization methods automatically realize a local behavior in the promising subregions without the necessity to stop the global optimization procedure. Moreover, all the trials executed during the local phases are used also in the course of the global ones. The resulting geometric and information global optimization methods have a similar structure, and a smart mixture of new and traditional computational steps leads to 22 different global optimization algorithms. All of them are studied and numerically compared on three test sets including 120 benchmark functions and 4 applied problems.

Optimal design of linear subsynchronous damping controllers for stabilising torsional interactions under all possible operating conditions

Torsional damping controllers, such as supplementary excitation damping controllers (SEDCs), are widely used to stabilise subsynchronous resonance (SSR) induced by torsional interactions (TIs) between turbo-generators and series-compensated power systems. However, because of the changeable operating situations of a power system, it is a great challenge to design them to guarantee torsional stability under all possible operating conditions. This study proposes a global optimal control-design procedure for tuning SEDCs to accommodate the variation of system conditions. Considering TI is a small-signal stability issue, the non-linear power system is converted into a family of linear parameter varying models and the parameter-tuning task for multiple SEDCs is formulated into a multi-model constrained non-linear optimisation problem. A global optimisation procedure based on genetic algorithm and simulated annealing is designed to efficiently solve this problem and obtain a set of robust or several sets of gain-scheduling SEDCs. The proposed method is applied to a multi-machine series-compensated power system. The results of both eigenvalue analysis and time-domain simulation have fully demonstrated the effectiveness of the optimised SEDCs in stabilising SSR under all possible operating conditions.

On the Selection of Integration Intervals for the Calculation of Mean Absorption Coefficients

In radiation modeling of thermal plasmas non-grey models are applied where the radiative transport is described in several frequency bands (spectral intervals). Hereby mean absorption coefficients have to be calculated by a spectral integration procedure, providing a constant mean absorption coefficient for each band. Depending on the number of bands, one or more integration boundaries have to be selected in order to do the integration. In this paper we evaluate the influence of the selection of these integration boundaries on the mean absorption coefficient and the also radiation transfer by applying the mean absorption coefficients in a radiation transport model. Using a simplified two-band model we demonstrate that the selection of the integration boundary has a large impact on the total model accuracy. We show that in some cases selecting a band boundary right at the frequency where the continuum absorption shows a jump can introduce a significant error into the radiation calculation. The process of the integration interval selection thus demands a global optimization procedure to properly evaluate the boundaries of each frequency band.

Timetable setting of single bus line using dynamic programming

The service time of a single bus line is divided into some time periods according to passenger flow intensity; it is supposed that passengers arrive evenly at the stop and bus runs are set evenly in each time period. The bus timetable setting problem is to determine bus run assignments in each time period to minimise the total waiting time of passengers on platforms if the number of total runs is known. This is a typical time-continuous multi-stage decision problem, and the dynamic programming method is appropriate to solve it. Global optimisation procedures using dynamic programming are developed to solve such a multi-stage decision problem. A numerical example is given to demonstrate the efficiency of the proposed method.

Bayesian statistical approach to binary asteroid orbit determination

AbstractThe problem of binary asteroids orbit determination is of particular interest, given knowledge of the orbit is the best way to derive the mass of the system. Orbit determination from observed points is a classic problem of celestial mechanics. However, in the case of binary asteroids, particularly with a small number of observations, the solution is not evident to derive. In the case of resolved binaries the problem consists in the determination of the relative orbit from observed relative positions of a secondary asteroid with respect to the primary. In this work, the problem is investigated as a statistical inverse problem. Within this context, we propose a method based on Bayesian modelling together with a global optimisation procedure that is based on the simulated annealing algorithm.

Test-retest reliability of dynamic causal modeling for fMRI

Dynamic causal modeling (DCM) is a Bayesian framework for inferring effective connectivity among brain regions from neuroimaging data. While the validity of DCM has been investigated in various previous studies, the reliability of DCM parameter estimates across sessions has been examined less systematically. Here, we report results of a software comparison with regard to test-retest reliability of DCM for fMRI, using a challenging scenario where complex models with many parameters were applied to relatively few data points. Specifically, we examined the reliability of different DCM implementations (in terms of the intra-class correlation coefficient, ICC) based on fMRI data from 35 human subjects performing a simple motor task in two separate sessions, one month apart. We constructed DCMs of motor regions with fair to excellent reliability of conventional activation measures. Using classical DCM (cDCM) in SPM5, we found that the test-retest reliability of DCM results was high, both concerning the model evidence (ICC=0.94) and the model parameter estimates (median ICC=0.47). However, when using a more recent DCM version (DCM10 in SPM8), test-retest reliability was reduced notably. Analyses indicated that, in our particular case, the prior distributions played a crucial role in this change in reliability across software versions. Specifically, when using cDCM priors for model inversion in DCM10, this not only restored reliability but yielded even better results than in cDCM. Analyzing each component of the objective function in DCM, we found a selective change in the reliability of posterior mean estimates. This suggests that tighter regularization afforded by cDCM priors reduces the possibility of local extrema in the objective function. We conclude this paper with an outlook to ongoing developments for overcoming the software-dependency of reliability observed in this study, including global optimization and empirical Bayesian procedures.

Bees Algorithm for multimodal function optimisation

The aim of multimodal optimisation is to find significant optima of a multimodal objective function including its global optimum. Many real-world applications are multimodal optimisation problems requiring multiple optimal solutions. The Bees Algorithm is a global optimisation procedure inspired by the foraging behaviour of honeybees. In this paper, several procedures are introduced to enhance the algorithm’s capability to find multiple optima in multimodal optimisation problems. In the proposed Bees Algorithm for multimodal optimisation, dynamic colony size is permitted to automatically adapt the search effort to different objective functions. A local search approach called balanced search technique is also proposed to speed up the algorithm. In addition, two procedures of radius estimation and optima elitism are added, to respectively enhance the Bees Algorithm’s ability to locate unevenly distributed optima, and eliminate insignificant local optima. The performance of the modified Bees Algorithm is evaluated on well-known benchmark problems, and the results are compared with those obtained by several other state-of-the-art algorithms. The results indicate that the proposed algorithm inherits excellent properties from the standard Bees Algorithm, obtaining notable efficiency for solving multimodal optimisation problems due to the introduced modifications.

Exploring lower peak sidelobe windows with the same mainlobe as rectangular window via nature-inspired methodology

Symmetrical windows are widely used as smoothing weighting for signals undergoing discrete Fourier transform (DFT) processing. Briefly speaking, the resolution of spectral analysis is governed by mainlobe width (MW) of a window, and the variance estimates are decreased by the sidelobes leakage with the window. It is generally believed that there has an optimal trade-off between MW and sidelobes ripple levels. The rectangular window (RW) has the smallest MW, but with the highest peak-sidelobe ratio (PSLR). The lower sidelobes of nonrectangular windows, however, have been achieved at the cost of the MW broadening. This paper poses a challenging question of whether the PSLR of a window can be reduced while, preserving the same MW as RW. To demystify this question, we present a global optimization procedure, firefly algorithm (FA), borrowed from nature-inspired methodology, to compute the proposed optimization formulation and perform an extensive number of experimental tests. The experimental results show that the PSLRs of optimized windows can be reduced by 0.98–4.04dB, while preserving the same MW as RW. Furthermore, adjusting the parameters of optimization algorithm, we find that the lower PSLR of optimized window generally leads to higher envelope level of the sidelobes ripple.

Vibrational spectra and structures of neutral Si₆X clusters (X = Be, B, C, N, O).

Neutral silicon clusters doped with first row elements (Si6X) have been generated (X = B, C, N, O) and characterized by infrared-ultraviolet (IR-UV) two-photon resonance-enhanced ionization spectroscopy (X = C, O) and quantum chemical calculations (X = Be, B, C, N, O, Si). In the near threshold UV photoionization, the ion signal of specific cluster sizes can be significantly enhanced by resonant excitation with tunable IR light prior to UV irradiation, allowing for the measurement of the IR spectra of Si7, Si6C, and Si6O clusters. Structural assignments are achieved with the help of a global optimization procedure using density functional theory (DFT). The most stable calculated structures show the best agreement between predicted and measured spectra. The dopant atoms in the Si6X clusters have a negative net charge and the Si atoms act as electron donors within the clusters. Moreover, the overall structures of the Si6X clusters depend strongly on the nature of the dopant atom, i.e., its size and valency. While in some of the Si6X clusters one Si atom in Si7 is simply substituted by the dopant atom (X = Be, B, C), other cases exhibit a completely different geometry (X = N, O). As a general trend, doping of the Si7 cluster with first-row dopants is predicted to shift the optically allowed electronic transitions into the visible or even near-IR spectral range due to symmetry reduction or the radical character of the doped cluster.

Ordinal regression by a generalized force-based model.

This paper introduces a new instance-based algorithm for multiclass classification problems where the classes have a natural order. The proposed algorithm extends the state-of-the-art gravitational models by generalizing the scaling behavior of the class-pattern interaction force. Like the other gravitational models, the proposed algorithm classifies new patterns by comparing the magnitude of the force that each class exerts on a given pattern. To address ordinal problems, the algorithm assumes that, given a pattern, the forces associated to each class follow a unimodal distribution. For this reason, a weight matrix that allows to modify the metric in the attributes space and a vector of parameters that allows to modify the force law for each class have been introduced in the model definition. Furthermore, a probabilistic formulation of the error function allows the estimation of the model parameters using global and local optimization procedures toward minimization of the errors and penalization of the non unimodal outputs. One of the strengths of the model is its competitive grade of interpretability which is a requisite in most of real applications. The proposed algorithm is compared to other well-known ordinal regression algorithms on discretized regression datasets and real ordinal regression datasets. Experimental results demonstrate that the proposed algorithm can achieve competitive generalization performance and it is validated using nonparametric statistical tests.

Comparative study of RPSALG algorithm for convex semi-infinite programming

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Proper motions of the optically visible open clusters based on the UCAC4 catalog

We present a catalog of mean proper motions and membership probabilities of individual stars for optically visible open clusters, which have been determined using data from the UCAC4 catalog in a homogeneous way. The mean proper motion of the cluster and the membership probabilities of the stars in the region of each cluster were determined by applying the statistical method in a modified fashion. In this study, we applied a global optimization procedure to fit the observed distribution of proper motions with two overlapping normal bivariate frequency functions, which also take the individual proper motion errors into account. For 724 clusters, this is the first determination of proper motion, and for the whole sample, we present results with a much larger number of identified astrometric member stars. Furthermore, it was possible to estimate the mean radial velocity of 364 clusters (102 unpublished so far) with the stellar membership using published radial velocity catalogs. These results provide an increase of 30% and 19% in the sample of open clusters with a determined mean absolute proper motion and mean radial velocity, respectively.