Automated, Parallel Optimization Algorithms for Stochastic Functions

The optimization algorithms for stochastic functions are desired specifically for real-world and simulation applications where results are obtained from sampling, and contain experimental error or random noise. We have developed a series of stochastic optimization algorithms based on the well-known classical down hill simplex algorithm. Our parallel implementation of these optimization algorithms, using a framework called MW, is based on a master-worker architecture where each worker runs a massively parallel program. This parallel implementation allows the sampling to proceed independently on many processors as demonstrated by scaling up to more than 100 vertices and 300 cores. This framework is highly suitable for clusters with an ever increasing number of cores per node. The new algorithms have been successfully applied to the reparameterization of a model for liquid water, achieving thermodynamic and structural results for liquid water that are better than a standard model used in molecular simulations, with the the advantage of a fully automated parameterization process

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Derivative-free hybrid methods in global optimization and their applications

In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.Doctor of Philosoph

Parameters optimization of a charge transport model for the electrical characterization of dielectric materials

Un modèle mathématique basé sur la physique des matériaux isolants a été développé dans notre laboratoire pour décrire le transport de charge bipolaire (BCT) dans le polyéthylène basse densité (LDPE) sous contrainte de courant continu. Les phénomènes de piégeage et de dé-piégeage, la hauteur de la barrière pour l'injection, la mobilité et le processus de recombinaison des charges positives et négatives sont considérés. Le modèle est basé sur l'équation de Poisson et la loi de conservation des charges. Ce modèle nécessite des entrées qui sont reliées aux conditions expérimentales telles que la température, la tension appliquée, l'épaisseur du diélectrique, etc., ainsi qu'un l'ensemble de paramètres tels que la barrière d'injection, la mobilité, les coefficients de piégeage et de dé-piégeage. La plupart de ces paramètres ne peuvent être prédits, observés ou estimés par des expériences indépendantes. Pour cette raison, un algorithme d'optimisation est utilisé pour optimiser le modèle BCT afin qu'il s'adapte aux mesures expérimentales, quelles que soient les conditions expérimentales. Le principe de ce type d'algorithme est basé sur la minimisation d'une fonction coût qui rend compte des écarts entre les données issues de l'expérience et celles issues du modèle. Les données expérimentales utilisées sont la densité de charge nette mesurée par la méthode électro-acoustique pulsée (PEA) ainsi que les mesures du courant de charge externe. Après avoir testé cinq algorithmes d'optimisation nous avons sélectionné l'algorithme Trust Region Reflective qui répond au mieux à nos critères. Cet algorithme a permis de trouver un ensemble de paramètres permettant une bonne corrélation entre les densités de courant et de charge simulées et celles obtenues expérimentalement. Cette optimisation a été réalisée en considérant différent champs électriques appliqués au matériau afin d'avoir un jeu de paramètre qui caractérise au mieux le matériau d'étude. En outre, l'algorithme d'optimisation a permis d'analyser la barrière d'injection lorsque les interfaces sont de natures différentes.A mathematical model based on the physics of insulating materials has been developed in our laboratory to describe the bipolar charge transport (BCT) in low-density polyethylene (LDPE) under DC stress. The phenomena of trapping and detrapping, the barrier height for injection, the mobility, and the recombination process of positive and negative charges are considered. The model is based on the Poisson equation and the law of conservation of charges. This model requires inputs that are related to the experimental conditions such as temperature, applied voltage, dielectric thickness, etc., as well as a set of parameters such as the injection barrier, mobility, trapping, and detrapping coefficients. Most of these parameters cannot be predicted, observed, or estimated by independent experiments. For this reason, an optimization algorithm is used to optimize the BCT model to fit the experimental measurements, whatever the experimental conditions, by minimizing the sum of squares of the deviations between the experimental data and the model data. The experimental data used are the net charge density measured by the pulsed electro-acoustic method (PEA) as well as the external charge current measurements. After testing five optimization algorithms we selected the following algorithm Trust Region Reflective which best meets our criteria. This algorithm has allowed us to find a set of parameters allowing a good correlation between the simulated current and charge densities with those obtained experimentally. This optimization was performed by considering different electric fields applied to the material in order to have a unique set of parameters that best characterizes the studied material. In addition, the optimization algorithm allowed to analyze the injection barrier when the interfaces are of different natures

Reducing the expense of electronic structure calculations for larger molecules : optimized auxiliary basis sets, and system-specifically reparametrized semiempirical methods

Optimization approaches using several global and local algorithms (genetic algorithms, direct search, simplex and implicit filtering) in the search for a global minimum are applied to optimize auxiliary basis sets for quantum chemistry ab-initio calculations and to reparametrize semiempirical methods. We optimize auxiliary basis sets for RI-MP2 and RI-HF, by minimizing a suitable difference measure to the analogous calculations without the RI technique. It is shown that our methods of generating optimal auxiliary basis sets are more systematic and can be automatized more easily than the traditional approach. Hence, they can reasonably be expected to be faster and more reliable. At the same time, the quality of our basis sets is at least as good as that from the traditional approach. As an application, we present the first systematically optimized and complete set of mixed Poisson and density auxiliary basis sets for the atoms H, B, C, N, O and F, complementing the standard basis sets cc-pVXZ (X = D, T, Q and 5). As soon as efficient integral routines for this new basis function type become available, calculations with them will be much more efficient than with traditional basis sets. Similarly, these global and local optimization methods are also employed to reparametrize semiempirical methods for a difficult double proton transfer system. System-specific reparametrization of the well-known AM1, PM3 and PM5 methods is done by minimizing the error of the semiempirical calculations compared to ab-initio reference data at the MP2/aug-cc-pVDZ level. This is done at a small set of selected geometries, leading to one- and two-dimensional potential energy surfaces that are quantitatively in agreement with the ab-initio data over a much broader range of geometries. With this system-specific adaption, these reparametrized methods lead to results far superior to those obtainable with standard parameters. Nevertheless, the full speed advantage of the semiempirical approach is retained, offering the possibility to do direct dynamics studies with the potential energy surface calculated on the fly at ab-initio quality but at a fraction of the ab-initio cost. In both cases, our combination of genetic algorithm global search and Powell local search is the fastest and most robust choice for optimization, comparing with the other methods. Therefore, in these cases, a combination of global and local search is actually better than a purely local algorithm

Building blocks and structural patterns in silicon clusters : global and local optimizations employing empirical potentials, density functionals, and ab-initio calculations

Sin clusters in the size range n=4-35 have been investigated, using a combination of global structure optimization methods with DFT and ab-initio calculations. One of the central aims is to provide explanations for the structural transition from prolate to spherical outer shapes at about n=25, as observed in ion mobility measurements. First, several empirical potentials for silicon and a newly generated variant of one of them were better adapted to small silicon clusters, by global optimization of their parameters. The best resulting empirical potentials were then employed in global cluster structure optimizations. The most promising structures from this stage were relaxed further at the DFT level with a hybrid B3LYP functional. For the resulting structures, single point energies have been calculated at the LMP2 level with cc-pVTZ basis set. Results obtained at the DFT level strongly support the shape transition form prolate to spherical structures beginning with Si26. In contrast, at the LMP2 level, the dominance of spherical structures after the transition region could not be confirmed

Improved Evolutionary Hybrids for Flexible Ligand Docking in Autodock

In this paper we evaluate the design of the hybrid evolutionary algorithms (EAs) that are currently used to perform flexible ligand binding in the Autodock docking software. Hybrid EAs incorporate specialized operators that exploit domain-specific features to accelerate an EA's search. We consider hybrid EAs that use an integrated local search operator to reline individuals within each iteration of the search. We evaluate several factors that impact the efficacy of a hybrid EA, and we propose new hybrid EAs that provide more robust convergence to low-energy docking configurations than the methods currently available in Autodock

Global optimization: techniques and applications

Optimization problems arise in a wide variety of scientific disciplines. In many practical problems, a global optimum is desired, yet the objective function has multiple local optima. A number of techniques aimed at solving the global optimization problem have emerged in the last 30 years of research. This thesis first reviews techniques for local optimization and then discusses many of the stochastic and deterministic methods for global optimization that are in use today. Finally, this thesis shows how to apply global optimization techniques to two practical problems: the image segmentation problem (from imaging science) and the 3-D registration problem (from computer vision)