Powell's Method Research Articles

Comparative Analysis of Inverse Problem-Solving Techniques: Integrating Deep Learning with Advanced Optimization Methods

This paper presents a comparative analysis of four distinct approaches to solving inverse problems in engineering and scientific applications. The studies under comparison integrate deep learning techniques, specifically using TensorFlow, with various optimization methods: Genetic Algorithm (GA), Ant Colony Optimization (ACO), LMFIT (employing Nelder-Mead and Powell methods), and Particle Swarm Optimization (PSO). All four approaches aim to predict design parameters for achieving desired response profiles. This analysis examines the methodologies, performance metrics, and unique features of each approach, providing insights into their relative strengths and potential applications.

A novel ensemble approach with deep transfer learning for accurate identification of foodborne bacteria from hyperspectral microscopy

The detection of foodborne bacteria is critical in ensuring both consumer safety and food safety. If these pathogens are not properly identified, it can lead to dangerous cross-contamination. One of the most common methods for classifying bacteria is through the examination of Hyperspectral microscope imaging (HMI). A widely used technique for measuring microbial growth is microscopic cell counting. HMI is a laborious and expensive process, producing voluminous data and needing specialized equipment, which might not be widely available. Machine learning (ML) methods are now frequently utilized to automatically interpret data from hyperspectral microscopy. The objective of our study is to devise a technique that employs deep transfer learning to address the challenge of limited data and utilizes four base classifiers - InceptionResNetV2, MobileNet, ResNet101V2, and Xception - to create an ensemble-based classification model for distinguishing live and dead bacterial cells of six pathogenic strains. In order to determine the optimal weights for the base classifiers, a Powell's optimization method was utilized in conjunction with a weighted average ensemble (WAVE) technique. We carried out an extensive experimental study to verify the efficiency of our proposed ensemble model on live and dead cell images of six different foodborne bacteria. In order to gain a better understanding of the regions, we performed a Grad-CAM analysis to explain the predictions made by our model. Through a series of experiments, our proposed framework has proven its capacity to effectively and precisely detect numerous bacterial pathogens. Specifically, it achieved a perfect identification rate of 100 % for Escherichia coli (EC), Listeria innocua (LI), and Salmonella Enteritidis (SE), while achieving rates of 96.30 % for Salmonella Typhimurium (ST), 87.13 % for Staphylococcus aureus (SA), and 94.12 % for Salmonella Heidelberg (SH). As a result, it can be considered as an effective tool for the identification of foodborne pathogens, due to its high level of efficiency.

Kinetics model with experimental validation for optimal microalgae generation in double-skin façades

Microalgae photobioreactors integrated into double-skin façades in cold climates enhance growth conditions for biomass generation, CO2 fixation, and O2 production, while reducing thermal loads. However, shading imposed by double-skin façade's assembly limits light interception for the photobioreactors. This study employs kinetics and shading models to estimate variations in biomass concentration within the light-constrained photobioreactor. To validate the accuracy and reliability of the model, the results were compared to experimental data collected by the authors from a full-scale constructed system. Biomass concentration was monitored using a developed RGB image-based monitoring technique. Direct search methods were employed to optimize the design and operational variables of the microalgae photobioreactors, with the goal of maximizing annual areal and volumetric productivities across 14 Canadian cities under various climatic conditions. Hooke-Jeeves algorithm was 65.6 % faster than Powell's conjugate direction method. This showed the system's adaptability by generating 1.3–3.0 kg/m2.year of biomass in different climates. The study established a framework for optimizing microalgae photobioreactors into façades to maximize biomass harvest.

An augmented memoryless Davidon–Fletcher–Powell method based on the Dai–Liao approach

ABSTRACT For the sake of enhancing computational efficiency of the memoryless Davidon–Fletcher–Powell method, we set a direct link between this method and the Dai–Liao technique. Thus, we make it possible to organize assistance for the memoryless Davidon–Fletcher–Powell method from the numerical viewpoint, in the framework of a two-parameter algorithm. One of the parameters of the method is determined based on a modified secant equation while the other can benefit from the classic adaptive formulas of the Dai–Liao parameter. We discuss when the sufficient descent condition holds and how it can serve for the convergence of the method. Then, we review some smoothing plans for a classic nonsmooth minimization model which frequently appears in the real-world applications. Ultimately, we perform computational tests to mirror the efficiency of the method and then, we report the results as well.

Estimating error rates for single molecule protein sequencing experiments.

The practical application of new single molecule protein sequencing (SMPS) technologies requires accurate estimates of their associated sequencing error rates. Here, we describe the development and application of two distinct parameter estimation methods for analyzing SMPS reads produced by fluorosequencing. A Hidden Markov Model (HMM) based approach, extends whatprot, where we previously used HMMs for SMPS peptide-read matching. This extension offers a principled approach for estimating key parameters for fluorosequencing experiments, including missed amino acid cleavages, dye loss, and peptide detachment. Specifically, we adapted the Baum-Welch algorithm, a standard technique to estimate transition probabilities for an HMM using expectation maximization, but modified here to estimate a small number of parameter values directly rather than estimating every transition probability independently. We demonstrate a high degree of accuracy on simulated data, but on experimental datasets, we observed that the model needed to be augmented with an additional error type, N-terminal blocking. This, in combination with data pre-processing, results in reasonable parameterizations of experimental datasets that agree with controlled experimental perturbations. A second independent implementation using a hybrid of DIRECT and Powell's method to reduce the root mean squared error (RMSE) between simulations and the real dataset was also developed. We compare these methods on both simulated and real data, finding that our Baum-Welch based approach outperforms DIRECT and Powell's method by most, but not all, criteria. Although some discrepancies between the results exist, we also find that both approaches provide similar error rate estimates from experimental single molecule fluorosequencing datasets.

Quantification of Gravitational Effects on Nasal Tip Geometry

Introduction: It is widely accepted in plastic surgery that patient positioning can affect the geometry of the nasal tip due to downward gravitational forces. However, empirical data supporting this principle is lacking. The primary objective of this study is to quantify gravitational effects on nasal tip geometry by calculating changes in tip rotation and projection between the supine and upright positions. This analysis will help further assess whether gravity affects the actual positional rotation of the nasal tip or if its impact is solely relative to neighboring landmarks. Methods: This study is a prospective case series that obtains upright and supine nasal measurements in 20 subjects. The nasolabial, nasofrontal, and columellar-facial angles, as well as the Goode, Crumley, Simon, and Powell ratios are used to calculate nasal tip rotation and projection changes. Results: Mean nasolabial angle demonstrated a statistically significant tip derotation of 3.2° in the upright position relative to supine. Mean nasofrontal angle and mean columellar-facial angle did not significantly differ between positions. The nasal tip appeared relatively less projected in the upright position using the Simon and Crumley methods, whereas no significant difference was seen with the Powell and Goode methods. Conclusion: Gravity can influence the apparent nasal tip geometry by altering lip position and length, but it does not impact the true nasal tip geometry when the upper lip is excluded as a reference point.

Machine Learning in Quasi-Newton Methods

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulate a quality functional and minimize it by using gradient machine learning algorithms. We demonstrate that this approach leads us to the well-known ways of updating metric matrices used in QNM. The learning algorithm for finding metric matrices performs minimization along a system of directions, the orthogonality of which determines the convergence rate of the learning process. The degree of learning vectors’ orthogonality can be increased both by choosing a QNM and by using additional orthogonalization methods. It has been shown theoretically that the orthogonality degree of learning vectors in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is higher than in the Davidon–Fletcher–Powell (DFP) method, which determines the advantage of the BFGS method. In our paper, we discuss some orthogonalization techniques. One of them is to include iterations with orthogonalization or an exact one-dimensional descent. As a result, it is theoretically possible to detect the cumulative effect of reducing the optimization space on quadratic functions. Another way to increase the orthogonality degree of learning vectors at the initial stages of the QNM is a special choice of initial metric matrices. Our computational experiments on problems with a high degree of conditionality have confirmed the stated theoretical assumptions.

Optimization of a centrifugal pump with high efficiency and low noise based on fast prediction method and vortex control

This study aims to develop a rapid optimization design method for the centrifugal pump with high efficiency and low noise. The improved delayed detached eddy simulation and Powell's vortex sound method were employed to calculate the flow and sound field. The prediction models of hydraulic loss and noise based on vortex characteristic quantities were built using linear regression (LR) and artificial neural network (ANN) methods respectively. The Kriging surrogate model and the NSGA-II genetic algorithm were utilized for minimizing the entropy production rate and average total sound pressure in the pump, where the objectives of the training dataset for Kriging model were calculated by prediction model (scheme I) and conventional unsteady numerical simulation (scheme II). Results show that the structure and performance of optimized pumps under both schemes are nearly identical, but the computational cost of scheme Iis much lower than that of scheme II. The shear of the optimized pump is significantly reduced and the rigid rotational strength is enhanced, leading to head and efficiency improved by 3.2 % and 3.7 % respectively, under the design flow condition. The average total sound pressure level is reduced by 1.07 % due to the fluctuation suppression of shear and rigid vorticity.

Some histological and biochemical evaluation on commercial hair dyes

The use of hair dyes as a means of beautification is currently increasing. This study aimed at evaluating the toxicity of different commercial hair dyes on the histology of the skin and biochemical parameters of the liver of Albino rats. This study was carried out in the Pathology Department, University of Calabar Teaching Hospital Calabar and College of Medical Sciences, University of Calabar, Calabar between May, 2019 and October, 2019. Four different colours of hair dyes were obtained from a cosmetic store in Watt daily market in Calabar, Cross River State. Twenty male Albino rats with average weight of 55g were used for this study. The rats were randomly divided into five (5) groups of four (4) rats each. Group 1 to 4 served as the test groups while group 5 served as the control group. Different colours of hair dye were applied topically on selected area of the back of Albino rats daily for 30 days after which, the rats were sacrificed using chloroform inhalation procedure. The skin of the rat was harvested for histology while heart puncture was used to collect 5 milliliters of blood from each rat for biochemical analysis. Plasma Alkaline phosphatase (ALP) was determined using Kind and King's method. Plasma Alanine amino transferase (ALT) and Aspartate Amino transferase (AST) were determined by Reitman and Frankel method. Serum protein (TP) was determined by Biurette's method while bilirubin was estimated using Powell's method. Liver tissues were processed using routine paraffin wax tissue processing method for histological analysis. The serum levels of ALP, AST, TP, Total bilirubin (TB) and conjugated bilirubin (CB) in all the test groups were significantly increased when compared with the control (P=0.001). Histological evaluations indicated evidence of cellular injury in all the test groups. Prolonged use of commercial hair dyes caused adverse effects to the skin and liver as seen in the Albino rat used in this study.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative (MAM) random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array, we introduce a derivative-free cat swarm optimization for parameter estimation. We embed the Powell method, which uses conjugate direction acceleration and does not need to derive the objective function, into the original cat swarm optimization to accelerate its convergence speed and search accuracy. We use the ordinary least squares, weighted least squares, original cat swarm optimization, particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity, respectively. The experimental results show that the improved cat swarm optimization has faster convergence speed, higher search accuracy, and better stability than the original cat swarm optimization and the particle swarm algorithm. At the same time, the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations. The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

Experimental and modeling study of the ignition kinetics of dimethyl carbonate

In this work, the ignition delay times (IDTs) of dimethyl carbonate (DMC) were measured by using a rapid compression machine (RCM) over a wide range of temperatures (778–1102 K), pressures (20 and 40 bar), equivalence ratios (φ= 0.5, 1.0, and 2.0) and fuel concentrations (1% and 2%), yielding results which are in substantial variance with those calculated with detailed kinetics in the literature over the entire range of conditions investigated. By further identifying the key reactions controlling ignition under different conditions by using sensitivity and path analyses, and taking the experimental data of typical working conditions as the target variable, the Arrhenius parameters of the main sensitive reactions are optimized through the global optimization using the genetic algorithm and the local optimization using the Powell's Direction Set method. Results show that the overall performance of the optimized kinetics model is in good agreement with the experimental data, and the IDTs of DMC can be predicted over the wide range of conditions.

A Hybrid Genetic/Powell Algorithm for Wind Measurement in Doppler Lidar

Doppler peaks extraction from massive raw data is a tricky part of coherent Doppler wind Lidar (CDWL) optimization. In this paper, a hybrid genetic/Powell algorithm (HGAP) is proposed to process the power spectrum of the measured signal from CDWL. The HGAP has excellent global exploration capability, which likes traditional genetic algorithms and fast convergence, which like the Powell method. Hence, the HGAP has advantages to find the center frequency of the Doppler peaks from massive raw data, especially to search multiple peaks in complex wind field measurement. Compared with other notable algorithms, the HGAP shows excellent performance in numerical optimization when we use it to solve 27 typical benchmark functions. Then, our algorithm is used to process the raw data in a field experiment of radial wind measurement. The results show that the HGAP can obtain wind speed components quickly and accurately and has value for application in complex wind field analysis.

Non-asymptotic superlinear convergence of standard quasi-Newton methods

In this paper, we study and prove the non-asymptotic superlinear convergence rate of the Broyden class of quasi-Newton algorithms which includes the Davidon–Fletcher–Powell (DFP) method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The asymptotic superlinear convergence rate of these quasi-Newton methods has been extensively studied in the literature, but their explicit finite–time local convergence rate is not fully investigated. In this paper, we provide a finite–time (non-asymptotic) convergence analysis for Broyden quasi-Newton algorithms under the assumptions that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal solution. We show that in a local neighborhood of the optimal solution, the iterates generated by both DFP and BFGS converge to the optimal solution at a superlinear rate of (1/k)^{k/2}, where k is the number of iterations. We also prove a similar local superlinear convergence result holds for the case that the objective function is self-concordant. Numerical experiments on several datasets confirm our explicit convergence rate bounds. Our theoretical guarantee is one of the first results that provide a non-asymptotic superlinear convergence rate for quasi-Newton methods.

Optimal wind turbine jacket structural design under ultimate loads using Powell's method

This paper developed an optimization procedure using Powell's method with symbolic search variables, so any one or more parameters in structural designs can be optimal. Powell's method was used to determine the optimal Offshore Wind Turbine (OWT) jacket geometry under IEC-61400-3-1 (Wind Turbines-part 3-1, Design requirements for fixed offshore wind turbines. 2019), tropical cyclone, and seismic loads to minimize the structural weight. A linear generator braking system was proposed to stop the rotor under the power production plus occurrence of fault, and analysis results indicate that this braking system can avoid the steel design dominated by this situation. When the soil resistance is strong enough, the three-leg structural type is superior; otherwise, the four-leg one is suggested. The length between two bottom legs of three-leg cases is larger than that of four-leg cases, while the average ratio of the three and four-leg cases can be set to near 1.39. The total required steel mass is roughly linearly proportional to the water depth, and it increases by around 40% from a water depth of 35 m–80 m, so the jacket type can still be used in the deep sea under not only IEC-61400-3-1 loads but also seismic and tropical cyclone loads.

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the variational form were better than those obtained when the form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.

Numerical Study of Divergence Cleaning and Coronal Heating/Acceleration Methods in the 3D COIN-TVD MHD Model

In the solar coronal numerical simulation, the coronal heating/acceleration and the magnetic divergence cleaning techniques are very important. The coronal–interplanetary total variation diminishing (COIN-TVD) magnetohydrodynamic (MHD) model is developed in recent years that can effectively realize the coronal–interplanetary three-dimensional (3D) solar wind simulation. In this study, we focus on the 3D coronal solar wind simulation by using the COIN-TVD MHD model. In order to simulate the heating and acceleration of solar wind in the coronal region, the volume heating term in the model is improved efficiently. Then, the influence of the different methods to reduce the ∇⋅B constraint error on the coronal solar wind structure is discussed. Here, we choose Carrington Rotation (CR) 2199 as a study case and try to make a comparison of the simulation results among the different magnetic divergence cleaning methods, including the diffusive method, the Powell method, and the composite diffusive/Powell method, by using the 3D COIN-TVD MHD model. Our simulation results show that with the different magnetic divergence cleaning methods, the ∇⋅B error can be reduced in different levels during the solar wind simulation. Among the three divergence cleaning methods we used, the composite diffusive/Powell method can maintain the divergence cleaning constraint better to a certain extent, and the relative magnetic field divergence error can be controlled in the order of 10−9. Although these numerical simulations are performed for the background solar corona, these methods are also suitable for the simulation of CME initiation and propagation.

A comparison of various classical optimizers for a variational quantum linear solver

Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that can be computed far more efficiently on a quantum device. The cost function is constructed such that finding the ansatz parameters that minimize its value, solves some problem of interest. We focus specifically on the Variational Quantum Linear Solver (VQLS), and examine the effect of several gradient-free and gradient-based classical optimizers on performance. We focus on both the average rate of convergence of the classical optimizers studied, as well as the distribution of their average termination cost values, and how these are affected by noise. Our work demonstrates that realistic noise levels on NISQ devices present a challenge to the optimization process. All classical optimizers appear to be very negatively affected by the presence of realistic noise. If noise levels are significantly improved, there may be a good reason for preferring gradient-based methods in the future, which performed better than the gradient-free methods with the only shot-noise present. The gradient-free optimizers, Simultaneous Perturbation Stochastic Approximation (SPSA) and Powell's method, and the gradient-based optimizers, AMSGrad and BFGS performed the best in the noisy simulation, and appear to be less affected by noise than the rest of the methods. SPSA appears to be the best performing method. COBYLA, Nelder-Mead and Conjugate-Gradient methods appear to be the most heavily affected by noise, with even slight noise levels significantly impacting their performance.

B-ФОРМА МЕТОДА ДАВИДОНА–ФЛЕТЧЕРА–ПАУЭЛЛА

A special form (B-form) of methods of Quasi-Newton type is discussed, which makes it easy to interpret these methods as gradient in appropriately transformed argument space. B-form of the Davidon–Fletcher–Powell method is given and compared with r-algorithms. To minimize smooth convex functions, a gradient method with space transformation is built, combining properties of both quasi-Newtonian methods and r-algorithms. Possible schemes of this type of methods for minimizing non-smooth convex functions are discussed.

Methodology of Processing Single-Strip Blocks of Imagery with Reduction and Optimization Number of Ground Control Points in UAV Photogrammetry

Unmanned aerial vehicle (UAV) systems are often used to collect high-resolution imagery. Data obtained from UAVs are now widely used for both military and civilian purposes. This article discusses the issues related to the use of UAVs for the imaging of restricted areas. Two methods of developing single-strip blocks with the optimal number of ground control points are presented. The proposed methodology is based on a modified linear regression model and an empirically modified Levenberg–Marquardt–Powell algorithm. The effectiveness of the proposed methods of adjusting a single-strip block were verified based on several test sets. For method I, the mean square errors (RMSE) values for the X, Y, Z coordinates of the control points were within the range of 0.03–0.13 m/0.08–0.09 m, and for the second method, 0.03–0.04 m/0.06–0.07 m. For independent control points, the RMSE values were 0.07–0.12 m/0.06–0.07 m for the first method and 0.07–0.12 m/0.07–0.09 m for the second method. The results of the single-strip block adjustment showed that the use of the modified Levenberg–Marquardt–Powell method improved the adjustment accuracy by 13% and 16%, respectively.

Метод пошуку екстремуму багатомірних функцій при вирішенні інженерних задач машин для лісотехнічних робіт

This article is devoted to the analysis of the most common optimization methods used in practical engineering problems of finding the extremum of multidimensional functions and the formation on the basis of the identified properties of recommendations for choosing the best on different data sets. In the process of analysis, various implementations of gradient descent methods, pulse methods, adaptive methods and quasi-Newtonian methods were considered, and the advantages and problems of each of the methods in their use were summarized. Developed computer program that implements the use of all considered methods. The computational experiment performed for the three functions showed that the zero -Rosenbrock and zero - Powell methods proved to be the most effective.