Powell Algorithm Research Articles

Implementing numerical algorithms to optimize the parameters in Kampmann–Wagner Numerical (KWN) precipitation models

The Kampmann–Wagner Numerical (KWN) model of precipitation is a powerful tool to simulate the precipitation of the second phase considering the nucleation, growth, and coarsening. Some quantities such as interfacial energy and nucleation site number density are required to accomplish the simulation. Practically, those quantities are hard to measure in the experiment directly, and the derivation of those quantities through modeling can also be costly. In this work, we hereby adopt the minimization algorithm implemented in the open-source Scipy Python package to derive that important information in terms of very limited experimental data. The convergence and robustness of different algorithms are discussed. Among those algorithms, the Nelder–Mead and Powell algorithms are successfully applied to optimize multiple parameters during KWN modeling. This work will shed light on the design of experiments/processes and facilitate integrated computational materials engineering (ICME).

Application of the Powell algorithm for estimating optical properties of a semitransparent medium based on time-domain information

Accurate estimation of the optical properties of a semitransparent medium is crucial in various engineering applications. This study introduces the Powell algorithm to estimate the optical properties of a 2D semitransparent slab. The time-domain radiative transfer equation is solved using the discrete ordinate method. The radiative intensity on the medium’s surface serves as the measurement signal for the inverse analysis. The results demonstrate that the Powell algorithm accurately estimates the absorption coefficient, scattering coefficient, and scattering asymmetry factor. For simultaneous reconstruction of these three parameters, it is recommended to use eight signal detectors on both the left and right sides of the medium. Even when the standard measurement error is increased to 15%, the relative errors for these three parameters remain low, at 1.87%, 1.379%, and 0.194%.

Wireless sensor node localization algorithm combined with PSO-DFP

Abstract In wireless communication technology, wireless sensor networks usually need to collect and process information in very harsh environment. Therefore, accurate positioning of sensors becomes the key to wireless communication technology. In this study, Davidon–Fletcher–Powell (DFP) algorithm was combined with particle swarm optimization (PSO) to reduce the influence of distance estimation error on positioning accuracy by using the characteristics of PSO iterative optimization. From the experimental results, among the average precision (AP) values of DFP, PSO, and PSO-DFP algorithms, the AP value of PSO-DFP was 0.9972. In the analysis of node positioning error, the maximum node positioning error of PSO-DFP was only about 21 mm. The results showed that the PSO-DFP algorithm had better performance, and the average positioning error of the algorithm was inversely proportional to the proportion of anchor nodes, node communication radius, and node density. In conclusion, the wireless sensor node location algorithm combined with PSO-DFP has a better location effect and higher stability than the traditional location algorithm.

Benchmarking of different optimizers in the variational quantum algorithms for applications in quantum chemistry.

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as hydrogen, lithium hydride, beryllium hydride, water, and hydrogen fluoride. The errors in the ground state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and finally a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster ansatz for simulations, and the number of qubits varied from two starting from the hydrogen molecule to ten qubits in hydrogen fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient, limited-memory Broyden-Fletcher-Goldfarb-Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers.

A comparative analysis between two heuristic algorithms for the graph vertex coloring problem

This study focuses on two heuristic algorithms for the graph vertex coloring problem: the sequential (greedy) coloring algorithm (SCA) and the Welsh–Powell algorithm (WPA). The code of the algorithms is presented and discussed. The methodology and conditions of the experiments are presented. The execution time of the algorithms was calculated as the average of four different starts of the algorithms for all analyzed graphs, taking into consideration the multitasking mode of the operating system. In the graphs with less than 600 vertices, in 90% of cases, both algorithms generated the same solutions. In only 10% of cases, the WPA algorithm generates better solutions. However, in the graphs with more than 1,000 vertices, in 35% of cases, the WPA algorithm generates better solutions. The results show that the difference in the execution time of the algorithms for all graphs is acceptable, but the quality of the solutions generated by the WPA algorithm in more than 20% of cases is better compared to the SC algorithm. The results also show that the quality of the solutions is not related to the number of iterations performed by the algorithms.

A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.

1 × 5 broadband photonic crystal power splitter designed by the Powell algorithm.

We propose a novel, to the best of our knowledge, 1×5 broadband power splitter based on the photonic crystal. The Powell algorithm is used to reverse-design the proposed broadband power splitter. The results show that the transmittance of each output port of the broadband photonic crystal power splitter can be adjusted by changing the radii and offsets of the dielectric rods at the junction area of each waveguide. According to the target splitting ratio, the reverse design of the structural parameters using the Powell algorithm significantly improves the optimization efficiency and splitting performance of the broadband power splitter. The designed power splitters have a wide working bandwidth of 1525-1565 nm, a flexible and designable power splitting ratio, excellent splitting performance, and a compact size, which have great application prospects in all-optical communication networks, high-density photon integration, and other fields.

Enhance the frame accumulation accuracy of breast multispectral transmission image by the improved Powell registration algorithm

Multispectral transmission imaging provides a new direction for the early screening of breast cancer. Frame accumulation technology can effectively solve the problem of low grayscale and poor multispectral transmission images quality, but the accuracy of the result will be reduced due to the shift between image frames caused by human respiration and jitter. Therefore, an improved Powell registration algorithm based on normalized mutual information is proposed to register sequence images to improve the accuracy of images after frame accumulation. Firstly, the video is acquired and preprocessed through the designed breast transmission image acquisition system. Then, the coarse registration parameters are obtained by the "Rotation Translation scanning" method, which are used as the initial point of Powell algorithm for fine registration to obtain the registered image sequence. Finally, frame accumulation is performed on the registered images. The registration accuracy and the image quality of frame accumulation after registration are evaluated respectively. The results show that the improved method can raise the registration accuracy of the set floating image to more than 98.9%. This method not only improves the registration accuracy of Powell algorithm, but also solves the influence of jitter on frame accumulation technology, and provides a reference for the recognition and segmentation of breast blood vessels or tumors in multispectral transmission images.

Penerapan Pewarnaan Graf Pada Penjadwalan Mata Kuliah Program Studi Matematika UIN Imam Bonjol Padang

A graph is a discrete structure consisting of vertices and edges connecting these vertices. One of the discussions in graph theory is graph coloring. In this research, graph coloring will be applied in making the schedule for the Mathematics study program at UIN Imam Bonjol Padang by assuming the subject as a vertice and the lecturer as an edge. One of the benefits of applying graph coloring in scheduling makes scheduling arrangements easier. The graph coloring algorithm use the Welsh Powell Algorithm. Based on the application of graph coloring with the Welsh Powell Algorithm obtained the lecturer's teaching schedule according to the SKS, time and classroom given.

Improved seagull optimization algorithm of partition and XGBoost of prediction for fuzzy time series forecasting of COVID-19 daily confirmed

The establishment of fuzzy relations and the fuzzification of time series are the top priorities of the model for predicting fuzzy time series. A lot of literature studied these two aspects to ameliorate the capability of the forecasting model. In this paper, we proposed a new method(FTSOAX) to forecast fuzzy time series derived from the improved seagull optimization algorithm(ISOA) and XGBoost. For increasing the accurateness of the forecasting model in fuzzy time series, ISOA is applied to partition the domain of discourse to get more suitable intervals. We improved the seagull optimization algorithm(SOA) with the help of the Powell algorithm and a random curve action to make SOA have better convergence ability. Using XGBoost to forecast the change of fuzzy membership in order to overcome the disadvantage that fuzzy relation leads to low accuracy. We obtained daily confirmed COVID-19 cases in 7 countries as a dataset to demonstrate the performance of FTSOAX. The results show that FTSOAX is superior to other fuzzy forecasting models in the application of prediction of COVID-19 daily confirmed cases.

Optimization of high-efficiency tooth surface accuracy of spiral bevel gears considering machine-tool motion errors

With the continuous improvement of the requirements of spiral bevel gear transmission for low noise and high precision, the optimization of high-efficiency tooth surface accuracy considering the motion axis error of machining machine tool has become a key point in the process of designing and manufacturing spiral bevel gear. Based on the theory of the multi-body dynamics system and the principle of gear meshing, a new tooth surface error model of spiral bevel gear considering the error of machine-tool moving axis is proposed and optimized, so as to obtain higher tooth surface accuracy and meshing efficiency. Firstly, according to the motion and machining principle of spiral bevel gear NC grinding machine, the corresponding relationship between the motion error of each axis of the NC gear grinding machine and the variation of cutting parameters of spiral bevel gear is analyzed, and the geometric motion error model of spiral bevel gear grinding machine is given; secondly, the tooth surface equation of the spiral bevel gear considering the machine-tool motion axis error is established; then, in view of Powell's dog leg optimization algorithm, the tooth surface considering the motion axis error of the machine tool is optimized, and the optimal cutting parameters of spiral bevel gear tooth surface machining are obtained. Finally, the simulation results show that the difference between the peak and peak values of transmission error and the maximum contact stress of the tooth surface is reduced by 72.6% and 1.62%, respectively, and the meshing efficiency is improved from 0.9798 to 0.9803 after optimization; by comparing the rolling experiment and simulation results, the maximum error between the quantitative parameters of the two groups of tooth surface contact marks is no more than 9%, which verifies the effectiveness and feasibility of this method, and provides a certain theoretical basis for practical production and processing.

Time-Variant Schwarz Based Model for DC Series Arc Fault Modeling in Photovoltaic Systems

DC series arc fault(DCSAF) in photovoltaic systems is a controversial issue owing to the challenges related to its modeling and protection. This article focuses on efficient models based on Schwarz model for DCSAF utilizing actual recorded data. The original Schwarz model has four parameters, containing two coefficients and two model orders, and all four parameters are constant. Despite the original Schwarz model that uses invariant parameters for arc modeling, the proposed models employ a Schwarz model in which the time-variant nature of the arc's parameters is taken into account. The first developed Schwarz model with two constant model orders and two time-variant coefficients is derived in the first part. While the first model provides more capability compared with the original Schwarz modeling, the second developed Schwarz model with full time-variant parameters is also presented in the second part. A novel optimization technique based on Powell's dog leg algorithm is proposed to estimate the arc coefficients in every simulation window. Therefore, the parameters in both modified Schwarz models are time-variant and change every simulation window. As a result, they are classified as a time series, which is examined using the autoregressive moving average process. By actual recorded data, the performance of the proposed models is assessed. Analyses show that the proposed models are more efficient to model DCSAF in comparison with the original Schwarz model.

Graph coloring program for variation of exam scheduling modeling at Binus University based on Welsh and Powell algorithm

In this article, we will design a computer program to solve graph colouring and to visualize the variation of exam scheduling modelling at Binus University in graphs based on the Welch and Powell Algorithm. A vertex colouring of graph G = (V, E) is an F: V → N mapping where the adjacent vertex are different colours in N, i.e. if the edge (u, v) are in E, then F (u) is not equal to F (v). The formulation of problems regarding computer programs based on a small experiment and variations in modelling exams is carried out in graph form using the Visual Basic Application.

Optimizing cropping pattern to improve the performance of irrigation network using system dynamics-Powell algorithm.

One of the strategies for agricultural development is the optimal use of irrigation and drainage networks, which leads to higher productivity and economic benefits. In this regard, quantitative and qualitative studies of drainage water from networks are essential for efficient water management. In the present study, we develop a model using a system dynamics approach to simulate the cropping pattern of an irrigation and drainage network as well as the discharge and salinity of drainage water from network farms. We apply the Powell algorithm to optimize the economic profitability of cultivated crops by considering the salinity and discharge of drainage water from the fields. With three aims, i.e., (1) maximizing benefit-cost ratio, (2) minimizing drainage water salinity and discharge of network, and (3) economic and environmental considerations simultaneously, the optimization of cropping pattern within the Kosar irrigation and drainage network is performed. Results based on five consecutive years under different scenarios showed that some crops, such as watermelon, are not economically recommened for production due to high costs, water consumption, and low selling price causes environmental pollution. On the other hand, wheat, grain maize, silage maize, sorghum, and alfalfa have different conditions, and their production is suitable by considering all scenarios. By comparing with experimental data, we find that the proposed model is accurate to simulate and optimize the irrigation network and to detect its cropping pattern.

A Fuel Optimization Method for the Pursuer in the Spacecraft Pursuit-Evasion Game

AbstractThe fuel optimization of the spacecraft is significant for its service life. In this paper, a fuel optimization method is proposed to solve the fuel optimization problem of the pursuer in the spacecraft pursuit-evasion game (SPE game). This method first takes both the magnitude and direction of the pursuer's thrust as the control variables to be optimized, then models the fuel optimization problem as a two-player zero-sum differential game whose payoff function is the fuel consumption of the pursuer, and finally obtains the optimal control strategy of the pursuer by solving the saddle point of the differential game. Considering that the solving of the saddle point usually leads to the solving of a high-dimensional (12-dimensional in this paper) two-point boundary value problem (TPBVP), which is very challenging, the proposed method adopts a dimension-reduction algorithm which can simplify the TPBVP to the solving of a four-dimensional nonlinear equations and a terminal constraint, and then presents an hybrid numerical algorithm combining the particle swarm optimization algorithm and the Powell algorithm to solve the nonlinear equations and terminal constraint. The simulation results show that the proposed method can achieve the fuel optimization of the pursuer in the SPE game and is robust to the orbital altitude, the initial relative state between the pursuer and evader and the magnitude of the evader's thrust.

An Orthopedic Auxiliary Diagnosis System Based on Image Recognition Technology.

There are many kinds of orthopedic diseases with complex professional background, and it is easy to miss diagnosis and misdiagnosis. The computer-aided diagnosis system of orthopedic diseases based on the key technology of medical image processing can locate and display the lesion location area by visualization, measuring and providing disease diagnosis indexes. It is of great significance to assist orthopedic doctors to diagnose orthopedic diseases from the perspective of visual vision and quantitative indicators, which can improve the diagnosis rate and accuracy of orthopedic diseases, reduce the pain of patients, and shorten the treatment time of diseases. To solve the problem of possible spatial inconsistency of medical images of orthopedic diseases, we propose an image registration method based on volume feature point selection and Powell. Through the linear search strategy of golden section method and Powell algorithm optimization, the best spatial transformation parameters are found, which maximizes the normalized mutual information between images to be registered, thus ensuring the consistency of two-dimensional spatial positions. According to the proposed algorithm, a computer-aided diagnosis system of orthopedic diseases is developed and designed independently. The system consists of five modules, which can complete many functions such as medical image input and output, algorithm processing, and effect display. The experimental results show that the system developed in this paper has good results in cartilage tissue segmentation, bone and urate agglomeration segmentation, urate agglomeration artifact removal, two-dimensional and three-dimensional image registration, and visualization. The system can be applied to clinical gout and cartilage defect diagnosis and evaluation, providing sufficient basis to assist doctors in making diagnosis decisions.

A Review of Well-Known Robust Line Search and Trust Region Numerical Optimization Algorithms for Solving Nonlinear Least-Squares Problems

The conditional, unconditional, or the exact maximum likelihood estimation and the least-squares estimation involve minimizing either the conditional or the unconditional residual sum of squares. The maximum likelihood estimation (MLE) approach and the nonlinear least squares (NLS) procedure involve an iterative search technique for obtaining global rather than local optimal estimates. Several authors have presented brief overviews of algorithms for solving NLS problems. Snezana S. Djordjevic (2019) presented a review of some unconstrained optimization methods based on the line search techniques. Mahaboob et al. (2017) proposed a different approach to estimate nonlinear regression models using numerical methods also based on the line search techniques. Mohammad, Waziri, and Santos (2019) have briefly reviewed methods for solving NLS problems, paying special attention to the structured quasi-Newton methods which are the family of the search line techniques. Ya-Xiang Yuan (2011) reviewed some recent results on numerical methods for nonlinear equations and NLS problems based on online searches and trust regions techniques, particularly on Levenberg-Marquardt type methods, quasi-Newton type methods, and trust regions algorithms. The purpose of this paper is to review some online searches and trust region's more well-known robust numerical optimization algorithms and the most used in practice for the estimation of time series models and other nonlinear regression models. The line searches algorithms considered are: Gradient algorithm, Steepest Descent (SD) algorithm, Newton-Raphson (NR) algorithm, Murray’s algorithm, Quasi-Newton (QN) algorithm, Gauss-Newton (GN) algorithm, Fletcher and Powell algorithm (FP), Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. While the only trust-region algorithm considered is the Levenberg-Marquardt (LM) algorithm. We also give some main advantages and disadvantages of these different algorithms.

Optimal decentralized control of a wind turbine and diesel generator system

AbstractThis article presents a decentralized optimal controller design technique for the frequency and power control of a coupled wind turbine and diesel generator. The decentralized controller consists of two proportional‐integral (PI)‐lead controllers which are designed and optimized simultaneously using a quasi‐Newton based optimization technique, namely, Davidon–Fletcher–Powell algorithm. The optimal PI‐lead controllers are designed in such a way that there are no communication links between them. Simulation results show the superior performance of the proposed controller with a lower order structure compared to the benchmark decentralized linear‐quadratic Gaussian integral controllers of orders 4 and 11. It is also shown that the proposed controller demonstrates an effective performance in damping the disturbances from load and wind power, as well as a robust performance against the parameter changes of the power system.

OPTIMIZING THE CONTENT OF THE SEDIMENTS IN THE PROCESS OF HUDRON′S HYDROCRACKING WITH THE USE OF MACHINE LEARNING METHODS

The paper proposes a mathematical model to optimize the operation of the tar hydrocracking unit. The purpose of modeling is to improve the economic effect of product output by selecting optimal parameters, such as hydrogen flow rate and reactor temperature. Hot Filtered Precipitation (HFT) is used as a target. The model involves the search for the minimum value of the functional with restrictions presented in the form of a fine imposed when the parameters go beyond the permissible values, as well as when the target parameter deviates from the specified value. The execution of the algorithm includes two stages. The first stage is the simulation of the HFT value for a given state of the installation at the selected parameters of temperature and hydrogen flow rate using a virtual analyzer, the second stage is to solve the optimization problem by selecting the control parameters of the installation. For the first stage, a model for assessing the HFT indicator by technological indicators was built, including the main factors determining it; machine learning methods were used to find the parameters of the models. The free standard library of optimum search tools scipy.optimize was used to solve the optimization problem. Powell's algorithm was chosen as the optimization method. The paper presents the results of testing the model on real data provided by an oil refinery in the city of Burgas in Bulgaria. The study period includes several operating modes of the installation, in particular, the intensive load mode during 2018-2019 and low load during the 2020 period. The results of testing the model on real data presented in the work have been verified by experts in the field of oil refining for compliance with real conditions.

Peritoneal physicochemical transport mechanisms: Hypotheses, models and controversies.

This study answers criticisms by Waniewski et al. of the recent paper by Wolf on peritoneal transport kinetic models. Their criticisms centre on the accuracy of the data used for model fits, the hypothesis presented, which involves changes in glucose membrane parameters at high peritoneal glucose concentration and on the necessary techniques required to achieve accurate model parameter estimation. In response, this article shows that (1) the mean values previously captured from graphical depictions of Heimburger et al. are not different than those captured from the recent Waniewski et al. graphs, (2) a much simpler hypothesis is proposed, which centres on intraperitoneal pressure-induced lymph flow during the dialysis dwell and (3) the finding that the new model predictions, with only two constant parameter values, as estimated by the Powell algorithm, give a closer fit than the Waniewski model, which uses many time-varying parameters. The current findings again bring into question of the validity of their vasodilation hypothesis, leading to transient changes in capillary surface area during the dwell.