Powell's Method Research Articles

Joint optimization of pricing and seat allocation with multistage and discriminatory strategies in high-speed rail networks

Pricing and seat allocation are complementary strategies of revenue management (RM) for railway industry, but these two strategies were typically considered as isolated problems in most of existing studies. To extend the literature, a nonlinear programming model is proposed for the joint optimization of pricing and seat allocation in high-speed rail (HSR) networks. Meanwhile, multistage and discriminatory pricing strategies are employed to attract more passengers and improve total revenue. Following the Davidon–Fletcher–Powell method, we design an efficient solution algorithm for large-scale joint HSR pricing and seat allocation problems. The sensitivity analysis is performed to capture the uncertain impacts of model inputs on the outputs. The advantages of joint RM strategy are demonstrated by a trade study where different RM strategies are compared. The results of a large-scale instance in the real HSR network show that the proposed model and solution algorithm can provide decision support for railway companies in their daily operation and management.

Synthesis and investigation of the control system for the process of сarbon article molding

Among the most energy-intensive industries is the production of carbon articles, therefore, the improvement of its efficiency is a relevant scientific and technical task. One of the ways to resolve the set task is to create a modern production management system. This paper considers the creation of a control system for one of the essential technological processes in carbon articles production – the process of their formation. Underlying the control system is the optimality criterion based on the specific cost of products taking into consideration their quality indicators. The control method used is Model Predictive Control (MPC). The results of studying the dependence of an optimality criterion on the setting parameters of an MPC-controller have made it possible to determine the optimum values for the prediction and control horizons, which could ensure the minimization of the products’ specific cost. The structure of the proposed control system, developed in the Simulink programming environment, makes it possible to investigate a given control system through computer simulations. The efficiency of the proposed system to control the process of carbon product molding was examined by comparing the quality of control by a given system and by the system that uses the classic PID control law. To this end, a three-circuit control system based on the PID-controllers was synthesized in the Simulink programming environment. Each controller was set, using a Powell method, for a minimum value of the integrated criterion. The results of the comparative study have demonstrated that at each operation cycle the optimality criterion value in the control system employing an MPC-controller was 8.8 % less than that in the system with PID-controllers at the same indicators of product quality. That testifies to the improvement in the technical and economic indicators of the formation process. This fact is of particular importance when taking into consideration the circularity of the technological process of carbon product formation.

MTMD to increase fatigue life for OWT jacket structures using Powell's method

The Powell's method was developed to determine the optimal stiffness and damping of multi-tuned mass dampers (MTMD) in offshore wind turbine (OWT) support structures under fatigue loads. Numerical examples indicated that the Powell's method results are always better than those using MTMD formulations. With the exception of the blade passing (3P) frequency, it was found in this work that a positive integer (n) multiple of the 3P frequency will also result in a large wind-induced vibration, which can be excited by the frequency of the first structural vertical rotation mode and will cause significant fatigue damage. The first translation mode TMD installed at the tower top is efficient to increase fatigue life at the tower and brace connections, but it cannot reduce fatigue damage at the column and brace connections below the platform. The second translation mode TMD can reduce fatigue damage resulting from large wave loads and thus increase the fatigue life of the braces and columns. The mode-3 TMD with a reduction in the 3(3P) vertical rotation can effectively increase the fatigue life of the braces and columns. Thus, the appropriate use of these TMDs can be effective for the fatigue problem of OWT support structures.

Phenomenological Model Development of Percentage Protein Present in Fermented African Locust Beans Seed

The optimum conditions for the fermentation of a local legume known as African locust bean (Parkia biglobosa) into a vegetable protein based food condiment or spice (Iru) were developed using Levenberg-Marquardt (or Powell) method (using PSI software) with three (3) variables namely; inoculum concentration (bacillus subtilis), temperature and the fermentation duration. P. biglobosa seeds were fermented at various temperature of 40 - 70 °C for five days (120 hours) with different concentrations of Inoculum. The proximate analysis shows that fermentation increased the percentage protein. Protein had the highest composition with about 51 % after 72 hours at the lowest fermentation temperature of 40°C.

Использование поисковых методов для уравнивания и оценки точности элементарных геодезических построений

The author provides information about the search methods of adjustment and assessment of the elementary geodetic constructions accuracy on the example of a geodesic triangle under various initial conditions. An algorithm for combining Powell and DSC search methods used to solve the problem posed in the article is given. To equalize the geodesic constructions under consideration by the search method, a program for finding the minimum of the objective function is made, it implements the algorithm described in the article. This program works in the Microsoft Excel format as a macro recorded in the VBA language. Examples of equalization calculations are given. Accuracy assessment of the adjustment results by the search method of the geodesic triangle under different initial conditions is performed. The obtained adjustment results and accuracy estimates are compared with the calculations performed in the NW program by Professor Kougiya V. A. confirmed the correctness of the search method application.

Inference of General Mass Action-Based State Equations for Oscillatory Biochemical Reaction Systems Using <i>k</i>-Step Genetic Programming

Systems biology requires the development of algorithms that use omics data to infer interaction networks among biomolecules working within an organism. One major type of evolutionary algorithm, genetic programming (GP), is useful for its high heuristic ability as a search method for obtaining suitable solutions expressed as tree structures. However, because GP determines the values of parameters such as coefficients by random values, it is difficult to apply in the inference of state equations that describe oscillatory biochemical reaction systems with high nonlinearity. Accordingly, in this study, we propose a new GP procedure called “k-step GP” intended for inferring the state equations of oscillatory biochemical reaction systems. The k-step GP procedure consists of two algorithms: 1) Parameter optimization using the modified Powell method—after genetic operations such as crossover and mutation, the values of parameters such as coefficients are optimized by applying the modified Powell method with secondary convergence. 2) GP using divided learning data—to improve the inference efficiency, imposes perturbations through the addition of learning data at various intervals and adaptations to these changes result in state equations with higher fitness. We are confident that k-step GP is an algorithm that is particularly well suited to inferring state equations for oscillatory biochemical reaction systems and contributes to solving inverse problems in systems biology.

Orbit Determination Using Pulsar Timing Data and Orientation Vector

X-ray Pulsar Navigation (XPNAV) uses the Time Difference of Arrival (TDOA) of the pulsar signal between the spacecraft and Solar System Barycentre (SSB) to determine position. In this paper, a novel method to improve the performance of XPNAV via exploiting the pulsar position vector is proposed. First, the field of view of the collimator is utilised to find the pulsar orientation direction. Then, a searching strategy based on the modified Powell method under given coordinate frames is proposed. We also mathematically prove the existence of the extreme value of the searching strategy. Subsequently, an observation model based on the pulsar radiation vector is presented and applied to formulate the observation function together with pulsar time transfer function. Finally, an Adaptive Divided Difference Filter (ADDF) algorithm is introduced to iteratively estimate the position and velocity of the spacecraft. Numerical simulations show that the vector searching method is feasible and the pulsar radiation direction can improve the navigation performance by 75%. The simulation results also show that the ADDF performs better than Unscented Kalman Filtering (UKF) and DDF in position estimation.

Forecasting Short-Term Traffic Flow by Fuzzy Wavelet Neural Network with Parameters Optimized by Biogeography-Based Optimization Algorithm.

Forecasting short-term traffic flow is a key task of intelligent transportation systems, which can influence the traveler behaviors and reduce traffic congestion, fuel consumption, and accident risks. This paper proposes a fuzzy wavelet neural network (FWNN) trained by improved biogeography-based optimization (BBO) algorithm for forecasting short-term traffic flow using past traffic data. The original BBO is enhanced by the ring topology and Powell's method to advance the exploration capability and increase the convergence speed. Our presented approach combines the strengths of fuzzy logic, wavelet transform, neural network, and the heuristic algorithm to detect the trends and patterns of transportation data and thus has been successfully applied to transport forecasting. Other different forecasting methods, including ANN-based model, FWNN-based model, and WNN-based model, are also developed to validate the proposed approach. In order to make the comparisons across different methods, the performance evaluation is based on root-mean-squared error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R). The performance indexes show that the FWNN model achieves lower RMSE and MAPE, as well as higher R, indicating that the FWNN model is a better predictor.

Evaluation of the mass transfer rate using computer simulation in a three-dimensional interwoven hollow fiber-type bioartificial liver.

To determine the most efficient design of a hollow fiber-based bioreactor device for a bioartificial liver support system through comparative bioengineering evaluations. We compared two types of hollow fiber-based bioreactors, the interwoven-type bioreactor (IWBAL) and the dialyzer-type bioreactor (DBAL), by evaluating the overall mass transfer coefficient (K) and the convective coefficient (X). The creatinine and albumin mass transfer coefficients and convective coefficients were calculated using our mathematical model based on the homoporous theory and the modified Powell method. Additionally, using our model, we simulated the mass transport efficiency in clinical-scale BALs. The results of this experiment demonstrate that the mass transfer coefficients for creatinine and albumin increased proportionally with velocity with the IWBAL, and were consistently greater than that found with the DBAL. These differences were further enhanced in the simulation of the large-scale model. Our findings indicate that the IWBAL with its unique 30° cross hollow fiber design can provide greater solute removal and more efficient metabolism when compared to the conventional DBAL design.

Enhanced mutual information‐based medical image registration using a hybrid optimisation technique

A medical image registration method is proposed. An enhanced mutual information is employed as the similarity measure. A hybrid optimisation technique based on Powell's method and cuckoo search is developed as the optimiser. Experimental results show the effectiveness of the proposed method.

A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization

Previous deconvolution algorithms based on B-splines are much easier to be understood and programmed for academic researchers and engineers. However, due to the use of a linear regularization, their stability is weaker than that of the commonly used von Schroeter et al.’s deconvolution algorithm in which a nonlinear regularization is used; the linear regularization can make the deconvolution algorithms less tolerant to data errors. Good stability for the deconvolution algorithms is very important in order to make deconvolution as a viable tool for well-test analysis. In the paper, in order to improve the stability of the deconvolution algorithms based on B-splines, a nonlinear regularization by minimizing the curvature of pressure derivative response, as used in von Schroeter et al.’s algorithm, is appended instead of the linear regularization. And the corresponding nonlinear regularization equations are appropriately deduced. In particular, the improved algorithm is based on the Duhamel principle directly, and the complex transformation by the nonlinear z function, as used in von Schroeter et al.’s algorithm, is avoided; it does simplify the whole deconvolution process; moreover, the sensitivity matrix of an involved basic linear system from the measured pressure and rate data can also be solved directly by the piecewise analytical integration method, which can largely improve the deconvolution computation speed. Ultimately, in combination with the nonlinear regularization equations, a nonlinear least-squares problem is formulated for the stability-improved deconvolution algorithm based on B-splines. Besides, a constraint condition for tuning the parameter values of the B-spline base and an involved smooth factor is presented for restricting the nonlinear regularization process. Through a simulated case study, it is found that the nonlinear least-squares problem can be solved stably by the advanced Powell's Dog Leg method due to its great convergence ability and numerical stability; and the solution accuracy is also verified. Then the effects of the two parameters on the type curves of the deconvolution results are analyzed. And the effect of the error in the initial formation pressure on the type curves of the deconvolution results is also analyzed. Then a statement on how to perform the nonlinear regularization is presented specifically.Furthermore, through the study on two simulated cases with added data errors and an actual case, it is demonstrated that when the nonlinear regularization is appended, the stability of the deconvolution algorithm based on B-splines can be largely improved for mitigating the effect of data errors; besides, the stability-improved algorithm based on B-splines even exhibits higher stability than von Schroeter et al.’s algorithm that takes the same nonlinear regularization method, and the reason can be attributed to the superior properties of the representation of the wellbore pressure derivative (to be deconvolved) by B-spline functions in the numerical stability of computations and the inherent smoothness. Through the test of some simulated cases, it is also concluded that the stability-improved algorithm based on B-splines by appending the nonlinear regularization still has a high-level computation speed, which is nearly twenty times more than that of von Schroeter et al.’s algorithm. It can be attributed to the more undetermined coefficients and the computational complexity resulted from the z-function transformation in the formulation of von Schroeter et al.’s algorithm.

Identifying Lightning Channel-Base Current Function Parameters by Powell Particle Swarm Optimization Method

This paper proposes the Powell (PPSO) method. The particle swarm optimization (PSO) algorithm is combined with the Powell algorithm to identify the parameters of lightning channel-base current function. The method can overcome the problem of premature convergence for PSO algorithm, and improve the analysis accuracy. The Heidler function is used to represent the lightning channel-base current. We have compared the PPSO method and genetic algorithm (GA) on reaching the desired peak value of the current $I_{m}$ and the maximum time rate of change of current ( di / dt )max. The results show that the parameters of Heidler function evaluated by the PPSO method can achieve more accurate values of $I_{m}$ and ( di / dt )max than those evaluated by GA. Also, we have compared the PPSO method, the Nelder–Mead particle swarm optimization (NMPSO) method, and PSO method using the measured channel-base current. The results show that the PPSO method is better than the NMPSO and PSO method to determine the channel-base current function parameters. The PPSO method is an efficient method to identify the channel-base function parameters, which can improve the digitalization of lightning monitoring equipment. This approach is also useful in research related to lightning characteristics and lightning protection.

Use of EPANET solver to manage water distribution in Smart City

Paper presents a method of using EPANET solver to support manage water distribution system in Smart City. The main task is to develop the application that allows remote access to the simulation model of the water distribution network developed in the EPANET environment. Application allows to perform both single and cyclic simulations with the specified step of changing the values of the selected process variables. In the paper the architecture of application was shown. The application supports the selection of the best device control algorithm using optimization methods. Optimization procedures are possible with following methods: brute force, SLSQP (Sequential Least SQuares Programming), Modified Powell Method. Article was supplemented by example of using developed computer tool.

Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy.

During image-guided prostate biopsy, needles are targeted at tissues that are suspicious of cancer to obtain specimen for histological examination. Unfortunately, patient motion causes targeting errors when using an MR-transrectal ultrasound (TRUS) fusion approach to augment the conventional biopsy procedure. This study aims to develop an automatic motion correction algorithm approaching the frame rate of an ultrasound system to be used in fusion-based prostate biopsy systems. Two modes of operation have been investigated for the clinical implementation of the algorithm: motion compensation using a single user initiated correction performed prior to biopsy, and real-time continuous motion compensation performed automatically as a background process. Retrospective 2D and 3D TRUS patient images acquired prior to biopsy gun firing were registered using an intensity-based algorithm utilizing normalized cross-correlation and Powell's method for optimization. 2D and 3D images were downsampled and cropped to estimate the optimal amount of image information that would perform registrations quickly and accurately. The optimal search order during optimization was also analyzed to avoid local optima in the search space. Error in the algorithm was computed using target registration errors (TREs) from manually identified homologous fiducials in a clinical patient dataset. The algorithm was evaluated for real-time performance using the two different modes of clinical implementations by way of user initiated and continuous motion compensation methods on a tissue mimicking prostate phantom. After implementation in a TRUS-guided system with an image downsampling factor of 4, the proposed approach resulted in a mean ± std TRE and computation time of 1.6 ± 0.6 mm and 57 ± 20 ms respectively. The user initiated mode performed registrations with in-plane, out-of-plane, and roll motions computation times of 108 ± 38 ms, 60 ± 23 ms, and 89 ± 27 ms, respectively, and corresponding registration errors of 0.4 ± 0.3 mm, 0.2 ± 0.4 mm, and 0.8 ± 0.5°. The continuous method performed registration significantly faster (P < 0.05) than the user initiated method, with observed computation times of 35 ± 8 ms, 43 ± 16 ms, and 27 ± 5 ms for in-plane, out-of-plane, and roll motions, respectively, and corresponding registration errors of 0.2 ± 0.3 mm, 0.7 ± 0.4 mm, and 0.8 ± 1.0°. The presented method encourages real-time implementation of motion compensation algorithms in prostate biopsy with clinically acceptable registration errors. Continuous motion compensation demonstrated registration accuracy with submillimeter and subdegree error, while performing < 50 ms computation times. Image registration technique approaching the frame rate of an ultrasound system offers a key advantage to be smoothly integrated to the clinical workflow. In addition, this technique could be used further for a variety of image-guided interventional procedures to treat and diagnose patients by improving targeting accuracy.

Comprehensive model for predicting surface roughness of ground workpieces considering the plowing effect

ABSTRACTDue to the stochastic nature of grinding process, a probabilistic model is considered to be the most appropriate solution for predicting the surface roughness of ground workpiece. However, the existing probabilistic models in the literature do not systematically take into account the contribution of plowing effect. As such, this work incorporates the pile-up ridges from plowing phenomenon and their overlapping effect into a probabilistic model. When the distance between two neighboring grooves left on the workpiece surface by the abrasive grains varies, the ridges will pile upon each other or the grooves will intersect with each other. These different interaction modes of grooves or ridges are discussed in the probabilistic model to predict the surface roughness. The improved Powell method is used to perform the prediction. A series of grinding experiments were performed to validate the proposed model and the result shows that the predicted values agree very well with the measured values with an average prediction accuracy of 90.4%.

Constitutive modeling of jugular vein-derived venous valve leaflet tissues.

Venous valve tissues, though used in vein reconstruction surgeries and bioprosthetic valves with moderate success, have not been extensively studied with respect to their structure. Their inherent anisotropic, non-linear behavior combined with severe diseases which affect veins, such as chronic venous insufficiency, warrant understanding the structure and material behavior of these tissues. Hence, before any bioprosthetic grafts may be used in place of tissues, it is of the utmost importance to understand the mechanical and structural properties of these tissues as this may lead to higher success rates for valve replacement surgeries. The longevity of the bioprosthetics may also increase if the manufactured grafts behave the same as native valves. Building on the scant information about the uniaxial and biaxial mechanical properties of jugular venous valves and wall tissues from previous studies, the current focus of our investigation lies in understanding the material behavior by establishing a phenomenological strain energy-based constitutive relation for the tissues. We used bovine veins to study the behavior of valve leaflet tissue and adjoining wall tissue (from the proximal and distal ends of the veins) under different biaxial testing protocols. We looked at the behavior of numerical partial derivatives of the strain energy to select a suitable functional form for the strain energy for wall and valve tissues. Using this strain energy descriptor, we determined the Cauchy stress and compared it with experimental results under additional sets of displacement-controlled biaxial testing protocols to find material specific model parameters by the Powell's method algorithm. Results show that whereas wall tissue strain energy can be explained using a polynomial non-linear function, the valve tissue, due to higher non-linearities, requires an exponential function. This study may provide useful information for the primary stages of bioprosthetic designs and replacement surgeries and may support future studies investigating structural models. It may also support the study of valvular diseases by providing a way to understand material properties and behavior and to form a continuum model when required for numerical analyses and computational simulations.

Auxiliary variables for numerically solving nonlinear equations with softly broken symmetries

General methods for solving simultaneous nonlinear equations work by generating a sequence of approximate solutions that successively improve a measure of the total error. However, if the total error function has a narrow curved valley, the available techniques tend to find the solution after a very large number of steps, if ever. The solver first converges rapidly to the valley, but once there it converges extremely slowly to the solution. In this paper we show that in the specific physically important case where these valleys are the result of a softly broken symmetry, the solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. We present a procedure for finding solutions in this case and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powell's hybrid method with the generalization to allow more variables than equations.

Robust 2-D-3-D Registration Optimization for Motion Compensation During 3-D TRUS-Guided Biopsy Using Learned Prostate Motion Data.

In magnetic resonance (MR)-targeted, 3-D transrectal ultrasound (TRUS)-guided biopsy, prostate motion during the procedure increases the needle targeting error and limits the ability to accurately sample MR-suspicious tumor volumes. The robustness of the 2-D-3-D registration methods for prostate motion compensation is impacted by local optima in the search space. In this paper, we analyzed the prostate motion characteristics and investigated methods to incorporate such knowledge into the registration optimization framework to improve robustness against local optima. Rigid motion of the prostate was analyzed adopting a mixture-of-Gaussian (MoG) model using 3-D TRUS images acquired at bilateral sextant probe positions with a mechanically assisted biopsy system. The learned motion characteristics were incorporated into Powell's direction set method by devising multiple initial search positions and initial search directions. Experiments were performed on data sets acquired during clinical biopsy procedures, and registration error was evaluated using target registration error (TRE) and converged image similarity metric values after optimization. After incorporating the learned initialization positions and directions in Powell's method, 2-D-3-D registration to compensate for motion during prostate biopsy was performed with rms ± std TRE of 2.33 ± 1.09 mm with ~3 s mean execution time per registration. This was an improvement over 3.12 ± 1.70 mm observed in Powell's standard approach. For the data acquired under clinical protocols, the converged image similarity metric value improved in ≥8% of the registrations whereas it degraded only ≤1% of the registrations. The reported improvements in optimization indicate useful advancements in robustness to ensure smooth clinical integration of a registration solution for motion compensation that facilitates accurate sampling of the smallest clinically significant tumors.

PERFORMANCE COMPARISON OF THE POWELL AND PSO METHODS FOR MEDICAL IMAGE ALIGNMENT

In the course of aligning medical images, the similarity metric (also called alignment function) is regarded as the objective function, and the optimization method as the tool for exploring the optimal transformation parameters. In this paper, the medical image alignment is represented first and then the optimization methods are depicted in detail. With this description, by the use of the mutual information (MI) as the similarity metric, the Powell method and the particle swarm optimization (PSO) method are employed to seek the optimal transformation parameters respectively, and their optimization performances are estimated and compared. The experimental results show that the Powell and PSO methods can cater to both the multi-modality medical image alignments.

Parameterizing sorption isotherms using a hybrid global-local fitting procedure

Predictive modeling of the transport and remediation of groundwater contaminants requires an accurate description of the sorption process, which is usually provided by fitting an isotherm model to site-specific laboratory data. Commonly used calibration procedures, listed in order of increasing sophistication, include: trial-and-error, linearization, non-linear regression, global search, and hybrid global-local search. Given the considerable variability in fitting procedures applied in published isotherm studies, we investigated the importance of algorithm selection through a series of numerical experiments involving 13 previously published sorption datasets. These datasets, considered representative of state-of-the-art for isotherm experiments, had been previously analyzed using trial-and-error, linearization, or non-linear regression methods. The isotherm expressions were re-fit using a 3-stage hybrid global-local search procedure (i.e. global search using particle swarm optimization followed by Powell's derivative free local search method and Gauss-Marquardt-Levenberg non-linear regression). The re-fitted expressions were then compared to previously published fits in terms of the optimized weighted sum of squared residuals (WSSR) fitness function, the final estimated parameters, and the influence on contaminant transport predictions – where easily computed concentration-dependent contaminant retardation factors served as a surrogate measure of likely transport behavior. Results suggest that many of the previously published calibrated isotherm parameter sets were local minima. In some cases, the updated hybrid global-local search yielded order-of-magnitude reductions in the fitness function. In particular, of the candidate isotherms, the Polanyi-type models were most likely to benefit from the use of the hybrid fitting procedure. In some cases, improvements in fitness function were associated with slight (<10%) changes in parameter values, but in other cases significant (>50%) changes in parameter values were noted. Despite these differences, the influence of isotherm misspecification on contaminant transport predictions was quite variable and difficult to predict from inspection of the isotherms.