Iterative Optimization Method Research Articles

Five-point thirty-two optimal order iterative method for solving non-linear equations

A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed to achieve optimal convergence order 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation to the derivative is computed around the initial guess. High order convergence is attained by constructing polynomials of quotients for functional values.

Integrated radar and communication waveform design based on a shared array

To reduce the consumption of spectrum and hardware resources, three methods are proposed to design the integrated radar and communication waveforms transmitted by a shared array. First, a minimum norm optimization (MNO) method is proposed to devise the transmit waveforms that can simultaneously synthesize desired radar and communication waveforms in different directions. The transmit beampattern formed by the designed waveforms has low sidelobe level (SLL). However, the designed waveforms may have high peak-to-average power ratio (PAPR). To reduce the PAPR, an iterative optimization (IO) method is proposed to devise the transmit waveforms with constant modulus. Then, to further reduce the SLL of the transmit beampattern formed by the designed constant modulus waveforms, the amplitude of each transmit waveform is iteratively optimized, which is referred to as iterative optimization with amplitude weighting (IO-AW) method. Finally, several numerical results show that the transmit waveforms designed by the proposed methods can simultaneously perform the radar and communication functions and can form the transmit beampattern with low SLL.

An Iterative Two-Phase Optimization Method Based on Divide and Conquer Framework for Integrated Scheduling of Multiple UAVs

Task scheduling of multiple UAVs has become a highly active area of research in recent years. Previous research has generally solved the problem in a whole manner, which makes it hard to efficiently generate high-quality task scheduling schemes due to prohibitive computational complexity. By contrast, the paper constructs a novel divide and conquer framework for multi-UAV task scheduling (DCF), which partitions the original multi-UAV scheduling problem into multiple scheduling sub-problems for all the UAVs. To be specific, DCF includes two phases: one is the task allocation phase which produces multiple scheduling sub-problems and the other is the single UAV scheduling phase which generates the scheduling scheme with sequential tasks for each single UAV considering constraints involving UAV capabilities and task demands. Two phases are iteratively performed until the predefined stopping criteria are met. In the task allocation phase, we propose a tabu-list-based simulated annealing (SATL) algorithm to realize task allocation among multiple UAVs. After obtaining the task allocation scheme, a satisfactory scheduling scheme of each single UAV is generated by variable neighborhood descent (VND) algorithm. Extensive experiments and comparative studies are conducted, demonstrating the efficiency of DCF and the proposed SATL-VND algorithm.

A digital twin-based big data virtual and real fusion learning reference framework supported by industrial internet towards smart manufacturing

Digital twin takes Industrial Internet as a carrier deeply coordinating and integrating virtual spaces with physical spaces, which effectively promotes smart factory development. Digital twin-based big data learning and analysis (BDLA) deepens virtual and real fusion, interaction and closed-loop iterative optimization in smart factories. This paper proposes a digital twin-based big data virtual and real fusion (DT-BDVRL) reference framework supported by Industrial Internet towards smart manufacturing. The reference framework is synthetically designed from three perspectives. The first one is an overall framework of DT-BDVRL supported by Industrial Internet. The second one is the establishment method and flow of BDLA models based on digital twin. The final one is digital thread of DT-BDVRL in virtual and real fusion analysis, iteration and closed-loop feedback in product full life cycle processes. For different virtual scenes, iterative optimization and verification methods and processes of BDLA models in virtual spaces are established. Moreover, the BDLA results can drive digital twin running in virtual spaces. By this, the BDLA results can be validated iteratively multiple times in virtual spaces. At same time, the BDLA results that run in virtual spaces are synchronized and executed in physical spaces through Industrial Internet platforms, effectively improving the physical execution effect of BDLA models. Finally, the above contents were applied and verified in the actual production case study of power switchgear equipment.

Ultrasound transmission tomography image reconstruction with a fully convolutional neural network

Image reconstruction of ultrasound computed tomography based on the wave equation is able to show much more structural details than simpler ray-based image reconstruction methods. However, to invert the wave-based forward model is computationally demanding. To address this problem, we develop an efficient fully learned image reconstruction method based on a convolutional neural network. The image is reconstructed via one forward propagation of the network given input sensor data, which is much faster than the reconstruction using conventional iterative optimization methods. To transform the ultrasound measured data in the sensor domain into the reconstructed image in the image domain, we apply multiple down-scaling and up-scaling convolutional units to efficiently increase the number of hidden layers with a large receptive and projective field that can cover all elements in inputs and outputs, respectively. For dataset generation, a paraxial approximation forward model is used to simulate ultrasound measurement data. The neural network is trained with a dataset derived from natural images in ImageNet and tested with a dataset derived from medical images in OA-Breast Phantom dataset. Test results show the superior efficiency of the proposed neural network to other reconstruction algorithms including popular neural networks. When compared with conventional iterative optimization algorithms, our neural network can reconstruct a 110 × 86 image more than 20 times faster on a CPU and 1000 times faster on a GPU with comparable image quality and is also more robust to noise.

Ultrasonic imaging recognition of coal-rock interface based on the improved variational mode decomposition

Extracting effective ultrasonic echo signals in multilayered media is the key technology for detection of coal-rock interface, which is the basis of automatic height adjustment of the shearer drums during automatic coal mining. However, it is tough to recognize echo signals of coal-rock interface efficiently and accurately through common signal processing methods such as Fourier Transform (FT), Wavelet Transform (WT) and Empirical Mode Decomposition (EMD). Therefore, an improved Empirical Variational Mode Decomposition (EVMD) method for ultrasonic echo signal processing is proposed in this paper. Firstly, EVMD is used to preprocess the received echoes of coal-rock interface. Secondly, the optimization iterative method of weight coefficient is introduced to fit part of distorted echo envelope with asymmetric Gaussian model, which can effectively reduce the calculation error. Finally, peak focusing imaging technique is used to image the processed envelopes. The experimental results show that the proposed method can recognize the coal-rock interface efficiently.

An excellent numerical technique for multiple roots

In recent times, some optimal eighth order iterative methods for computing multiple zeros of nonlinear functions have been appeared in literature. Different from these existing optimal methods, here we propose a new eighth order iterative method for multiple zeros. With four evaluations per iteration, the method satisfies the criterion of attaining optimal convergence of eighth order. Accuracy and computational efficiency are demonstrated by implementing the algorithm on different numerical problems. Moreover, the obtained results show its good convergence compared to existing optimal eighth order techniques. Besides, it also challenges the accuracy of existing methods which is the main advantage.

Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation

Abstract In this study, a modified fractional form of FitzHugh-Nagumo equation is investigated via a newly developed semi-analytical method. The classical equation has been modified with a new fractional operator and the optimal perturbation iteration algorithms have been adapted accordingly for solving the fractional model. An illustration has been deeply analyzed for different values of physical parameters. Figures and tables are given to show the errors of different order approximations. Obtained results prove the accuracy and effectiveness of the proposed technique.

3D TOF-PET image reconstruction using total variation regularization.

In this paper we introduce a semi-analytic algorithm for 3-dimensional image reconstruction for positron emission tomography (PET). The method consists of the back-projection of the acquired data into the most likely image voxel according to time-of-flight (TOF) information, followed by the filtering step in the image space using an iterative optimization algorithm with a total variation (TV) regularization. TV regularization in image space is more computationally efficient than usual iterative optimization methods for PET reconstruction with full system matrix that use TV regularization. The efficiency comes from the one-time TOF back-projection step that might also be described as a reformatting of the acquired data. An important aspect of our work concerns the evaluation of the filter operator of the linear transform mapping an original radioactive tracer distribution into the TOF back-projected image. We obtain concise, closed-form analytical formula for the filter operator. The proposed method is validated with the Monte Carlo simulations of the NEMA IEC phantom using a one-layer, 50cm-long cylindrical device called Jagiellonian PET scanner. The results show a better image quality compared with the reference TOF maximum likelihood expectation maximization algorithm.

Weight and bias initialization routines for Sigmoidal Feedforward Network

The success of the Sigmoidal Feedforward Networks in the solution of complex learning task can be attributed to their Universal Approximation Property. These networks are trained using non-linear iterative optimization method (of first-order or second-order) to solve a learning task. The convergence rate in Sigmoidal Feedforward Network training is affected by the initial choice of weights, therefore, in this paper, we propose two new weight initialization routines (Routine-1 and Routine-2) using characteristics of input and output data and property of activation function. Routine-1 uses the linear dependency of weight update step size on derivative of activation function and thus, initialize weights and bias to activate the activation function region near zero (input), where the derivative is maximum, therefore, increasing the weight update step size, and hence, the convergence speed. The same principle is used to derive Routine-2, that initialize weights and bias to activate distinct point in the significant range of activation function (where significant range defines the non-saturated region in activation function), such that, each node evolves independently of each other, and act as distinct feature identifier. Initializing weights in significant range reduces chances of (hidden) nodes getting stuck in saturated state. The networks initialized using proposed routines has higher convergence and higher probability to achieve deeper minima. The efficiency of proposed routines is evaluated by comparing them to conventional random weight initialization routine and 11 weight initialization routines proposed in literature (4 well established routines and 7 recently proposed routines) for several benchmark problems. The proposed routine is also tested for larger networks sizes and larger datasets such as MNIST. The results show that the performance of proposed routines is better than conventional random weight initialization routine and 11 established weight initialization routines.

Explicit Sensitivity Coefficients for Estimation of Temperature-Dependent Thermophysical Properties in Inverse Transient Heat Conduction Problems

Explicit expressions are obtained for sensitivity coefficients to separately estimate temperature-dependent thermophysical properties, such as specific heat and thermal conductivity, in two-dimensional inverse transient heat conduction problems for bodies with irregular shape from temperature measurement readings of a single sensor inside the body. The proposed sensitivity analysis scheme allows for the computation of all sensitivity coefficients in only one direct problem solution at each iteration with no need to solve the sensitivity and adjoint problems. In this method, a boundary-fitted grid generation (elliptic) method is used to mesh the irregular shape of the heat conducting body. Explicit expressions are obtained to calculate the sensitivity coefficients efficiently and the conjugate gradient method as an iterative gradient-based optimization method is used to minimize the objective function and reach the solution. A test case with different initial guesses and sensor locations is presented to investigate the proposed inverse analysis.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Guiding iterative optimisation methods to a predefined kind of optima for unconstrained optimisation problems

One of the most fundamental issues in the field of mathematical optimisation is the convergence of an iterative optimisation method and by this we are referring to two things. First, will the method find an optimum and second, will this optimum be a local one or a global one? A recently proposed technique (Nikolakakou et al., 2015b) that is used in order to lessen the dependence a locally convergent iterative optimisation method has on the initial guess, is exploited in this paper. A way so that such a method may be guided to a predefined kind of minimum (local or global) is presented. Well known test functions were used for experimentation. Statistical analysis was conducted by applying a logistic regression classification model on data arisen from the numerical results which confirmed that iterative optimisation methods can be guided to a predefined kind of optimum.

Dictionary adaptation and variational mode decomposition for gyroscope signal enhancement

The paper proposes an approach to signal denoising based on a combination of Variational Mode Decomposition with the Split Augmented Lagrangian Shrinkage Algorithm.In our research, we found that the proposed approach gives a great improvement of denoising gyroscopic signals. In turn, the results for the synthetic signals are not straightforward. For the bumps synthetic signals, the proposed algorithm gives the best results for different levels of signal degradation. While for the Doppler and blocks synthetic signals the reference methods give better results. However, for heavisine test signal the proposed algorithm gives better results in almost all cases.A weak point of the presented algorithm is its time complexity. The proposed approach is based on the Split Augmented Lagrangian Shrinkage Algorithm, which is the iterative optimization method since the time of computation strongly depends on the number of iterations.The presented results show that the proposed approach gives a great improvement in signal denoising and it is a promising direction of future research.

Graph-based Multi-view Binary Learning for image clustering

Hashing techniques, also known as binary code learning, have recently attracted increasing attention in large-scale data analysis and storage. Generally, most existing hash clustering methods are single-view ones, which lack complete structure or complementary information from multiple views. For clustering tasks, most hashing research mainly mapped the original data into the Hamming space while heavily ignoring the original feature space structure. To solve these problems, we propose a novel binary code algorithm for clustering, which adopts graph embedding to preserve the original data structure, called Graph-based Multi-view Binary Learning (GMBL). The binary code learning combines the graph structure of original data and the complementary information of different views for clustering. Specifically, GMBL preserves the local linear relationship utilizing the Laplacian matrix aim to maintain the graph-based structure of the original data in Hamming space. Moreover, by automatically assigning weights for each view to improve clustering performance, which takes distinctive contributions of multiple views into considerations. Besides, an alternating iterative optimization method is designed to solve the resulting optimization problems. Extensive experimental results on five public datasets are provided to reveal the effectiveness of the algorithm and its superior performance over other state-of-the-art alternatives.

Axis optimisation of arch-shaped pylons for high-speed railway cable-stayed bridges

In order to obtain reasonable arch-shaped pylon axes for high-speed railway cable-stayed bridges, an iterative optimisation method based on force-balance analysis, a fixed point iterative method for nonlinear equations, and finite element analysis was proposed. The developed method was used to optimise the axes of the arch-shaped pylons of two high-speed railway arch-shaped pylon cable-stayed bridges. The results showed that the arch-shaped pylon axis of a cable-stayed bridge with main spans of 2 × 80 m converged after seven iterations. The absolute maximum bending moments under the service load of the optimised arch-shaped pylons were reduced by 53.15–83.53%, and the maximum and minimum stresses under the service load were reduced by 79.81–106.80% and 52.63–66.74%, respectively. Under a double-line ZK-live load, the maximum upward and minimum downward deflections of the optimised arch-shaped pylons were reduced by 21.30–25.0% and 12.4–21.6%, respectively, which resulted in increased stiffness of the bridge. The optimised axes obtained after inputting different initial axes to the proposed method were identical, and the obtained axis was adopted as the final arch-shaped pylon axis design for the actual bridge. For the second arch-shaped pylon cable-stayed bridge, which had main spans of 2 × 90 m, the absolute maximum bending moments of the optimised arch-shaped pylons were reduced by 77.05–92.08%, and the maximum and minimum stresses under the service load decreased by 117.82–173.91% and 39.00–41.38%, respectively. The results obtained illustrate the suitability of the proposed arch-shaped pylon axis optimisation method and demonstrate its reliability.

Correntropy induced loss based sparse robust graph regularized extreme learning machine for cancer classification

BackgroundAs a machine learning method with high performance and excellent generalization ability, extreme learning machine (ELM) is gaining popularity in various studies. Various ELM-based methods for different fields have been proposed. However, the robustness to noise and outliers is always the main problem affecting the performance of ELM.ResultsIn this paper, an integrated method named correntropy induced loss based sparse robust graph regularized extreme learning machine (CSRGELM) is proposed. The introduction of correntropy induced loss improves the robustness of ELM and weakens the negative effects of noise and outliers. By using the L2,1-norm to constrain the output weight matrix, we tend to obtain a sparse output weight matrix to construct a simpler single hidden layer feedforward neural network model. By introducing the graph regularization to preserve the local structural information of the data, the classification performance of the new method is further improved. Besides, we design an iterative optimization method based on the idea of half quadratic optimization to solve the non-convex problem of CSRGELM.ConclusionsThe classification results on the benchmark dataset show that CSRGELM can obtain better classification results compared with other methods. More importantly, we also apply the new method to the classification problems of cancer samples and get a good classification effect.

Antenna Array Directivity Maximization With Sidelobe Level Constraints Using Convex Optimization

New methods for maximizing the directivities of the array antennas are proposed. First, the array pencil beam (PB) directivity maximization problems without or with sidelobe constraints are formulated as convex optimization problems, which are solved optimally to achieve better optimized directivity results, compared with traditional method with radiation intensity maximization only. Then, to deal with the nonconvexity in the wide beam (WB) directivity maximization problem, a novel iterative directivity optimization method based on Taylor expansion of the quadratic function is proposed, and the original nonconvex problem can be efficiently solved by the convex optimization methods in an iterative way. Finally, a two-stage iterative directivity maximization method is further proposed to deal with the sidelobe constraints in the WB directivity maximization problem. Two initial point schemes for the iterative algorithms are studied in detail with the performance comparisons. The two-stage algorithm can be used to yield very good results, even under very wide beamwidth and strict sidelobe constraint conditions. With the proposed methods, the array directivity maximization problems can be solved by the convex optimization methods in a very efficient way. Several representative examples are presented to demonstrate the excellent performance of the proposed methods.

The Strength Analysis and Structural Modification of VPX Chassis in Flight Environment

The aircraft has severe mechanical conditions such as overload and vibration during operation. The environment in which VPX chassis are located is complex and harsh. In order to reduce the effect of high level vibration and shock on the VPX chassis in Flight Environment, the Strength Analysis of the whole chassis is made. Therefore the structure is modified according to the analysis result to improve its ability of anti-vibration and anti-shock. This paper proposes a iterative optimization method based on the variation characteristics of structural strength through iterative optimization, and by using the Finite Element Method for simulation calculation, the thickness of the area of the lugs of the equipment was adjusted to make the deformation and the stress and the weight suffices requirements of the design. It can shorten the period of product development and lower the product cost by the method presented in this paper.

Efficient Quantum and Simulated Annealing of Potts Models Using a Half-hot Constraint

The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time required to obtain the ground states by simulated annealing exponentially increases with the system size. This study analytically confirms that the transverse magnetic-field quantum annealing induces a first-order phase transition. This result implies that quantum annealing does not exponentially accelerate the ground-state search of the ferromagnetic Potts model. To avoid the first-order phase transition, we propose an iterative optimization method using a half-hot constraint that is applicable to both quantum and simulated annealing. In the limit of $Q \to \infty$, a saddle point equation under the half-hot constraint is identical to the equation describing the behavior of the fully connected ferromagnetic Ising model, thus confirming a second-order phase transition. Furthermore, we verify the same relation between the fully connected Potts glass model and the Sherrington--Kirkpatrick model under assumptions of static approximation and replica symmetric solution. The proposed method is expected to obtain low-energy states of the Potts models with high efficiency using Ising-type computers such as the D-Wave quantum annealer and the Fujitsu Digital Annealer.