Low Convergence Rate Research Articles

ACO-SA: ENHANCED OPTIMIZATION FOR TSP

Traveling salesman problem (TSP) is traditional combinatorial-optimization problem and a NP-problem in operation research. Swarm intelligence (SI) algorithms be capable of efficiently achieve best tours with minimum lengths. ACO is type of probability technology use to get the optimal path in the graph. Through the analysis on the main reasons resulting in low convergence rate to overcome it simulated annealing optimization are used. In this, new hybrid ACO-SA algorithm for solving TSP depended on ACO with SA optimization technique which avoids trapping in the local-minima points. Experiments have performed using data set obtained from TSPLIB and contrast the new results of proposed method with existing methods. The results illustrate that both the average cost and number of the iteration to the best known solution of proposed method are better than existing methods.

Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes

ABSTRACTThis article presents a numerical method of pricing the surrender risk in Ratchet equity-index annuities (EIAs). We assume that log-returns of the underlying fund belong to a class of regime-switching models where the parameters are allowed to change randomly according to a hidden Markov chain. The defining feature of these models is the fact that in each regime the characteristic function of log-returns is assumed to have an analytical form. The presented method provides an unified pricing framework within this class and includes the recently developed COS method as a particular case. This aspect of the method is particularly useful when pricing Ratchet options embedded in EIAs, for which the COS method exhibits a low rate of convergence. Our numerical results confirm that for models considered in this article the proposed approach improves convergence of the COS method without increasing the computational burden.

A Novel Fast Tensor-Based Preconditioner for Image Restoration.

Image restoration is one of the main parts of image processing. Mathematically, this problem can be modeled as a large-scale structured ill-posed linear system. Ill-posedness of this problem results in low-convergence rate of iterative solvers. For speeding up the convergence, preconditioning usually is used. Despite the existing preconditioners for image restoration, which are constructed based on approximations of the blurring matrix, in this paper, we propose a novel preconditioner with a different viewpoint. Here, we show that image restoration problem can be modeled as a tensor contractive linear equation. This modeling enables us to propose a new preconditioner based on an approximation of the blurring tensor operator. Due to the particular structure of the blurring tensor for zero boundaries, we show that the truncated higher order singular value decomposition of the blurring tensor is obtained very fast and so could be used as a preconditioner. Experimental results confirm the efficiency of this new preconditioner in image restoration and its outperformance in comparison with the other well-known preconditioners.

Evaluation Criteria on the Design for Assimilating Remote Sensing Data Using Variational Approaches

Abstract Remote sensing, as a powerful tool for monitoring atmospheric phenomena, has been playing an increasingly important role in inverse modeling. Remote sensing instruments measure quantities that often combine several state variables as one. This creates very strong correlations between the state variables that share the same observation variable. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates in gradient-based variational assimilation if improper error statistics are used. In this paper, two criteria or scoring rules are proposed to quantify the numerical robustness of assimilating a specific set of remote sensing observations and to quantify the reliability of the estimates of the parameters. The criteria are derived by analyzing how the correlations are created via shared observation data and how they may influence the process of variational data assimilation. Experimental tests are conducted and show a good level of agreement with theory. The results illustrate the capability of the criteria to indicate the reliability of the assimilation process. Both criteria can be used with observing system simulation experiments (OSSEs) and in combination with other verification scores.

Statistical Convergence Analysis for Optimal Control of DFT-Domain Adaptive Echo Canceler

The frequency-domain adaptive filter (FDAF) is widely used in echo cancellation systems due to its low complexity and fast convergence rate. However, the FDAF algorithm with a fixed step size exhibits a tradeoff among the convergence rate, steady-state misalignment, tracking ability, and robustness to near-end speech interferences. Several variable step-size FDAF algorithms were presented to address this problem. However, the state-of-the-art variable step-size FDAF algorithms did not handle this problem comprehensively. This paper presents a new robust variable step-size control approach to the FDAF algorithm. Based on a statistical analysis of the FDAF algorithm, an optimal step size for each frequency bin is derived by minimizing the mean-square deviation (MSD) between the true weight vector and estimated weight vector at each frame. Calculation of the step size requires the system distance and the observation noise power spectral density (PSD). The system distance is estimated using the deterministic recursive equations of MSD and the noise PSD is computed using the magnitude squared coherence function between the far-end signal and error signal. Moreover, a close link between the proposed FDAF and the frequency-domain Kalman filter is revealed. Specifically, the work presented here can be understood as a means to adaptively monitor and control the underlying acoustic state space of the Kalman filter, including means for fast readaptation of the adaptive filter after abrupt echo path changes. Simulation results demonstrate that the proposed algorithm can achieve fast convergence and low steady-state misalignment. Furthermore, the algorithm is robust to the double-talk interferences, but it does not require an explicit double-talk detector.

Feature selection via a novel chaotic crow search algorithm

Crow search algorithm (CSA) is a new natural inspired algorithm proposed by Askarzadeh in 2016. The main inspiration of CSA came from crow search mechanism for hiding their food. Like most of the optimization algorithms, CSA suffers from low convergence rate and entrapment in local optima. In this paper, a novel meta-heuristic optimizer, namely chaotic crow search algorithm (CCSA), is proposed to overcome these problems. The proposed CCSA is applied to optimize feature selection problem for 20 benchmark datasets. Ten chaotic maps are employed during the optimization process of CSA. The performance of CCSA is compared with other well-known and recent optimization algorithms. Experimental results reveal the capability of CCSA to find an optimal feature subset which maximizes the classification performance and minimizes the number of selected features. Moreover, the results show that CCSA is superior compared to CSA and the other algorithms. In addition, the experiments show that sine chaotic map is the appropriate map to significantly boost the performance of CSA.

Fast Variable Structure Stochastic Automaton for Discovering and Tracking Spatiotemporal Event Patterns.

Discovering and tracking spatiotemporal event patterns have many applications. For example, in a smart-home project, a set of spatiotemporal pattern learning automata are used to monitor a user's repetitive activities, by which the home's automaticity can be promoted while some of his/her burdens can be reduced. Existing algorithms for spatiotemporal event pattern recognition in dynamic noisy environment are based on fixed structure stochastic automata whose state transition function is fixed and predesigned to guarantee their immunity to noise. However, such design is conservative because it needs continuous and identical feedbacks to converge, thus leading to its very low convergence rate. In many real-life applications, such as ambient assisted living, consecutive nonoccurrences of an elder resident's routine activities should be treated with an alert as quickly as possible. On the other hand, no alert should be output even for some occurrences in order to diminish the effects caused by noise. Clearly, confronting a pattern's change, slow speed and low accuracy may degrade a user's life security. This paper proposes a fast and accurate leaning automaton based on variable structure stochastic automata to satisfy the realistic requirements for both speed and accuracy. Bias toward alert is necessary for elder residents while the existing method can only support the bias toward "no alert." This paper introduces a method to allow bias toward alert or no alert to meet a user's specific bias requirement. Experimental results show its better performance than the state-of-the-art methods.

Cuckoo Search Based on Acceleration Operator and Refraction Disturbance

Aimed at the problem that cuckoo search algorithm shows low convergence rate and poor optimization accuracy in multi-dimensional function optimization. This paper presented a Cuckoo Search based on Acceleration Operator and Refraction Disturbance and designed an acceleration operator to improve the optimum speed. Besides, it brought the refraction disturbance of water wave optimization (WWO) to avoid trapping in local optimum and improve the search precision. The comparison of other improved Cuckoo Search algorithms proves the effectiveness of the algorithm.

System reliability analysis of tunnels reinforced by rockbolts

System reliability analysis of tunnelling problems is illustrated by using an iterative closed-form formulation for a circular tunnel reinforced by end-anchored rockbolts. Three performance functions, namely, the mobilized tensile force in the rockbolt, the maximum displacement and the plastic zone size of the tunnel, are considered. The bimodal bounds method and the multivariate normal cumulative distribution function (mvncdf) method are applied to the solution. Results show that the system probability of failure (Pf) estimated from the mvncdf method lies within the lower bound and upper bound set by the bimodal bounds method for the cases studied. The second-order reliability method (SORM) is used to refine the reliability indices and to improve the accuracy of the estimated system Pf. The influence of the correlation coefficient between the cohesion and the friction angle and the influence of the rockbolt installation position on the system Pf are discussed. A modified hybrid approach using the linear response surface method (RSM) to locate the design point and the artificial neural network (ANN) to approximate the actual limit state surface (LSS) is suggested to be used in the system reliability analysis for problems where closed-form solutions are not available. Traditional second-order RSM without cross terms may be inaccurate and may suffer from the problem of low convergence rate and the second-order RSM with cross terms may encounter the “false branch” problem. It is also shown in this paper that the “false branch” problem can be overcome by the importance sampling technique. Comparison with the second-order RSM shows that the proposed approach is efficient, accurate and robust for the system reliability analysis.

Active contour model by combining edge and region information discrete dynamic systems

The basic idea of active contour model upon the image segmentation problem is evolved into a closed curve about the functional minimization problems. Active contour model based on edge information takes advantage of gradient information, and it has some shortcomings such as cannot separate weak boundary, fuzzy boundary, and discontinuous boundary object. Chan–Vese active contour model without edges can overcome the shortcomings of model based on gradient, but it cannot separate gray inhomogeneous target and evolves slowly, moreover, segmentation efficiency is low. The aim of this article is to overcome the shortage of the geodesic active contour model such as lower convergence rate and more easily trapped in local minimum .The article puts forward a new active contour model control system where the edge information is combined with regional one effectively, and it makes good use of the gradient information and the area information. A large amount of simulation results show that the proposed algorithm’s convergence speed is much faster than geodesic active contour model, and it can segment serious noisy image. It inherited the edge and the region information as well, so the new model performs well in resisting noise and has high segmentation efficiency.

Prediction of Air Pollutants Concentration Based on an Extreme Learning Machine: The Case of Hong Kong.

With the development of the economy and society all over the world, most metropolitan cities are experiencing elevated concentrations of ground-level air pollutants. It is urgent to predict and evaluate the concentration of air pollutants for some local environmental or health agencies. Feed-forward artificial neural networks have been widely used in the prediction of air pollutants concentration. However, there are some drawbacks, such as the low convergence rate and the local minimum. The extreme learning machine for single hidden layer feed-forward neural networks tends to provide good generalization performance at an extremely fast learning speed. The major sources of air pollutants in Hong Kong are mobile, stationary, and from trans-boundary sources. We propose predicting the concentration of air pollutants by the use of trained extreme learning machines based on the data obtained from eight air quality parameters in two monitoring stations, including Sham Shui Po and Tap Mun in Hong Kong for six years. The experimental results show that our proposed algorithm performs better on the Hong Kong data both quantitatively and qualitatively. Particularly, our algorithm shows better predictive ability, with increased and root mean square error values decreased respectively.

Quasi-cyclic Expansion Algorithm for Protograph LDPC Codes Based on PEG and PH

One of the important code of modern coding theory, the protograph LDPC code technology has been gained more and more attention due to its low encoding complexity, fast decoding speed, low BER, and simple optimization analysis process etc. the quasi-cyclic expansion algorithm of the protograph LDPC codes, named as PQCE algorithms, can complete the extension of protograph and eventually get the protograph LDPC codes. However, the existing PQCE algorithms may be with a low convergence rate, or exist many short cycles in the check matrix. To solve the above problem, a Quasi-cyclic expansion algorithm for protograph LDPC codes based on PEG and PH is proposed in this paper, referred as PEG-PH-PQCE algorithm. In the proposed algorithm, base matrix is acquired by PEG parallel edges elimination expansion algorithm during the first-step expansion of protograph. Then, the second-step expansion is completed, in which the initial index matrix is obtained by PEG quasi-cyclic expansion algorithm, and the check matrix is acquired by using the Hill Climbing algorithm to optimizing the initial index matrix. Simulation results demonstrate the effectiveness the validity of the proposed algorithm, such as, a small number of short cycles and high convergence rate, etc.

A Novel LMS Beamformer for Adaptive Antenna Array

Least Mean Square (LMS) beamforming algorithm is one of the most popular method in array signal processing due to its low complexity. The main downside of this method is low convergence rate which limits its application in many wireless communications. In this paper, we proposed a novel LMS algorithm which produces satisfactory performance within 6 iterations. We used novel structure which consists of two LMS modules, one converse speediness module and speediness module. The experimental results show that novel LMS algorithm is superior in convergence rate and has about 92.5% of improvement over classical LMS algorithm.

A Low-Complexity Massive MIMO Precoding Algorithm Based on Chebyshev Iteration

Precoding algorithm is used to transmit signals effectively and to reduce the interferences from other user terminals in the massive multiple-input-multiple-output (MIMO) systems. In order to decrease the computational complexity of the precoding matrix, this paper proposes a new precoding algorithm. We use Chebyshev iteration to estimate the matrix inversion in the regularized zero-forcing precoding (RZF) algorithm. It does not need to compute the matrix inversion directly but uses iterations to estimate the matrix inversion. Therefore, the computational complexity can be decreased in this way. Furthermore, Chebyshev iteration has lower convergence rate, and it can gain precoding matrix quickly. This paper analyzes the performance of the Chebyshev-RZF precoding algorithm using average achievable rate and computes the complexity of the algorithm. Then, this paper optimizes initial values of the Chebyshev iteration algorithm on the basis of the feature of massive MIMO systems and makes initial values easier to be obtained. Simulation results show that after two iterations, the Chebyshev-RZF precoding algorithm can get similar average achievable rate as the RZF precoding algorithm does. An optimized Chebyshev-RZF precoding algorithm gets similar performance to the Chebyshev-RZF precoding algorithm after one iteration.

Rate of Convergence of General Phase Field Equations in Strongly Heterogeneous Media Toward Their Homogenized Limit

Over the last few decades, phase field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g., geometric PDEs and mean curvature flow, materials science for the study of phase transitions) but also engineering ones (e.g., as a computational tool in chemical engineering for interfacial flow studies). Here, we focus on phase field equations in strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we provide the first derivation of error estimates for fourth order, homogenized, and nonlinear evolution equations. Our fourth order problem induces a slightly lower convergence rate, i.e., $\epsilon^{1/4}$, where $\epsilon$ denotes the material's specific heterogeneity, than established for second order elliptic problems (e.g., [V. Zhikov, Dokl. Math., 73 (2006), pp. 96--99, https://doi.org/10.1134/S1064562406010261.]) for the error between the effective macroscopic solution of the (new) upscaled formulation and the so...

Dynamics of unstable continental subduction: Insights from numerical modeling

Numerical experiments are used in this study to systematically investigate the effects of convergence rate, crustal rheological strength, and lithospheric thermal structure on the dynamics of continental collision. The study focuses on the types, conditions and processes of unstable continental subduction. Modelling results suggest that the development of unstable continental subduction can be promoted by conditions that tend to decrease rheological strength of the lithosphere, such as low crustal rheological strength, “hot” thermal structure of the lithosphere, or low convergence rate. Unstable subduction mode can be further categorized into three types: (1) multi-stage slab breakoff, (2) continuously “flowing” of fluid-like slab into the upper mantle, and (3) large-scale detachment of the thickened orogenic root. These three types of unstable continental subduction are respectively associated with (1) a low convergence rate, (2) “hot” thermal structure of the lithosphere with a high convergence rate, and (3) moderate-high crustal rheological strength with a low convergence rate. It is also revealed that the evolution of crustal melting is dominated by the deformation pattern of continental collision, which is mainly controlled by crustal rheological strength. The modelling results have important implications for understanding of continental subduction mode selection under specific geodynamic conditions.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier–Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton–Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier–Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor–Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge–Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42–74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge–Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge–Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Study on Water Production Function of Rice Based on RAGA-BP Neural Network Model

The water production function model of rice based on RAGA-BP neural network model is established by taking the advantages of RAGA-BP neural network model (high ability in solving nonlinear problem, high rate of convergence, etc.). Compared with traditional Jensen model, this method is featured by high flexibility and intelligence, avoiding the inconvenience caused by pre-establishing mathematical expression. Compared with classical BP neural network model, this method can overcome the problem in local minimum value and low rate of convergence. The deficient irrigation experiment of rice in 2015 shows that RAGA-BP neural network model has high adaptability during the process of fitting for solution of water production function of rice; the accuracy and speed are high, which provides new effective method for calculation of water production function of rice.

Stochastic convex sparse principal component analysis.

Principal component analysis (PCA) is a dimensionality reduction and data analysis tool commonly used in many areas. The main idea of PCA is to represent high-dimensional data with a few representative components that capture most of the variance present in the data. However, there is an obvious disadvantage of traditional PCA when it is applied to analyze data where interpretability is important. In applications, where the features have some physical meanings, we lose the ability to interpret the principal components extracted by conventional PCA because each principal component is a linear combination of all the original features. For this reason, sparse PCA has been proposed to improve the interpretability of traditional PCA by introducing sparsity to the loading vectors of principal components. The sparse PCA can be formulated as an ℓ 1 regularized optimization problem, which can be solved by proximal gradient methods. However, these methods do not scale well because computation of the exact gradient is generally required at each iteration. Stochastic gradient framework addresses this challenge by computing an expected gradient at each iteration. Nevertheless, stochastic approaches typically have low convergence rates due to the high variance. In this paper, we propose a convex sparse principal component analysis (Cvx-SPCA), which leverages a proximal variance reduced stochastic scheme to achieve a geometric convergence rate. We further show that the convergence analysis can be significantly simplified by using a weak condition which allows a broader class of objectives to be applied. The efficiency and effectiveness of the proposed method are demonstrated on a large-scale electronic medical record cohort.

Lattice Boltzmann model for a steady radiative transfer equation.

A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.