An Effective Runge-Kutta Optimizer Based on Adaptive Population Size and Search Step Size

A newly proposed competent population-based optimization algorithm called RUN,which uses the principle of slope variations calculated by applying the Runge Kutta method as the key search mechanism,has gained wider interest in solving optimization problems.However,in high-dimensional problems,the search capabilities,convergence speed,and runtime of RUN deteriorate.This work aims at filling this gap by proposing an improved variant of the RUN algorithm called the Adaptive-RUN.Population size plays a vital role in both runtime efficiency and optimization effectiveness of metaheuristic algorithms.Unlike the original RUN where population size is fixed throughout the search process,Adaptive-RUN automatically adjusts population size according to two population size adaptation techniques,which are linear staircase reduction and iterative halving,during the search process to achieve a good balance between exploration and exploitation characteristics.In addition,the proposed methodology employs an adaptive search step size technique to determine a better solution in the early stages of evolution to improve the solution quality,fitness,and convergence speed of the original RUN.Adaptive-RUN performance is analyzed over 23 IEEE CEC-2017 benchmark functions for two cases,where the first one applies linear staircase reduction with adaptive search step size(LSRUN),and the second one applies iterative halving with adaptive search step size(HRUN),with the original RUN.To promote green computing,the carbon footprint metric is included in the performance evaluation in addition to runtime and fitness.Simulation results based on the Friedman andWilcoxon tests revealed that Adaptive-RUN can produce high-quality solutions with lower runtime and carbon footprint values as compared to the original RUN and three recent metaheuristics.Therefore,with its higher computation efficiency,Adaptive-RUN is a much more favorable choice as compared to RUN in time stringent applications.

Effect of Time Step Size and Turbulence Model on the Open Water Hydrodynamic Performance Prediction of Contra-Rotating Propellers

A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.

Novel LMS adaptive filtering algorithm with variable step size

By analyzing algorithms available for variable step size least mean square(LMS)adaptive filter,a new modified LMS adaptive filtering algorithm with variable step size is proposed,along with performance analysis based on different parameters.Compared with the existing algorithms through the simulation,the proposed algorithm has faster convergence speed and smaller steady state error.

A Simple Method of Calculating the Optimal Step Size in 4DVAR Technique

In four—dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational efficiency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one—dimensional advection equation and two—dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is properly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important improvement on 4DVAR theory, but also has useful practical application in improving the computational efficiency and saving the computational time. Key words 4DVAR - Optimal step size - Iterative convergence rate This work was supported by the National Natural Science Foundation under grants: 49735180 and 49675259, the “973 Project? CHERES(G 1998040907), the Project of Natural Science Foundation of Jiangsu Province(BK99020), and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars.

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.

Joint receiving mechanism based on blind equalization with variable step size for M-QAM modulation

The problem of inter symbol interference（ ISI） in wireless communication systems caused by multipath propagation when using high order modulation like M-Q AMis solved. Since the wireless receiver doesn＇t require a training sequence,a blind equalization channel is implemented in the receiver to increase the throughput of the system. To improve the performances of both the blind equalizer and the system,a joint receiving mechanismincluding variable step size（ VSS） modified constant modulus algorithms（ MC-MA） and modified decision directed modulus algorithms（ MD DMA） is proposed to ameliorate the convergence speed and mean square error（ MSE） performance and combat the phase error when using high order QAM modulation. The VSS scheme is based on the selection of step size according to the distance between the output of the equalizer and the desired output in the constellation plane. Analysis and simulations showthat the performance of the proposed VSS-MCMA-MD DMA mechanismis better than that of algorithms with a fixed step size. In addition,the MCMA-MDDMA with VSS can performthe phase recovery by itself.

Step Sized DGS结构的毫米波带通滤波器的设计

文中利用一种渐变尺寸的 DGS(Defected Ground Structure)结构的带阻特性,以改善毫米波滤波器的阻带性能.仿真及实验结果证明了优化的渐变尺寸周期 DGS 结构能有效地改善滤波器带外抑制特性,同时对通带内插入损耗影响较小.

Noise cancellation of a multi-reference full-wave magnetic resonance sounding signal based on a modified sigmoid variable step size least mean square algorithm

Nano-volt magnetic resonance sounding(MRS) signals are sufficiently weak so that during the actual measurement, they are affected by environmental electromagnetic noise, leading to inaccuracy of the extracted characteristic parameters and hindering effective inverse interpretation. Considering the complexity and non-homogeneous spatial distribution of environmental noise and based on the theory of adaptive noise cancellation, a model system for noise cancellation using multi-reference coils was constructed to receive MRS signals. The feasibility of this system with theoretical calculation and experiments was analyzed and a modified sigmoid variable step size least mean square(SVSLMS) algorithm for noise cancellation was presented. The simulation results show that, the multi-reference coil method performs better than the single one on both signal-to-noise ratio(SNR) improvement and signal waveform optimization after filtering, under the condition of different noise correlations in the reference coils and primary detecting coils and different SNRs. In particular, when the noise correlation is poor and the SNR<0, the SNR can be improved by more than 8 dB after filtering with multi-reference coils. And the average fitting errors for initial amplitude and relaxation time are within 5%. Compared with the normalized least mean square(NLMS) algorithm and multichannel Wiener filter and processing field test data, the effectiveness of the proposed method is verified.

Convergence Properties and Step Size Estimation for MLMS Algorithm

According to the exact expression of the maladjustment, an equation for calculating the boundary of step-size in MLMS algorithm is derived and the relationship between the convergence rate and step-size is discussed in detail. It is shown that the threshold of the step-size is constrained by maladjustment. Three different properties are presented between the LMS and MLMS algorithms based on comparison. It is indicated that MLMS does not differ significantly from LMS when the given maladjustment is small.

Interval of effective time-step size for the numerical computation of nonlinear ordinary differential equations

由于满足计算的不确定性原理,需适当选取时间步长以保证非线性常微分方程组数值解的可靠性,目前尚未见关于有效步长区间的理论结果。本文对于给定的误差限,将方法截断误差与机器舍入误差的相关曲线分别进行平移,从而得到一种确定有效步长近似区间的方法,并推导出近似区间相比于原区间的相对误差公式。另外,研究了有效步长区间随积分时间的变化规律,并对已有的数值结果给出解释。本文所得结论可为数值求解常微分方程组选取有效步长并得到可靠的数值解提供理论支持。

Study of Variable Step Size LMS Adaptive Algorithm Based on Variable Region

This paper puts forward a new variable step size LMS adaptive algorithm based on variable region. The step size μ(k) in the algorithm varies with the variation of the region of deviation e(k) to ensure the optimization of the three performance objectives including initial convergent speed, trace ability of the time-varying system and steady disregulation. The paper demonstrates the convergence of the algorithm accompanied by random noise.

Design of digital calibration based on variable step size of sub-binary SAR ADC

Addressing the impact of capacitor mismatch on the conversion accuracy of successive approximation register analog-to-digital converter(SAR ADC),a 12-bit 1 MS/s sub-binary SAR ADC designed using variable step size digital calibration was proposed.The least mean square(LMS)calibration algorithm was employed with a ramp signal used as the calibration input.Weight errors,extracted under injected disturbances,underwent iterative training to optimize weight values.To address the trade-off between conversion accuracy and speed caused by a fixed step size,a novel variable step size algorithm tailored for SAR ADC calibration was proposed.The core circuit and layout of the SAR ADC were implemented using the Taiwan Semiconductor Manufacturing Company(TSMC)0.35μm complementary metal-oxide-semiconductor(CMOS)commercial process.Simulation of the SAR ADC calibration algorithm was conducted using Simulink,demonstrating quick convergence and meeting conversion accuracy requirements compared to fixed step size simulation.The results indicated that the convergence speed of the LMS digital calibration algorithm with variable step size was approximately eight times faster than that with a fixed step size,also yielding a lower mean square error(MSE).After calibration,the simulation results for the SAR ADC exhibited an effective number of bit(ENOB)of 11.79 bit and a signal-to-noise and distortion ratio(SNDR)of 72.72 dB,signifying a notable enhancement in the SAR ADC performance.

EFFICIENT NONNEGATIVE MATRIX FACTORIZATION VIA MODIFIED MONOTONE BARZILAI-BORWEIN METHOD WITH ADAPTIVE STEP SIZES STRATEGY

In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

Computational uncertainty and optimal grid size and time step of the Lax-Friedrichs scheme for the 1D advection equation

本文对于应用Lax-Friedrichs格式数值求解一维平流方程,研究数值求解过程中产生的截断误差与舍入误差,以及两种误差逐层向高时间层传播的累积,得到新的数值解总误差上界的理论近似公式,以及最优格距和最优时间步长的理论公式.通过数值算例验证了所得公式的可靠性。然后,发现了两种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系.最后,理论验证了在网格比固定的情况下,此问题满足数值计算的不确定性原理,以及在机器有限精度下最优时间步长的必然存在。

An LQP-Based Symmetric Alternating Direction Method of Multipliers with Larger Step Sizes

Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.

An NLMS algorithm with optimized preparatory step-size parameters for SQUID-based MCG data processing

We present a new least-mean-square algorithm of adaptive filtering to improve the signal to noise ratio for magneto-cardiography data collected with high-temperature SQUID-based magnetometers. By frequently adjusting the adaptive parameter a go systematic optimum values in the course of the programmed procedure, the convergence is accelerated with a highest speed and the minimum steady-state error is obtained simultaneously. This algorithm may be applied to eliminate other non-steady relevant noises as well.

An algorithm of adaptive step size factor in adaptive filtering

In this paper a model of transversal filter is presented to study the adaptive match of the time variant channel. The least mean square error filtering method is used to obtain the weighting coefficients of the filter. With the purpose of speeding up the convergence of the iteration equation of adaptive filtering, an adaptive factor of the iteration step size μa is derived in this paper. The result of computer simulation shows that in the case of using adaptive μa, the convergence speed of the iteration equation is increased 2 times approximately in comparison with constant μ1. The study suggests that the adaptive filter with adaptive μa have the performance to follow the change of time-variant characteristics of the channel.

Some new step-size rules for optimization problems

The step-size procedure is very important for solving optimization problems. The Armijo step-size rule, the Armijo-Goldstein step-size rule and the Wolfe-Powell step-size rule are three well-known line search methods. On the basis of the above three types of line search methods and the idea of the proximal point methods, a new class of step-size rules was proposed. Instead of a single objective function f, f ＋1/2（x - xk）^TBk（x-Xk） was used as the merit function in iteration k, where Sk is a given symmetric positive definite matrix. The existence of the steplength for the new rules was proved. Some convergence properties were also discussed.

基于RRT^(*)-DR算法的机械臂避障路径规划

为使机械臂在障碍物环境下快速规划较优路径,提出了一种基于动态区域采样的改进RRT^(*)-DR路径规划算法,将整个规划过程分为快速探索路径和优化初始路径两个步骤。首先利用半目标导向扩展快速探索,找到连接起始点和目标点的路径。随后利用动态区域采样方法,始终在当前最优路径的周边范围内采样,优先密化当前最优路径附近的节点树,节省计算资源,使初始路径经过迭代快速向渐进最优路径收敛。同时,提出一种近障碍节点变步长机制,有选择性地缩短靠近障碍节点的扩展步长,可有效减少碰撞检测失败次数,提高算法效率。最后,在MATLAB和ROS系统下进行路径规划算法仿真,结果表明RRT^(*)-DR算法可在更短时间内实现路径规划,同时有效缩小路径代价。进一步通过实体机器人路径规划避障实验,验证了该算法的实用性和有效性。

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.