Iteration Count Research Articles

Optimized IoT Cryptoprocessor Based on QC-MPDC Key Encapsulation Mechanism

The key encapsulation mechanism (KEM) is an important cryptographic tool to protect communication in the Internet of Things (IoT). In the near future, classical algorithms used to construct KEMs, such as RSA and elliptic curve cryptography, will be vulnerable to attacks from quantum computers. Recently, Yamada et al. proposed the quasicyclic medium density parity check (QC-MDPC) KEM, which is considered one of the most advanced code-based cryptosystems to resist quantum attacks. In this article, an optimized implementation of QC-MDPC KEM for IoT applications is presented. Our main contributions are threefold: 1) the fastest QC-MDPC McEliece decryption in field-programmable gate array (FPGA); 2) the first QC-MDPC KEM implementation in FPGA; and 3) the first iteration count attack-resistant QC-MDPC decoder in FPGA. To improve the decryption speed, we introduce a novel customized rotation engine (CRE) and incorporated several recent techniques reported in the literature, including adaptive threshold and Hamming weight estimation. The best-achieved throughput in our implementation on Xilinx Virtex 7 FPGA is 12.7% faster than the state-of-the-art result reported by Heyse et al. The proposed CRE was then integrated with QC-MDPC KEM to produce a fast and secure KEM. Furthermore, to prevent timing attacks demonstrated recently, a constant-time implementation of the QC-MDPC McEliece decoder was presented.

Global maximum power point tracking technique based on adaptive salp swarm algorithm and P&O techniques for a PV string under partially shaded conditions

ABSTRACT A Bio-inspired salp swarm algorithm (SSA) based soft computing technique is easy to implement with a single control parameter, which is dependent on maximum iteration count. But the maximum iteration count required for the on-line/hardware search process like maximum power point tracking (MPPT) of photovoltaic (PV) system is not known initially. Wrongly estimated maximum iteration count results in the unnecessary exploration of search space even after reaching the global peak (GP) region, which is the main cause for the slow-tracking of global maximum power point (GMPP) by conventional SSA. Hence, In this paper, a modified SSA based MPPT is proposed with an adaptive control parameter, and it is named Adaptive SSA (ASSA) based global maximum power point tracking (GMPPT) technique. Further, to achieve faster tracking of GMPP, ASSA is used only to identify the GP region, and in that region, variable step size P&O continues tracking. During irradiance changes, search space is limited for the reinitialization of ASSA. The proposed hybrid algorithm is simulated and experimentally validated using a boost DC-DC converter as an MPPT controller with direct duty ratio control. The proposed GMPPT technique results in faster-tracking of GMPP with the combined effect of adaptive parameter tuning, GP region identification with ASSA, and variable step size P&O. From the simulation and experimental results, it is evident that the proposed GMPPT technique is more than 1.3 times faster as compared to the conventional SSA based MPPT technique.

Research and Study of the Hybrid Algorithms Based on the Collective Behavior of Fish Schools and Classical Optimization Methods

Inspired by biological systems, swarm intelligence algorithms are widely used to solve multimodal optimization problems. In this study, we consider the hybridization problem of an algorithm based on the collective behavior of fish schools. The algorithm is computationally inexpensive compared to other population-based algorithms. Accuracy of fish school search increases with the increase of predefined iteration count, but this also affects computation time required to find a suboptimal solution. We propose two hybrid approaches, intending to improve the evolutionary-inspired algorithm accuracy by using classical optimization methods, such as gradient descent and Newton’s optimization method. The study shows the effectiveness of the proposed hybrid algorithms, and the strong advantage of the hybrid algorithm based on fish school search and gradient descent. We provide a solution for the linearly inseparable exclusive disjunction problem using the developed algorithm and a perceptron with one hidden layer. To demonstrate the effectiveness of the algorithms, we visualize high dimensional loss surfaces near global extreme points. In addition, we apply the distributed version of the most effective hybrid algorithm to the hyperparameter optimization problem of a neural network.

Intelligent Data-Driven Adaptive Method for Optimizing System Integration Scaling Factors for Touch Panel Lamination Machines

This paper presents a new intelligent data-driven adaptive method (IDAM) of performing automatic online searches in real time. An online implementation of the proposed IDAM achieved rapid real-time optimization of system integration scaling factors for an automatic touch panel lamination machine. The proposed IDAM combines three-level orthogonal arrays (OAs), signal-to-noise ratios (SNRs), the best combined strategy, and a stepwise ratio. Three-level OA experiments with factor values are used to perform positional experiments, and SNRs are calculated for each experimental value. After the best combination of factor values (in terms of factor effect) is determined, new three-level factor values are derived by applying a stepwise ratio and used in further three-level OA experiments. These steps are repeated until the stopping criterion is met. Compared to conventional methods, the use of the IDAM in practical industrial applications, i.e., online real-time precision positioning for automatic touch panel lamination machines, reduces the number of experiments needed to obtain the system integration scaling factors that minimize the iteration count. For example, the IDAM required less than 40 online real-time experiments with a specific stepwise ratio for system integration scaling factors that met the minimum requirement of two iterations. In 50 independent experimental runs using the robust scaling factors obtained by the method, an average of 2.15 iterations was needed to achieve a positional accuracy within 5 ${\mu }\text{m}$ . The main advantage of the proposed IDAM over conventional methods is its effectiveness for automatically finding robust parameters for online alignment systems in real time and with fewer experiments.

An on-node scalable sparse incomplete LU factorization for a many-core iterative solver with Javelin

We present a scalable incomplete LU factorization to be used as a preconditioner for solving sparse linear systems with iterative methods in the package called Javelin. Javelin allows for improved parallel factorization on shared-memory many-core systems by packaging the coefficient matrix into a format that allows for high performance sparse matrix-vector multiplication and sparse triangular solves with minimal overheads. The framework achieves these goals by using a collection of traditional permutations, point-to-point thread synchronizations, tasking, and segmented prefix scans in a conventional compressed sparse row (CSR) format. Moreover, this framework stresses the importance of co-designing dependent tasks, such as sparse factorization and triangular solves, on highly-threaded architectures. We compare our method to the past distributed methods for incomplete factorization (Aztec) and current multithreaded packages (WSMP) in order to demonstrate the importance of having highly threaded factorizations on many-core systems. Using these changes, traditional fill-in and drop tolerance methods can be used, while still being able to have observed speedups of up to ~ 42 × on 68 Intel Knights Landing cores and ~ 12 × on 14 Intel Haswell cores. Moreover, this work provides insight into how the new data-structure impacts iteration counts, and provides insight into future improvements, such as point to GPUs.

Inner approximation algorithm for solving linear multiobjective optimization problems

ABSTRACT Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex enumeration on the other. Their separation provides a deeper insight into Benson's algorithm, and points toward a dual approach. Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems yields different algorithms, such as a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the dual algorithm of Ehrgott et al. [A dual variant of Benson's ‘outer approximation algorithm’ for multiple objective linear programming. J Glob Optim. 2012;52:757–778]. The implemented version is well suited to handle highly degenerate problems where there are many linear dependencies among the constraints. On problems with 10 or more objectives, it shows a significant increase in efficiency compared to Bensolve – due to the reduced number of iterations and the improved combinatorial handling.

Coordination Mechanism for PV Battery Systems with Local Optimizing Energy Management

This publication presents a coordination mechanism for neighboring photovoltaic (PV) battery systems with local optimizing energy management (EM). The aim of this coordination is a high degree of self-sufficiency for the neighborhood while maintaining a high individual degree of self-sufficiency and relieving the grid. A financial incentive to increase the energy exchanged within the neighborhood is introduced. The local EM of the individual PV battery system uses model predictive control based on deterministic dynamic programming in order to minimize the individual economic costs and extreme grid power values. By using a coordination algorithm involving a central information processing unit, the neighboring PV battery systems are given information about the sum of the planned consumption and feed-in power profiles of the neighborhood, as well as the neighborhood tariffs. Based on these data, the PV battery systems successively optimize the operation of their batteries until either convergence or a maximum count of iterations is achieved. The operating principle of the distributed EM concept with coordination is demonstrated through a simulation of a residential neighborhood comprising eight households with different load profiles and varying PV peak powers and battery capacities. Its performance is compared with three EM concepts: two distributed concepts without coordination and another one with central optimizing EM representing ideal coordination. The resulting power flow distributions are analyzed, and the benefits and weaknesses of the developed coordination mechanism are discussed based on a number of evaluation criteria.

A Parallax Shift Effect Correction Based on Cloud Height for Geostationary Satellites and Radar Observations

The effect of cloud parallax shift occurs in satellite imaging, particularly for high angles of satellite observations. This study demonstrates new methods of parallax effect correction for clouds observed by geostationary satellites. The analytical method that could be found in literature, namely the Vicente et al./Koenig method, is presented at the beginning. It approximates a cloud position using an ellipsoid with semi-axes increased by the cloud height. The error values of this method reach up to 50 meters. The second method, which is proposed by the author, is an augmented version of the Vicente et al./Koenig approach. With this augmentation, the error can be reduced to centimeters. The third method, also proposed by the author, incorporates geodetic coordinates. It is described as a set of equations that are solved with the numerical method, and its error can be driven to near zero by adjusting the count of iterations. A sample numerical solution procedure with application of the Newton method is presented. Also, a simulation experiment that evaluates the proposed methods is described in the paper. The results of an experiment are described and contrasted with current technology. Currently, operating geostationary Earth Observation (EO) satellite resolutions vary from 0.5 km up to 8 km. The pixel sizes of these satellites are much greater than for maximal error of the least precise method presented in this paper. Therefore, the chosen method will be important when the resolution of geostationary EO satellites reaches 50 m. To validate the parallax correction, procedure data from on-ground radars and the Meteosat Second Generation (MSG) satellite, which describes stormy events, was compared before and after correction. Comparison was performed by correlating the logarithm of the cloud optical thickness (COT) with radar reflectance in dBZ (radar reflectance – Z in logarithmic form).

Optimization of non-circular failure surface in slope based on particle swarm models

This article presents results of slope analyses employing a simple technique of generating segmented non-circular failure surfaces. The formulation of slope analysis is performed as an optimization problem with four constrained control variables characterizing the failure surface. In this study, different variants of particle swarm optimization (PSO) methods such as inertia weight equipped and contemporary standard PSO (CS-PSO) are utilized to obtain optimum control variables and associated critical failure surface. The factor of safety of the slope or the objective function of the constrained optimization problem is determined by Morgenstern–Price method. To explore the competence of proposed method with different PSO models, three benchmark problems are analysed for different maximum number of function evaluations such as 1000, 2500 and 5000. A series of sensitivity analyses are performed for various parameters such as swarm size with maximum iteration count of 100. The swarm diversity behaviour is also studied in relation with converged or promising global optimum solution. It is found that contemporary standard PSO (CS-PSO) with or without velocity clamping maintains better swarm diversity and preserves the balance between swarm “exploration” and “exploitation” efficiently. Velocity clamping and positional clamping are recommended as they prevent the solution/control variable from overflying the swarm best position.

Grey wolf optimization approach for searching critical failure surface in soil slopes

Detection of critical failure surface and associated minimum factor of safety (F) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count $$ (k_{\hbox{max} } ) $$ range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best $$ F_{\text{b}} $$, worst $$ F_{\text{w}} $$, mean $$ \overline{F} $$, standard deviation (SD) and % error (%E) of the optimum solutions i.e. factor of safety (F) from 10 independent runs. The effect of GWO parameters such as NP and $$ k_{\hbox{max} } $$ to obtain optimum solution are also presented. The $$ F_{\text{b}} , \, F_{\text{w}} , \, \overline{F} \;{\text{and}}\;{\text{SD}} $$ for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (%E) in best $$ F_{\text{b}} $$ from optimum (F) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.

FPGA-Based Hardware/Software Co-Design of a Bio-Inspired SAT Solver

For various kinds of Internet of Things (IoT) systems whose control rules can be expressed in a Satisfiability (SAT) problem, this work aims at realizing an IoT-oriented FPGA-based SAT solver leveraging a bio-inspired algorithm, AmoebaSAT, using a hardware/software co-design approach. With regard to the software component, we extended the baseline algorithm to escape from local minima more quickly and achieve significant reduction in iteration count. With regard to hardware, we fully extracted the fine-grained parallelism of the algorithm to further accelerate the solution search. Through our evaluations using several benchmarks of varying variable count and complexity, we demonstrated the efficiency of our solver, especially for larger practical SAT instances. Compared with three state-of-the-art solvers (i.e., one software implementation of the original AmoebaSAT algorithm and two FPGA-based hardware solvers), we achieved an average of $15.9\times $ and up to $48\times $ reduction in iteration count. Furthermore, through in-depth analyses of the experimental results, we provided the essential findings on the relationship between the problem’s complexity and the SAT algorithm that can be leveraged for extensions of both the hardware and software designs.

The research and development of the hybrid algorithm based on the collective behavior of Fish schools and the classical optimization methods

In this paper, we consider the hybridization problem of the evolutionary-inspired Fish School Search algorithm. The algorithm shows accurate results on solving multi-extremal optimization problems, outperforms most other swarm intelligence algorithms and is computationally inexpensive. But, the accuracy of the algorithm highly depends on the defined iteration count to compute. The accuracy increases with the increase of iteration count, but this also affects computation time required to find the suboptimal solution. In this paper, we propose two hybrid approaches which intend to accelerate the Fish School Search algorithm using either gradient descent or Newton’s algorithm. We provide the comparative analysis of the original algorithm and the two hybrid algorithms applied to the Styblinsky-Tang, Eggholder and other test functions for optimization, including multi-extremal and multi-dimensional ones. The obtained results confirm that the proposed hybrid algorithms are more effective, compared to the original population-based algorithm. The results demonstrate the strong advantage of the hybrid algorithm, where the gradient descent is used as its part. Additionally, we provide the solution of the XOR problem using a perceptron with one hidden layer, where the most effective hybrid approach is used to train the network. We visualize the loss function surface near the global extreme point to show the effectiveness of the proposed hybrid algorithm.

Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET

Many imaging problems, such as total variation reconstruction of X-ray computed tomography (CT) and positron-emission tomography (PET), are solved via a convex optimization problem with near-circulant, but not actually circulant, linear systems. The popular methods to solve these problems, alternating direction method of multipliers (ADMM) and primal-dual hybrid gradient (PDHG), do not directly utilize this structure. Consequently, ADMM requires a costly matrix inversion as a subroutine, and PDHG takes too many iterations to converge. In this paper, we present near-circulant splitting (NCS), a novel splitting method that leverages the near-circulant structure. We show that NCS can converge with an iteration count close to that of ADMM, while paying a computational cost per iteration close to that of PDHG. Through experiments on a CUDA GPU, we empirically validate the theory and demonstrate that NCS can effectively utilize the parallel computing capabilities of CUDA.

Parallel Simulation of Audio- and Radio-Magnetotelluric Data

This paper presents a novel numerical method for simulation controlled-source audio-magnetotellurics (CSAMT) and radio-magnetotellurics (CSRMT) data. These methods are widely used in mineral exploration. Interpretation of the CSAMT and CSRMT data collected over an area with the complex geology requires application of effective methods of numerical modeling capable to represent the geoelectrical model of a deposit well. In this paper, we considered an approach to 3D electromagnetic (EM) modeling based on new types of preconditioned iterative solvers for finite-difference (FD) EM simulation. The first preconditioner used fast direct inversion of the layered Earth FD matrix (Green’s function preconditioner). The other combined the first with a contraction operator transformation. To illustrate the effectiveness of the developed numerical modeling methods, a 3D resistivity model of Aleksandrovka study area in Kaluga Region, Russia, was prepared based on drilling data, AMT, and a detailed CSRMT survey. We conducted parallel EM simulation of the full CSRMT survey. Our results indicated that the developed methods can be effectively used for modeling EM responses over a realistic complex geoelectrical model for a controlled source EM survey with hundreds of receiver stations. The contraction-operator preconditioner outperformed the Green’s function preconditioner by factor of 7–10, both with respect to run-time and iteration count, and even more at higher frequencies.

Research on the Convergence of Iterative Method Using Mixed Precision Calculation Solving Complex Symmetric Linear Equation

This article investigates the complex symmetric linear equations that appear in high-frequency electromagnetic-field analysis. As an efficient linear solver, we propose a mixed-precision iterative method with double- and double-double (DD)-precision floating-point numbers and an efficient implementation of DD-precision arithmetic with fused multiply-add instructions. Using the proposed method, we successfully reduce both iteration count and calculation time compared with the conventional method. Moreover, we demonstrate the relationship between multiple-precision arithmetic and the acceleration factor of the incomplete Cholesky factorization.

Design of digital signal processor based adaptive beamformer using hybrid residual least mean square algorithm for improved performance

This paper proposes a novel hybrid residual least mean square (HRLMS) algorithm for adaptive filtering followed by an antenna beamformer using 16-element linear array. The hybridization process involves a switching between the residual-LMS (RLMS) and the conventional-LMS (CLMS) algorithms after the eighth iteration, if the square errors for four consecutive iterations are less than a threshold. The novelty of HRLMS lies in estimating best step size factor through residuals for speedy convergence followed by the CLMS switching for minimum steady state error (SSE). The novelty also includes in realizing a real-time antenna beamformer with significant sidelobe level (SLL) reduction and improved interference nulling by integration of HRLMS and space selective digital filter (SSDF). The adaptive filter and smart beamformer, based on HRLMS and HRLMS-SSDF have been implemented on TMS320VC5416 digital signal processor. The comparative performance evaluation of HRLMS has been done for convergence speed, SSE, interference nulling and SLL reduction with the existing variable step size LMS (VSSLMS) algorithms. The iteration count for convergence has been reduced by about 50% with paltry additional computational burden over the other VSSLMS algorithms. The HRLMS-SSDF provide attenuations of about 76, 33, and >50 dB, respectively for interfering signals, first SLL and higher order SLLs of beamformer.

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection‐diffusion equations

SummaryIn this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection‐diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid‐point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second‐order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations

The discretizations of two- and three-dimensional spatial fractional diffusion equations with the shifted finite-difference formulas of the Grünwald-Letnikov type can result in discrete linear systems whose coefficient matrices are of the form D+T, where D is a nonnegative diagonal matrix and T is a block-Toeplitz with Toeplitz-block matrix or a block-Toeplitz with each block being block-Toeplitz with Toeplitz-block matrix. For these discrete spatial fractional diffusion matrices, we construct diagonal and block-circulant with circulant-block splitting preconditioner for the two-dimensional case, and diagonal and block-circulant with each block being block-circulant with circulant-block splitting preconditioner for the three-dimensional case, to further accelerate the convergence rates of Krylov subspace iteration methods, and we analyze the eigenvalue distributions for the corresponding preconditioned matrices. Theoretical results show that except for a small number of outliners the eigenvalues of the preconditioned matrices are located within a complex disk centered at 1 with the radius being exactly less than 1, and numerical experiments demonstrate that these structured preconditioners can significantly improve the convergence behavior of the Krylov subspace iteration methods. Moreover, this approach is superior to the geometric multigrid method and the preconditioned conjugate gradient methods incorporated with the approximate inverse circulant-plus-diagonal preconditioners in both iteration counts and computing times.

Performance Evaluation of Sc-IDMA & Of DM- IDMA in Impulsive Media

In this paper, we analyzed the working phenomenon of Single and Multi carrier IDMA in Non Gaussian Impulsive medium and also compared their relative performances. The performance comparison is evaluated under the following constraints; by varying the iteration count, impulsive constant, control parameters and no. of users etc. The multi user detection for these schemes can be realized with complexity (per user) strictly independent of number of users. The simulation result concludes that multicarrier IDMA outperforms the single carrier IDMA in impulsive non Gaussian channel as a medium.

Exclusion Radius Particle Swarm Optimizer

Function optimization is a problem that has existed since modern engineering began. With multiple variables, brute-forcing or simple regression models become unfeasible. This paper proposes a shrinking population control method for a dynamic population particle swarm optimizer. The proposed control mechanism creates an exclusion zone, where particles are periodically purged from the simulation. The selection of particles purged relies on their particle best i.e. the position where it found its personal best fitness. Particles with their particle best outside of the exclusion zone with a predetermined radius from the current global best are removed from the simulation. The purging is done periodically in stages of equal iteration counts, and the radius is shrunk by a factor after every stage. By testing 5 benchmark mathematical functions, the results show that the proposed population control mechanism achieves better final optima than only a basic particle swarm optimizer and a simple shrinking dynamic population particle swarm optimizer where the worst performing particle is removed every so often.