Minimization Algorithm Research Articles

Refining DIIS algorithms for Si and GaAs solar cells: incorporation of weight regularization, conjugate gradient, and reverse automatic differentiation techniques.

Pivotal enhancements in electronic minimization algorithms, which are vital for the advancement of computational materials science, are introduced in this research. Our research is dedicated to refining the DIIS algorithm specifically for electronic structure calculations of silicon (Si) and gallium arsenide (GaAs) solar cells, aiming to enhance their efficiency and stability. We have enriched DIIS by integrating a weight regularization factor, significantly bolstering its convergence stability. This modification enhances iteration robustness and curtails the average iteration duration, thus streamlining the convergence process. Furthermore, we have incorporated the conjugate gradient (CG) algorithm to proficiently resolve symmetric positive definite residual matrices. This inclusion substantially accelerates the solution-finding process within the DIIS framework. A novel aspect of our research is the application of reverse automatic differentiation (AD), deployed in two distinct methodologies: the construction of the Jacobian matrix and direct chain rule application for gradient computation. These approaches involve sophisticated mathematical techniques that enhance computational precision and efficiency specifically for Si and GaAs solar cell materials in determining the optimal weights for residual combinations during DIIS iterations. The integration of these advanced methods into the DIIS algorithm not only augments its convergence stability but also ensures a substantial reduction in total computational time. Our findings demonstrate that the enhanced DIIS, CG-enhanced DIIS, and AD-integrated DIIS methods collectively lead to a more efficient electronic minimization process. This balance of stability and efficiency is crucial in high-performance computational materials science, particularly for complex systems analysis. The findings of this research represent a notable advancement in computational strategies for Si and GaAs solar cell materials, providing enhanced methodologies and insights that significantly improve the efficiency and stability of electronic structure calculations in these critical components of renewable energy technologies.

Comparative Study: Electric Distribution Optimization with Loss Minimization Algorithm and Particle Swarm Optimization

Comparative Study: Electric Distribution Optimization with Loss Minimization Algorithm and Particle Swarm Optimization

Loss Minimization Algorithm for Surface-Mounted PMSM Using Ripple-Based Extremum Seeking

Loss Minimization Algorithm for Surface-Mounted PMSM Using Ripple-Based Extremum Seeking

Excitation Control of Brushless Induction Excited Synchronous Motor with Induction Machine Operating in Deep-Plugging Mode

Abstract The popularity of electrified transportation is rising at a sharp pace due to environmental concerns over internal combustion (IC) engines. Researchers are nowadays looking for a brushless and permanent magnet (PM)-less solution for electric vehicle (EV) motors. Wound-field synchronous motor (WFSM) is a potential solution for EVs and is being used in Renault Zoe EV and BMW iX3 e-Drive models. A Brushless Induction excited Synchronous Motor (BINSYM) is a WFSM where the exciter, an induction machine (IM), is embedded inside the synchronous machine (SM) frame. Two machines (SM and IM) are configured for different numbers of poles to achieve magnetic decoupling, which facilitates independent control of both machines. The purpose of IM is to maintain the excitation requirement of SM. The IM is controlled in deep-plugging mode at a constant slip frequency over the entire speed range to minimise its reactive power demand. The maximum torque per ampere (MTPA) and root mean square (rms) current minimisation algorithms are used to control the SM. Simulation of the BINSYM-based system under dynamic conditions (MTPA with varying field current and load transient) has been carried out in MATLAB/Simulink to validate the control strategies. Experimental findings from the laboratory prototype machine closely match the simulation results.

RISIR: Rapid Infrared Spectral Imaging Restoration Model for Industrial Material Detection in Intelligent Video Systems

Material detection by industrial infrared imaging spectrometer (IRIS) is a key technique in multiple industrial applications, including garbage collection, material analysis, and robot vision. However, IRIS often suffers from overlapped bands and random noises, which limit the precision of subsequent processing. In this article, we propose a novel Gabor transform-based mid-wave infrared (MWIR) spectrum restoration model by successfully exploring the intrinsic structure of the clean MWIR spectrum from the degraded one. First, a total variation-regularized Gabor coefficient adjustment descriptor is designed and incorporated into the spectrum restoration model. In addition to adjusting the Gabor coefficient distribution by total variation-norm, the L2-norm of gradient is leveraged to regulate the smoothness of the instrument degradation function. Then, the proposed model is inferred using an efficient optimization approach based on split Bregman iteration method and alternating minimization algorithm. Quantitative and qualitative experimental results demonstrate that the proposed model favorably outperforms the state-of-the-art approaches. The restored high-resolution MWIR spectrum can be used to rapidly detect different materials in intelligent video systems.

A note on the relation between recognisable series and regular sequences, and their minimal linear representations

In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and q-regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we show that the minimisation algorithm for recognisable series can also be used to minimise linear representations of q-regular sequences.

Priority based energy and load aware routing algorithms for SDN enabled data center network

Nowadays, to accommodate the swift expansion of cloud computing, big data, and other emerging technologies, integrating data center networks and SDN (Software Defined Network) is suggested, which also improves the network management’s convenience and flexibility. As network devices in these data centers continue to increase at a high rate, efficient route management to handle these devices’ vast amounts of data has emerged as a significant concern. This work suggests a novel admission and routing scheme considering the importance or priorities of the network flows, path energy, and routing path load. Using the SDN paradigm in DCN (Data Center Network), we first develop a Mixed Integer Linear Programming (MILP) formulation by jointly considering flow priority, path energy, and path load. The MILP formulation can maximize the number of flows as well as minimize the energy consumption and load variance in the network, or it can make a trade-off among all three. However, due to the potentially long running time, later, we introduce two greedy methods, Priority Based Energy Minimization Algorithm (PEMA) and Priority Based Evenly Load Distribution Algorithm (PEDL), where PEMA aims to maximize the flow with less energy, and PEDL focuses on maximizing the flow with reduced load variation. Finally, the developed routing strategies are implemented, and the simulation results demonstrate the out-performance of our work compared to the existing works in terms of successful flow ratio, energy savings, and load balancing.

Estimation of extreme multivariate expectiles with functional covariates

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate, belonging to an infinite-dimensional space. By using the first order optimality condition, we interpret these expectiles as solutions of a multidimensional nonlinear optimum problem. Then the inference is based on a minimization algorithm of gradient descent type, coupled with consistent kernel estimations of our key statistical quantities such as conditional quantiles, conditional tail index and conditional tail dependence functions. The method is valid for equivalently heavy-tailed marginals and under a multivariate regular variation condition on the underlying unknown random vector with arbitrary dependence structure. Our main result establishes the consistency in probability of the optimum approximated solution vectors with a speed rate. This allows us to estimate the global computational cost of the whole procedure according to the data sample size. The finite-sample performance of our methodology is provided via a numerical illustration of simulated datasets.

Zero-One Composite Optimization: Lyapunov Exact Penalty and a Globally Convergent Inexact Augmented Lagrangian Method

We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely the zero-one composite optimization problem (0/1-COP). It has a vast body of applications, including the support vector machine (SVM), calcium dynamics fitting (CDF), one-bit compressive sensing (1-bCS), and so on. However, it remains challenging to design a globally convergent algorithm for the original model of 0/1-COP because of the nonconvex and discontinuous zero-one loss function. This paper aims to develop an inexact augmented Lagrangian method (IALM), in which the generated whole sequence converges to a local minimizer of 0/1-COP under reasonable assumptions. In the iteration process, IALM performs minimization on a Lyapunov function with an adaptively adjusted multiplier. The involved Lyapunov penalty subproblem is shown to admit the exact penalty theorem for 0/1-COP, provided that the multiplier is optimal in the sense of the proximal-type stationarity. An efficient zero-one Bregman alternating linearized minimization algorithm is also designed to achieve an approximate solution of the underlying subproblem in finite steps. Numerical experiments for handling SVM, CDF, and 1-bCS demonstrate the satisfactory performance of the proposed method in terms of solution accuracy and time efficiency. Funding: This work was supported by the Fundamental Research Funds for the Central Universities [Grant 2022YJS099] and the National Natural Science Foundation of China [Grants 12131004 and 12271022].

Calculation of Phase Equilibria of Pure Light Hydrocarbons Using the PC-SAFT Equation of State and the Direct Energy Minimization Algorithm

In the oil and gas industry, there is growing interest in using the PC-SAFT equation of state for predicting the phase behaviour and physical properties of hydrocarbons. This article demonstrates how this equation of state can be used in combination with the direct energy minimization algorithm of an isochoric-isothermal system for calculating vapour-liquid equilibrium parameters of hydrocarbons. The proposed approach is tested on four substances: methane, ethane, propane, and n-butane.

Adaptation and assessement of projected Nesterov accelerated gradient flow to compute stationary states of nonlinear Schrödinger equations

The aim of the paper is to derive minimization algorithms based on the Nesterov accelerated gradient flow [Y. Nesterov, Gradient methods for minimizing composite objective function. Core discussion paper, (2007). Available at http://www.ecore.be/DPs/dp_1191313936.pdf; Y. Nesterov, A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) . In Doklady Akademii Nauk, Vol. 269, Russian Academy of Sciences, 1983, pp. 543–547; Y. Nesterov, Introductory Lectures on Convex Optimization: A basic course, Kluwer Academic Publishers, Massachusetts, 2004.] to compute the ground state of nonlinear Schrödinger equations, which can potentially include a fractional laplacian term. A comparison is developed with standard gradient flow formulations showing that the Nesterov accelerated gradient flow has some interesting properties but at the same time finds also some limitations due to the nature of the problem. A few simulations are finally reported to understand the behaviour of the algorithms and open the path to further complicate questions that require more advanced studies concerning the application of the Nesterov accelerated gradient flow to nonlinear Schrödinger equations.

Cloud-Edge-End Collaborative Caching Based on Graph Learning for Cyber-Physical Virtual Reality

Virtual reality (VR) is an important landing scenario for 5G and a key enabling technology for the digital economy, and the core challenge it faces is how to ensure real-time interaction and content distribution efficiency. Existing solutions rely on adaptive delivery, overall content edge caching, or asynchronous rendering in the cloud, with drawbacks such as high caching and computing costs and difficulty in ensuring real time. This article is oriented to content generation and synchronization of virtual reality, and aims at realizing intelligent transmission of VR content with high efficiency and low delay guarantee, and carries out research on cloud-edge-end collaborative mechanisms. First, for AI-aided VR content generation, a cloud-edge-end collaborative service architecture is constructed to support independent encoding and distribution of background and interactive content generation. Second, to address the issue that the MEC node with limited cache space cannot meet the dynamical demands of VR user, a cloud-edge collaborative caching strategy based on graph neural networks is proposed to achieve optimal caching and updating of background content, in which the background content is first cached MEC node according to the content request with node sharing scheme, then the content is updated according to a minimal cost update algorithm based on the graph neural networks (GNN)-aided request prediction. Finally, the proposed algorithm is simulated and tested, the simulation results show that the proposed caching and update algorithm achieve better quality of experiment (QoE) and higher cache hit ratio compared with comparison algorithms.

Shared energy storage-assisted and tolerance-based alliance strategy for wind power generators based on cooperative game and resource dependence theories

The variability of wind power will affect the market performance of wind power generators (WPGs) and make them suffer energy deviation settlement. Energy storage, as a controllable resource, is widely used to cope with the problem. However, independent construction of large-scale energy storage will bring high investment costs and risks to WPGs. The sharing of energy storage in the alliance formed by different types of WPGs provides a new solution to the problem, but alliance cooperation and alliance selection are crucial issues that warrant diligent attention by WPGs from the perspective of the cooperative game. Given this background, a shared energy storage (SES)-assisted and tolerance-based alliance strategy based on cooperative game and resource dependence theories is formulated for WPGs. First, a robust-based market profit model of WPGs is developed. On this basis, transaction cost theory is implemented to analyze cooperation costs, and the dual theory-based alliance profit model considering SES is developed. Then, a modified profit allocation approach based on multiple indexes and deviation minimization algorithm (MI-DMA) is innovatively developed to allocate alliance profits. Finally, since the difficulty in meeting the maximum interests of all WPGs within an alliance simultaneously, the tolerance index is proposed to assist WPGs in making concession decisions for cooperation and the tolerance-based alliance strategy is formulated to balance the satisfactions of WPGs and formations of alliances. Compared to the strategies based on non-cooperative games, the proposed strategy based on cooperative games can fully leverage the complementary advantages of each WPG, consider the interests of all WPGs, and foster cooperation and fairness. Simulation results show that WPGs can obtain satisfactory returns by selecting appropriate cooperators under the tolerance-based alliance strategy. It also demonstrates that the proposed MI-DMA-based profit allocation method is more targeted and comprehensive than commonly used cooperative game-based methods.

Risk-based path planning for preventing collisions and groundings of maritime autonomous surface ships

In this paper, we propose and demonstrate a method for risk-based path planning, generating risk-acceptable trajectories for an autonomous surface ship. This objective is achieved in two steps. The first step uses a dynamic probabilistic risk assessment method called K-shortest-paths Probabilistic Risk Assessment (KPRA), alongside risk models and dynamic system simulation, whose output is a list of paths ranked with respect to risk. Multiple risk influencing factors and accident types may be considered in this step. In this work, collision and powered grounding accidents, and their risk-influencing factors and indicators, are considered. The second step is to perform risk evaluation on the ranked scenarios, comparing them to predefined risk acceptance criteria and defining which scenarios have acceptable risk. Evaluating multiple paths allows operators to choose how strict the autonomous ship’s decision-making should be regarding risk, avoiding the problem of minimization algorithms being too conservative in terms of risk. One of the risk-acceptable paths is then chosen as a local plan to be acted by the autonomous ship. This paper has two main scientific contributions. First, an online Bayesian belief network risk model for navigation accident probability is designed and integrated to improve KPRA. Second, we propose a modified guidance, navigation, and control framework for autonomous ships, to include risk-based planning. We implement the modified framework into a real autonomous surface vehicle (ASV) named Grethe and demonstrate the method’s capabilities in field trials, where the ASV uses the method to generate local plans that avoid possible collision and grounding accidents.

Distributed algorithm for social cost minimization with second-order nonlinear dynamics over weight-unbalanced digraphs

In this paper, the emerging social cost minimization framework of second-order nonlinear systems over weight-unbalanced digraphs is studied. It provides a general framework containing several important classes of problems. Therein each local cost function depends on a global decision variable consisting of all the agents’ decisions not limited to the form of aggregative terms. Under the partial decision and cost function information setting, distributed algorithms are designed based on the state feedback and left eigenvector estimation mechanism to overcome the challenges posed by second-order nonlinear systems and weight-unbalanced digraphs. The asymptotic convergence of the algorithm is demonstrated via the Lyapunov stability theory. Finally, numerical simulations of the vehicle monitoring problem are provided to support the algorithm design.

A fusion non-convex group sparsity difference method and its application in rolling bearing fault diagnosis

Bearing fault is a common factor leading to machine failures. How to extract the periodic transient signal due to bearing faults submerged in strong noise is a challenging problem for bearing fault diagnosis. Total variation denoising is a method used to remove noise and extract features. However, it solely relies on the sparsity of the first-order difference of the signal, resulting in the loss of important features and underestimation of amplitude. Additionally, it fails to capture the periodicity of the signal. To address these issues, a novel approach called fusion non-convex group sparsity difference (FNC-GSD) method is proposed for bearing fault diagnosis. Firstly, it is recognized that noise does not exhibit sparsity in the difference domain, while transient signal exhibits group sparsity in the difference domain. This grouping property enhances the feature selection ability of sparse model. Inspired by this, the group sparsity of the transient signal in the difference domain is used to preserve the fault features as much as possible. Additionally, in order to promote sparsity of the signal itself in the time domain to preserve the potential impulse component, a l 1-norm regularization term is introduced. Furthermore, a non-convex sparsity-inducing penalty function strategy is employed to prevent amplitude underestimation. The proposed sparse model considers both the group sparsity in the difference domain and the sparsity in the time domain of the transient signal, and its solution is derived according to the majorization–minimization algorithm. And the particle swarm optimization algorithm is used to adaptively search the regularization parameters of FNC-GSD. Finally, multiple bearing fault diagnosis experiments are conducted to demonstrate the performance of the FNC-GSD. The results show that it has advantages in fault feature extraction compared with some other methods.

Hybrid distributed online and alternating convex optimization‐based initial value accelerated hybrid precoding for millimeter wave multiple‐input‐multiple‐output

SummaryThe hybrid precoding problem is considered a Frobenius norm reduction problem for the narrowband channel in a millimeter wave (mmWave) with multiple inputs and outputs (mmWave MIMO). This work proposes a hybrid distributed online and alternating convex optimization (HDO‐ACO) algorithm to improve hybrid precoding (HP), interpreted as a trace minimization problem. HDO‐ACO alternately determines the digital and analog precoders to reduce the trace by keeping the other constant. Initially, HDO‐ACO uses Lagrange's method to determine the digital precoding subproblem. Then, it uses the integrated distributed online convex optimization and alternating minimization algorithm in the analog precoder design. In the HP method, the digital and analog precoders are iteratively updated until the highest number of iterations or convergence is reached. But this hybrid precoding method requires an initial analog precoding matrix input to begin the iteration. The algorithms converge gradually and fall into a suboptimal solution when the initial analog precoding matrix is set randomly. Hence, an initial value acceleration‐based heuristic approach is used in the HDO‐ACO alternating minimization algorithm that calculates the initial feasible value of an alternating minimization method using channel conditions. The simulation results of the proposed HDO‐ACO algorithm are presented under bit error rate (BER), spectral efficiency (SE), and convergence behavior by comparing it with modified block coordinate descent–HP (MBCD‐HP), manifold optimization–alternating minimization (MO‐AltMin), and semi‐definite relaxation‐based alternating optimization (SDR‐AO). The proposed HDO‐ACO attains maximum SE and less BER than other hyper‐precoding designs.

Digital Calibration of Input Offset Voltage and Its Implementation in FDDA Circuits

This article deals with the calibration method of analog integrated circuits (ICs) designed in CMOS nanotechnology. A brief analysis of various methods and techniques (e.g., fuse trimming, chopper stabilization, auto-zero technique, etc.) for calibration of a specific IC’s parameter is given, leading to motivation for this research that is focused on the digital calibration. Then, the principle and overall design of the calibration subcircuit, which was generally used to calibrate the input offset voltage VIN_OFF of the operational amplifier (OPAMP). The essence of this work is verification of the proposed digital calibration algorithm for minimization the VIN_OFF of a bulk-driven fully differential difference amplifier (FDDA) with the power supply voltage VDD = 0.4 V. Evaluation of ASIC prototyped chip samples with silicon-proved results has been done. This evaluation contains comparison of selected parameters and characteristics obtained from both simulations and measurements of non-calibrated and calibrated FDDA configurations.

A stochastic two-step inertial Bregman proximal alternating linearized minimization algorithm for nonconvex and nonsmooth problems

A stochastic two-step inertial Bregman proximal alternating linearized minimization algorithm for nonconvex and nonsmooth problems

Minimal Determinization Algorithm for Fuzzy Automata

The determinization of fuzzy automata is a well-studied problem in theoretical computer science celebrated for its practical applications. Indeed, in the fields of fuzzy discrete event systems, fault diagnosis, clinical monitoring, decision-making systems, and model checking, when a suitable model of a fuzzy automaton is employed, it is desirable to find its language-equivalent deterministic version because of its computational efficiency. Although many methods have been developed to convert a fuzzy automaton to its language equivalent fuzzy deterministic finite automaton (FDfA), they can be applied only for fuzzy automata defined over specific underlying sets of truth values. For example, recently developed determinization methods employ the concept of maximal factorization, which can be defined only on non-locally finite lattices or the Boolean lattice. In addition, not all such determinization methods result in a minimal FDfA. On the other hand, even though such determinization methods have been developed for fuzzy automata over specific underlying structures, these methods cannot be generalized for fuzzy automata over locally finite lattices. This article focuses on filling this gap and develops a novel method for computing a minimal FDfA for a fuzzy automaton defined over a locally finite and divisible residuated lattice. Our method uses the new concept of a reduction graph that emerges from the strict order relation on the resulting fuzzy states, according to which we can construct all minimal FDfAs equivalent to a given fuzzy automaton.