Bisection Method Research Articles

A Matching Strategy Based on Full-Permutation Bisection for Data Converters

This paper presents a top-to-bottom element-matching strategy based on a full-permutation bisection algorithm for data converters. By bisecting the composing elements and recombining them for a minimal weight difference, the linearity of the data converter can be significantly improved. Three different approaches have been implemented for the proposed algorithm, and they are based on linear programming, stochastic quantization, and maximal linearly independent subset (MLIS) respectively. Their pros and cons have been discussed and simulated exhaustively, and all of them have been silicon proved via capacitive digital to analog converters in 180-nm technology. Measurement results of twenty dies for each approach verified the aforementioned theoretical analysis, and all three approaches could achieve sub-30 ppm for all codes after calibration. The worst integral nonlinearity at the most significant bit after calibration can be improved from 402 ppm to 10.9 ppm, which is equivalent to a 5.2-bit boost, indicating a promising potential of the proposed matching strategy. Besides, the MLIS-based approach is the first optimal-combination-algorithm-based matching strategy that achieves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{O}(N)$</tex-math> </inline-formula> time complexity, as the authors know.

A variable projection method for large-scale inverse problems with ℓ1 regularization

Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine learning. With ever-increasing model complexities and larger data sets, new specially designed methods are urgently needed to recover meaningful quantities of interest. We consider the broad spectrum of linear inverse problems where the aim is to reconstruct quantities with a sparse representation on some vector space. We provide a new variable projection augmented Lagrangian algorithm to solve the underlying ℓ1 regularized inverse problem that is both efficient and effective. We present the proof of convergence for an algorithm using an inexact step for the projected problem at each iteration. The performance and convergence properties for various imaging problems are investigated. The efficiency of the algorithm makes it feasible to automatically find the regularization parameter, here illustrated using an argument based on the degrees of freedom of the objective function equipped with a bisection algorithm for root-finding.

RPCGB Method for Large-Scale Global Optimization Problems

In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency.

Switched-Resistor Passive Balancing of Li-Ion Battery Pack and Estimation of Power Limits for Battery Management System

The battery pack performance and expected lifespan are crucial in electric vehicle applications. Balancing the charge on a battery pack connected in series and parallel is crucial due to manufacturing discrepancies and distinct performance of each cell in a standard battery pack. In this paper, a switched-resistor passive balancing-based method is proposed for balancing cells in a battery management system (BMS). The value of the available voltage at the battery cell terminals is balanced using resistors in an electrical circuit, and the excess voltage is eliminated. The cell balancing outcome demonstrates that the electrical circuit can maintain an even voltage across each cell. The procedure of balancing involves individually adjusting each cell’s level of charge. Passive balancing releases energy as heat by draining charge from cells that have too much charge. A passive cell balancer is a cost-effective solution and easy to install, but due to thermal loss from a resistor, it has a low energy efficiency for cell balancing and necessitates a lengthy balancing process. This passive cell balancer is an effective and reliable method for low-power devices and portable applications such as electrical vehicles. The power limits during charging and discharging are estimated using the bisection method.

Optimal operation of distribution networks and multiple community energy prosumers based on mixed game theory

Community energy systems are currently transitioning from conventional consumers to prosumers. Under this context, the coordinated management of multiple community energy prosumers (CEPs) is explored this study in accordance with the same distribution network. The aim of this study is to facilitate the coordination of unit operations, demand response, and peer-to-peer (P2P) energy trading among CEP coalitions based on the distribution network operator (DSO) by setting electricity prices. Thus, a mixed game-based optimal operation model of DSO and CEP alliances is developed, integrating Stackelberg and cooperative games. The upper layer aims at maximizing DSO revenue, whereas the lower layer minimizes the operation costs of CEP cooperative alliances while allocating benefits in accordance with the Nash-Harsanyi bargaining theory. The model is solved with a two-stage distributed algorithm that integrates the bisection method and the alternating direction method of multipliers (ADMM). Furthermore, cloud energy storage (CES) is introduced to optimize the economics of CEP. The effectiveness of the proposed method is verified through a case study, demonstrating the collaborative optimal scheduling of multiple CEPs and reasonable benefit distribution. Accordingly, this study is conducive to expediting the effective and economical management of CEPs under distribution networks.

Graphical User Interface for Solving Non-Linear Equations for Undergraduate Students

Solving non-linear equations problems for root-finding is more challenging rather than linear equations problems. Generally, this is because it cannot be solved by using the standard formula. The numerical method is one of the ways that can be applied, consisting of an iterative procedure. A simulator named Root Calculator to Solve Non-Linear Equations was developed, where it is a graphical user interface (GUI) system that can be used to approximate the root based on the equation and interval given. Four methods were chosen which are the Graphical Method, the Bisection Method, Newton’s Method, and the Secant Method to produce the approximation root. App Designer in MATLAB R2020b software was used for this development.

Joint Offloading and Resource Allocation With Diverse Battery Level Consideration in MEC System

Most of existing works related to mobile edge computing (MEC) focused on the total energy consumption or task completion time. However, for the applications with multiple players as a whole, the diverse battery levels of players should be considered to achieve better quality of experience (QoE), which is reflected in the metrics of task completion time and the lifespan of service. In this paper, we focus on QoE and diversity of devices. By jointly considering the individual battery level of different devices, we formulate an optimization problem to minimize the task completion time of the system. Firstly, we propose two necessary conditions to achieve the optimal solution of the formulated problem. In addition, we transform the formulated problem into another problem, which can be used to judge whether a given value is feasible for the formulated problem based on the proposed optimal conditions and bisection searching (BSS) algorithm. Then, we propose a method named sub-channel (SC) matching based on virtual computation resource (SMVCR) to solve the transformed problem with low computational complexity. Simulation results indicate that the BSS-SMVCR algorithm has a good performance in task completion time compared with some existing algorithms, and also can significantly extend the lifespan of the corresponding service, which is reflected in the supporting number of offloading tasks.

追い越し待避に対応した遅延時の列車群制御手法の提案および処理の高速化について

With the recent developments in information and communication technologies, automatic train operations have been attracting increasing attention. In this paper, we propose a novel train group control method that utilizes train operation forecasts under complex timetable disruptions. In particular, we examine the effects of the proposed method using simulation results. The results reveal that the proposed method reduces the number of iterations required for searching the optimal cruising speed compared with bisection methods.

Resource allocation of backscatter communication based on reconfigurable intelligent surface

AbstractIn this article, we propose a double reconfigurable intelligent surface (RIS)‐aided ambient backscatter communication (AmBC) network combined with non‐orthogonal multiple access (NOMA) technology, which not only successfully assists the base station (BS) in connecting with the cell edge user, but also enhances backscatter communication rate, energy efficiency, and spectrum efficiency. In an effort to obtain the highest backscatter communication rate, we design a RIS and BS‐based resource allocation problem which is solved by determining the optimal phase shifts of RISs and the optimal power allocation for signals of NOMA users. We break it down into two smaller challenges in order to discover the best solution. For one thing, we iterate the optimal phase shifts between the two RIS combinations using an alternating optimization technique. For another, the bisection method is used to provide the NOMA user with the ideal power allocation. Finally, the results of the simulation substantiate the viability of the proposed scheme.

A Geometrical, Reachable Set Approach for Constrained Pursuit–Evasion Games with Multiple Pursuers and Evaders

This paper presents a solution strategy for deterministic time-optimal pursuit–evasion games with linear state constraints, convex control constraints, and linear dynamics that is consistent with linearized relative orbital motion models such as the Clohessy–Wiltshire equations and relative orbital elements. The strategy first generates polytopic inner approximations of the players’ reachable sets by solving a sequence of convex programs. A bisection method then computes the optimal termination time, which is the least time at which a set containment condition is satisfied. The pursuit–evasion games considered are games with (1) a single pursuer and single evader, (2) multiple pursuers and a single evader, and (3) a single pursuer and multiple evaders. Compared to variational methods, this reachable set strategy leads to a tractable formulation even when there are state and control constraints. The efficacy of the strategy is demonstrated in three numerical simulations for a constellation of satellites in close proximity in low earth orbit.

Efficient single-grid and multi-grid solvers for real-space orbital-free density functional theory

To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved bisection method to accelerate the line search process in the outer iteration, and extended the single-grid solver to a multi-grid solver. Numerical examples show that while maintaining high level of accuracy, the proposed single-grid solver can improve the computational efficiencies by two orders of magnitude comparing with the methods in the literature (For example, the ground state energy of a 45×45×45 FCC Aluminum cluster (376786 atoms) can be computed within 4h27min on a desktop computer.) and the multi-grid solver can improve the computational efficiencies even once for the cases where high-resolution electron densities are needed.

Bisection Method and Falsi Regulation Method to Determine The Roots of Polynomial Equations

Some simple polynomial equations can be solved by the remainder theorem, so there is no need for numerical methods to solve them, because the roots of equations are very easy to do using analytical methods, while there are some polynomial equations that are difficult and complex to find roots using analytical methods.&#x0D; In this literature review, researchers will use the bisection method and the false rule to find the roots of polynomial equations. Based on the steps or sequence of calculation of the polynomial roots of , using the bisection method, the author states that from the first step to the eleventh step, if the calculation continues then in the second step f(a)*f(c)&gt;0 or away from zero as shown in table 1 above. The author states that if the twelfth step continues, then f(a)*f(c) will approach zero and it can be seen that there are looping process approaches resulting from f(a)*f(c). This research study concludes that the roots of the polynomial of , using the bisection method are 1.36474675. Based on the steps or sequence of calculating the roots of the polynomial of on, using the false position method (false rule), the author states that from the first step to the 366th step it turns out that f(c)=0.003195 when c=1,365423447. Thus the polynomial roots of using the false position method (regulation false) are 1.365423447.&#x0D; Keywords: Roots of polynomial equations.

An interface preserving and residual-based adaptivity for phase-field modeling of fully Eulerian fluid-structure interaction

In this paper, we present a novel interface preserving and residual-based adaptivity procedure for the phase-field modeling of a fully Eulerian fluid-structure interaction. The proposed adaptive fully Eulerian procedure involves a fixed background unstructured finite element mesh on which the fluid-structure boundary is treated implicitly via a diffused interface description. We employ the stabilized finite element formulation and a partitioned iterative procedure to solve the coupled system of the Allen-Cahn phase-field equation with the unified momentum equation comprising solid and fluid dynamics. To evaluate the solid stresses, the left Cauchy-Green deformation tensor is convected at each time step to trace the evolution of the solid strain in the Eulerian reference frame. We utilize a residual based error indicator and the newest vertex bisection algorithm for the adaptive refinement/coarsening of the unstructured mesh. Through the adaptive finite element method, we aim to preserve the profile of the diffused interface in the presence of convective distortion. We propose an early stopping criterion for the adaptivity of the interface dynamics by combining the effects of the phase-field interface thickness parameter and the mesh resolution. In addition, we control the size of the refined/coarsened elements by introducing a characteristic length scale governed by a weighted harmonic mean of the desired bulk and the interface mesh resolutions. The proposed stopping criterion and the characteristic length scale provide significant reductions in the computational cost while simultaneously ensuring convergence properties of the coupled fluid-structure system. We perform a detailed convergence and accuracy analysis via two benchmark problems namely, the pure solid system and a coupled fluid-solid system with an interface in a rectangular domain. We further provide a comparative study between feature- and residual based adaptive strategies. We systematically assess the performance of the adaptive procedure in terms of conservation properties and computational efficiency. Finally, we demonstrate our fully Eulerian adaptive solver to simulate the contact and bouncing phenomenon between an elastic solid and a rigid wall.

Energy Minimization for Wireless-Powered Federated Learning Network With NOMA

Limited energy resources remain a challenge for wireless devices in federated learning (FL) networks. To tackle this issue, a joint resource allocation problem is formulated to minimize the total energy consumption for wireless-powered FL networks with non-orthogonal multiple access. A two-dimensional search algorithm (TDSA) is first proposed to obtain the optimal solution for this challenging problem. To lower the computational complexity, the bisection algorithm (BA) is further employed by exploiting the inherent structure of the formulated problem. Numerical results verify the equal performance between the BA and TDSA, and the superiority of the proposed scheme over the benchmark schemes in energy minimization.

Asynchronous Cell-Free Massive MIMO With Rate-Splitting

In practical cell-free (CF) massive multiple-input multiple-output (MIMO) networks with distributed and low-cost access points, the asynchronous arrival of signals at the user equipments increases multi-user interference that degrades the system performance. Meanwhile, rate-splitting (RS), exploiting the transmission of both common and private messages, has demonstrated to offer considerable spectral efficiency (SE) improvements and its robustness against channel state information (CSI) imperfection. The signal performance of a CF massive MIMO system is first analyzed for asynchronous reception capturing the joint effects of propagation delays and oscillator phases of transceivers. Taking into account the imperfect CSI caused by asynchronous phases and pilot contamination, we derive novel and closed-form downlink SE expressions for characterizing the performance of both the RS-assisted and conventional non-RS-based systems adopting coherent and non-coherent data transmission schemes, respectively. Moreover, we formulate the design of robust precoding for the common messages as an optimization problem that maximizes the minimum individual SE of the common message. To address the non-convexity of the design problem, a bisection method is proposed to solve the problem optimally. Simulation results show that asynchronous reception indeed destroys both the orthogonality of the pilots and the coherent data transmission resulting in poor system performance. Besides, thanks to the uniform coverage properties of CF massive MIMO systems, RS with a simple low-complexity precoding for the common message obtained by the equal ratio sum of the private precoding is able to achieve substantial downlink sum SE gains, while the application of robust precoding to the common message is shown to be useful in some extreme cases, e.g., serious oscillator mismatch and unknown delay phase.

Secure Computation Offloading for Marine IoT: An Energy-Efficient Design via Cooperative Jamming

In smart ocean, the Marine Internet of Things (M-IoT) is ubiquitously used for data acquisition, communication connections, task computation, and so on. However, high-efficient energy consumption and secure yet low-latency transmission are subject to IoT devices' computation capacity and transmit power limitation, as well as wireless communication's broadcast characteristics. In this paper, we investigate the secure computation offloading in M-IoT with the assistance of unmanned surface vehicles (USVs) subject to the eavesdropping attack. In particular, we consider a scenario in which USVs are firstly scheduled to set up a high-quality communication link to the high altitude platform (HAP) and then exploited to provide cooperative jamming for the communication security at the physical layer when the HAP is performing computation offloading. We jointly optimize the USVs' positions, the duration of data uploading, the workload offloaded by HAP, the HAP's transmission power, and each USV's jamming signal power to minimize the system-wise energy consumption for completing the total workloads under the latency constraint. Despite the non-convexity, we decompose the problem vertically into a top problem that optimizes the USVs' positions and a bottom problem that optimizes the other variables. The Polyblock outer Approximation and bisection Search based algorithm (PAS-Algorithm) is proposed to alternatively optimize the variables in the bottom problem. And the Code bAsed croSs Entropy algorithm (CASE-Algorithm) is proposed to obtain the suboptimal solution to the formulated joint optimization problem. Numerical results validate the accuracy and effectiveness of our algorithms as well as the performance of optimizing the total energy consumption compared with the benchmark algorithms

Specific order and bisection search aided joint 3D beamforming and RIS reflecting optimization

In this paper, a three-node transmission model is conceived, where the base station (BS) node leverages 3D beamforming, the reconfigurable intelligent surface (RIS) node can constructively reconfigure the wireless channel, the user node only has a single antenna due to a limited price. Maximization of its downlink spectral efficiency is a joint optimization problem of three variables, namely phase-shift matrix Φ of RIS, tilt angle θ and beamforming vector w used in BS 3D beamforming. We solve this problem by employing the alternating optimization (AO) algorithm. But, in each iteration, a specific optimization order of firstly Φ, secondly θ and finally w is proposed, which facilitates the search of optimal θ in the way of narrowing its trust region and enabling unimodal property over the narrowed trust region. It finally results in a better combination of {Φ, θ, w}.

Vectorizing binary image boundaries with symmetric shape detection, bisection and optimal parameterization

AbstractBinary image boundary vectorization is the process of converting raster images into vector images represented with a sequence of Bézier curves. Two main factors in reconstructing parametric curves are to approximate the underlying structure of the boundaries as much as possible while using as few curves as possible. Existing methods do not perform well when considering both of these two main factors. In this article, we mimic the process of human vectorizing image boundaries by first segmenting the boundary points into multiple segments with the corner points. For the boundary points in each segment, we adopt the bisection method to find the largest number of points, which a single curve can fit. More curves will be added if the fitting error is larger than a predefined threshold. The process is repeated until all the points in the segment are fitted, thus minimizing the number of Bézier curves. Besides, symmetric image boundaries can be detected and used to further decrease the number of curves required. Our method can also choose the optimal parameterization method case by case to further reduce the fitting error. We make a comparison with both new and classical methods and show that our method outperforms them.

Deep learning-based energy harvesting with intelligent deployment of RIS-assisted UAV-CFmMIMOs

The ever-evolving internet of things (IoT) has spawned hundreds of wireless sensors that communicate via the internet infrastructure. The lifetime and self-sustainability of these sensors are pivotal factors dictating the performance of respective application infrastructure. Radio frequency energy harvesting (RFEH) technology has exhibited the capability of effectively augmenting the battery lifetime of these sensors. In this work, we introduce a novel framework called CURe, which combines the advantages of cell-free massive multiple-input multiple-output (CFmMIMO) and reconfigurable intelligent surfaces (RISs) to provide uninterrupted energy harvesting for IoT devices through RFEH. CFmMIMO integrates the advantages of distributed systems and massive MIMO, while RIS improves the signal strength of the information transfer and RFEH via its passive reflection capabilities. Moreover, we consider unmanned aerial vehicles (UAVs) equipped with CFmMIMO as mobile access points (APs) to better serve the moving sensory devices. To further enhance RFEH, we propose DeNCE, a channel estimation technique based on deep learning (DL) that eliminates the need for traditional closed-form equation-based channel estimation methods. Through evaluation, we first validate the performance of CURe by comparing it with the modified bisection search for max–min fairness (MBS-MMF) algorithm and later corroborate that DeNCE significantly improves the performances of both models. Finally, to optimize the UAV deployment and ensure continuous RFEH coverage, we propose dARL, a deep reinforcement learning (DRL)-based scheduling framework that enables UAV-CFmMIMO swarms to perform continuous energy harvesting in the coverage area collaboratively.

Bisection Method for the Heavy Fuel Oil Tank Filling Problem at a Liquefied Natural Gas Carrier

The commingling of the two types of heavy fuel oils (fuel remaining in the tanks and fuel loaded) is determined by the company’s guidance and safety management system. Remained heavy fuel oil must be distributed in the heavy fuel oil tanks before bunkering efficiently, in order to obtain maximum bunker loading. This paper proposes the use of the bisection method to calculate the distribution of the remaining fuel in heavy fuel oil tanks on the liquefied natural gas carrier. The use of this method is illustrated by three examples. The first and second examples show that the iterations converge quickly to the solution. It is found that maximum tank filling with fuel commingling is achievable if the bunker intervals satisfy the company policy of 10% as a lower limit of tank filling, and 90% to 100% as an upper limit. The third example illustrates a situation when the proposed mathematical model does not allow maximization of the total tank capacity without risk assessment. The mathematical spectrum of the possible tank filling solution is presented. Despite its limitations, the bisection method is suitable for onboard applications because it is simple and fast, and can be easily programmed.