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Pareto Ranking bisection algorithm for EM-Driven Multi-Objective Design of Antennas in Highly-Dimensional Parameter Spaces

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Procedia Computer Science 2017年 108卷 1453-1462页

作者： Adrian Bekasiewicz Slawomir Koziel Leifur Leifsson Xiaosong Du Reykjavik University Reykjavik Iceland Gdansk University of Technology Gdansk Poland Iowa State University Ames Iowa USA

A deterministic technique for fast surrogate-assisted multi-objective design optimization of antennas in highly-dimensional parameters spaces has been discussed. In this two-stage approach, the initial approximation of the Pareto set representing the best compromise between conflicting objectives is obtained using a bisection algorithm which finds new Pareto-optimal designs by dividing the line segments interconnecting previously found optimal points, and executing poll-type search that involves Pareto ranking. The initial Pareto front is generated at the level of the coarsely-discretized EM model of the antenna. In the second stage of the algorithm, the high-fidelity Pareto designs are obtained through optimization of corrected local-approximation models. The considered optimization method is verified using a 17-variable uniplanar antenna operating in ultra-wideband frequency range. The method is compared to three state-of-the-art surrogate-assisted multi-objective optimization algorithms.

关键词： antenna design multi-objective optimization EM-driven design bisection algorithm variable-fidelity simulations surrogate modeling

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Computer simulation of clonal growth cancer models .1. Parameter estimation using an iterative absolute bisection algorithm

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RISK ANALYSIS 1997年第1期17卷 115-126页

作者： Kramer, DA Conolly, RB CHEM IND INST TOXICOL RES TRIANGLE PKNC 27709

Quantitative models of the relationship between exposure to chemical carcinogens and carcinogenic response are useful for hypothesis evaluation and risk assessment. The degree to which such models accurately depict the underlying biology is often a function of the need for mathematical tractability. When closed-form expressions are used, the need for tractability may significantly limit their complexity. This problem can be minimized by using numerical computer simulation methods to solve the model, thereby allowing more complex and realistic descriptions of the biology to be used. Unfortunately, formal methods of parameter estimation for numerical models are not as well developed as they are for analytical models. In this report, we develop a formal parameter estimation routine and apply it to a numerical clonal growth simulation (CGS) model of the growth of preneoplastic lesions consisting of initiated cells. An iterative bisection algorithm was used to estimate parameters from time-course data on the number of initiated cells and the number of clones of these cells. The algorithm successfully estimated parameter values to give a best fit to the observed dataset and was robust vis-a-vis starting values of the parameters. Furthermore, the number of data points to which the model was fit, the number of stochastic repetitions and other variables were examined with respect to their effects on the parameter estimates. This algorithm facilitates the application of CGS models for hypothesis evaluation and risk assessment by ensuring uniformity and reproducibility of parameter estimates.

关键词： carcinogenesis simulation modeling parameter estimation bisection algorithm clonal growth

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Determination of Power Transfer Capability by a bisection-Like algorithm via Power-Flow Solutions

Determination of Power Transfer Capability by a Bisection-Li...

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IEEE Texas Power and Energy Conference (TPEC)

作者： Bilir, Bulent Yilmaz, Mutlu Izmir Univ Econ Dept Elect & Elect Engn Izmir Turkey IEEE Toronto ON Canada

ISBN: (纸本)9781538692844

The objective of this study is to present an algorithm that can determine power transfer capability of transmission lines via power-flow solutions. The calculation of transfer capability is carried out by obtaining power flows for various scenarios of operation under various amounts of power transfer. This paper deals with the bisection-like algorithm to compute transfer capability. The main motivation in this work results from the need to develop an efficient algorithm that can calculate maximum power transfer between selected buses and perform the numerical simulations for corresponding power-flow solutions. The accompanying program is easily expandable with new applications when necessary.

关键词： power transfer bisection algorithm available transfer capability power flow

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Optimizing Clustered Cell-Free Networking for Sum Ergodic Capacity Maximization With Joint Processing Constraint

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2025年第1期24卷 571-584页

作者： Xia, Funing Wang, Junyuan Dai, Lin Tongji Univ Coll Elect & Informat Engn Shanghai 201804 Peoples R China Tongji Univ Inst Adv Study Coll Elect & Informat Engn Shanghai 201804 Peoples R China Tongji Univ Shanghai Inst Intelligent Sci & Technol Shanghai 201804 Peoples R China City Univ Hong Kong Dept Elect Engn SAR Hong Kong Peoples R China

Clustered cell-free networking has been considered as an effective scheme to trade off between the low complexity of current cellular networks and the superior performance of fully cooperative networks. With clustered cell-free networking, the wireless network is decomposed into a number of disjoint parallel operating subnetworks with joint processing adopted inside each subnetwork independently for intra-subnetwork interference mitigation. Different from the existing works that aim to maximize the number of subnetworks without considering the limited processing capability of base-stations (BSs), this paper investigates the clustered cell-free networking problem with the objective of maximizing the sum ergodic capacity while imposing a limit on the number of user equipments (UEs) in each subnetwork to constrain the joint processing complexity. By successfully transforming the combinatorial NP-hard clustered cell-free networking problem into an integer convex programming problem, the problem is solved by the branch-and-bound method. To further reduce the computational complexity, a bisection clustered cell-free networking ((BCF)-F-2-Net) algorithm is proposed to decompose the network hierarchically. Simulation results show that compared to the branch-and-bound based scheme, the proposed (BCF)-F-2-Net algorithm significantly reduces the computational complexity yet achieves nearly the same network decomposition result. Moreover, our (BCF)-F-2-Net algorithm achieves near-optimal performance and outperforms the state-of-the-art benchmarks with up to 25% capacity gain.

关键词： Clustering algorithms Wireless networks Partitioning algorithms Interference Cellular networks Simulation Signal processing algorithms Uplink Optimization Computer architecture Clustered cell-free networking sum ergodic capacity maximization joint processing constraint bisection algorithm

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Implementation of reduced gradient with bisection algorithms for non-convex optimization problem via stochastic perturbation

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NUMERICAL algorithmS 2018年第1期78卷 41-62页

作者： El Mouatasim, Abdelkrim Univ Ibn Zohr FPO Dept Math Informat & Gest Ouarzazate 45800 Morocco

In this paper, we proposed an implementation of stochastic perturbation of reduced gradient and bisection (SPRGB) method for optimizing a non-convex differentiable function subject to linear equality constraints and non-negativity bounds on the variables. In particular, at each iteration, we compute a search direction by reduced gradient, and optimal line search by bisection algorithm along this direction yields a decrease in the objective value. SPRGB method is desired to establish the global convergence of the algorithm. An implementation and tests of SPRGB algorithm are given, and some numerical results of large-scale problems are presented, which show the efficient of this approach.

关键词： Large-scale problem Linear constraints Non-convex optimization Reduced gradient algorithm bisection algorithm Stochastic perturbation

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bisection acceleration for the symmetric tridiagonal eigenvalue problem

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NUMERICAL algorithmS 1999年第1期22卷 13-39页

作者： Pan, VY Linzer, E CUNY Herbert H Lehman Coll Dept Math & Comp Sci Bronx NY 10468 USA DiviCom White Plains NY 10601 USA

We present new algorithms that accelerate the bisection method for the symmetric tridiagonal eigenvalue problem. The algorithms rely on some new techniques, including a new variant of Newton's iteration that reaches cubic convergence (right from the start) to the well separated eigenvalues and can be further applied to acceleration of some other iterative processes, in particular, of the divide-and-conquer methods for the symmetric tridiagonal eigenvalue problem.

关键词： symmetric eigenvalue problem bisection algorithm divide-and-conquer eigenvalue algorithms Newton's iteration convergence acceleration approximating polynomial zeros

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A bisection method for measuring the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle

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BIT NUMERICAL MATHEMATICS 2014年第1期54卷 189-200页

作者： Malyshev, Alexander Sadkane, Miloud Univ Bergen Dept Math N-5020 Bergen Norway Univ Brest Lab Math Bretagne Atlantique CNRS UMR 6205 F-29238 Brest 3 France

The computation of the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle is investigated. The emphasis is placed on backward stable methods that transform the computation of the distance to a palindromic eigenvalue problem for which structure-preserving eigensolvers can be utilized in conjunction with a bisection algorithm. Reliability of the suggested methods is guaranteed by a novel error analysis.

关键词： Distance to instability Quadratic matrix polynomial bisection algorithm Level set algorithm Error analysis

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Mixed Precision bisection

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MATHEMATICS IN COMPUTER SCIENCE 2018年第2期12卷 173-181页

作者： Ralha, Rui Univ Minho Sch Sci Ctr Math Braga Portugal

We discuss the implementation of the bisection algorithm for the computation of the eigenvalues of symmetric tridiagonal matrices in a context of mixed precision arithmetic. This approach is motivated by the emergence of processors which carry out floating-point operations much faster in single precision than they do in double precision. Perturbation theory results are used to decide when to switch from single to double precision. Numerical examples are presented.

关键词： Eigenvalues bisection algorithm Mixed precision

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Improving Energy Efficiency of Massive MIMO Relay Systems using Power bisection Allocation for Cell-Edge Users 27

Improving Energy Efficiency of Massive MIMO Relay Systems us...

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27th Iranian Conference on Electrical Engineering (ICEE)

作者： Koolivand, Mohammad Bahonar, Mohammad Hossein Fazel, Mohammad Sadegh Isfahan Univ Technol Dept Elect & Comp Engn Esfahan Iran

ISBN: (纸本)9781728115085

This paper studies downlink energy efficiency (EE) of a cellular massive Multiple Input Multiple Output (MIMO) system with massive number of antennas at both base station (BS) and relay considering cell-edge users which is less investigated in the literature. Some improving methods for base station (BS) and relay power allocation under quality of service constraints are proposed. The EE optimization problem is provided over BS and relay power variables (power dimensions). Considering the quasi-concavity property of the EE function relative to each power variable, we propose to use a power bisection algorithm (PBA) in one dimension, followed by the exhaustive search in the other dimension (ODS algorithm) which is called PB-ODS algorithm and also a method to limit the range of power variables. The results show that the performance of the PB-ODS algorithm approaches the performance of optimal solution which is exhaustive search in both dimensions while it has a lower complexity. In addition to that we suggest to use the PBA in two dimensions alternatively as the sub-optimal alternative optimization (AOP) algorithm. The complexity can highly be reduced using the AOP algorithm with a slight but acceptable degradation in performance which makes the algorithm much suitable for practical use.

关键词： Energy efficiency bisection algorithm massive MIMO relay system alternative algorithm quasi-concave function

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Chance-Constrained Programming Models and Approximations for General Stochastic Bottleneck Spanning Tree Problems

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INFORMS JOURNAL ON COMPUTING 2015年第2期27卷 301-316页

作者： Shen, Siqian Kurt, Murat Wang, Jue Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA SUNY Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA

We consider a balance-constrained stochastic bottleneck spanning tree problem (BCSBSTP) where edge weights are independently distributed but may follow arbitrary continuous distributions. The goal is to minimize a threshold variable that may be exceeded by the maximum edge weight at certain risk, subject to the minimum edge weight being no less than a fixed threshold with a probability guarantee. We characterize these two requirements as chance constraints, which are typically used for bounding the risk of undesirable random outcomes. Given independently distributed edge weights, we reformulate BCSBSTP as a mixed-integer nonlinear program, approximated by two mixed-integer linear programs based on special ordered set of type one (SOS1) and special ordered set of type two (SOS2) variables. By relaxing the probabilistic guarantee on the minimum edge weight in BCSBSTP, we also consider a stochastic bottleneck spanning tree problem (SBSTP), of which optimal tree solutions are approximated via a bisection algorithm in pseudopolynomial time. We demonstrate computational results of our models and algorithms by testing randomly generated instances with edge weights following a diverse set of independent distributions.

关键词： stochastic bottleneck spanning tree chance-constrained programming special ordered sets bisection algorithm NP-complete

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