Frame-Based Ray Search Algorithms in Unconstrained Optimization

This paper describes a class of frame-based direct search methods for unconstrained optimization without derivatives. A template for convergent direct search methods is developed, some requiring only the relative ordering of function values. At each iteration, the template considers a number of search steps which form a positive basis and conducts a ray search along a step giving adequate decrease. Various ray search strategies are possible, including discrete equivalents of the Goldstein–Armijo and one-sided Wolfe–Powell ray searches. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.     

遗传算法的物理解释

提出了一种理想化的模拟仿生搜索算法——扰动算法 ,以此方法为基础 ,分析了遗传算法的搜索过程和效率问题 ,阐明了遗传算法作为一种次优算法的有效性 .相对于遗传算法的生物解释 ,本文给出了相应的物理解释 .同时 ,本文为遗传算法、进化策略和模拟退火算法找到了一种统一的物理解释 ,揭示了这些重要的仿生类算法实质上的相似性 .     

On the Convergence of a Population-Based Global Optimization Algorithm

In global optimization, a typical population-based stochastic search method works on a set of sample points from the feasible region. In this paper, we study a recently proposed method of this sort. The method utilizes an attraction-repulsion mechanism to move sample points toward optimality and is thus referred to as electromagnetism-like method (EM). The computational results showed that EM is robust in practice, so we further investigate the theoretical structure. After reviewing the original method, we present some necessary modifications for the convergence proof. We show that in the limit, the modified method converges to the vicinity of global optimum with probability one.     

Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition

Conjugate gradient methods are appealing for large scale nonlinear optimization problems. Recently, expecting the fast convergence of the methods, Dai and Liao (2001) used secant condition of quasi-Newton methods. In this paper, we make use of modified secant condition given by Zhang et al. (1999) and Zhang and Xu (2001) and propose a new conjugate gradient method following to Dai and Liao (2001). It is new features that this method takes both available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective function. The method is shown to be globally convergent under some assumptions. Numerical results are reported.     

A gradient-related algorithm with inexact line searches

In this paper, a new gradient-related algorithm for solving large-scale unconstrained optimization problems is proposed. The new algorithm is a kind of line search method. The basic idea is to choose a combination of the current gradient and some previous search directions as a new search direction and to find a step-size by using various inexact line searches. Using more information at the current iterative step may improve the performance of the algorithm. This motivates us to find some new gradient algorithms which may be more effective than standard conjugate gradient methods. Uniformly gradient-related conception is useful and it can be used to analyze global convergence of the new algorithm. The global convergence and linear convergence rate of the new algorithm are investigated under diverse weak conditions. Numerical experiments show that the new algorithm seems to converge more stably and is superior to other similar methods in many situations.     

Conjugate Gradient Methods with Armijo-type Line Searches

Abstract Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods.Under these line searches, global convergence results are established for several famous conjugate gradientmethods, including the Fletcher-Reeves method, the Polak-Ribiere-Polyak method, and the conjugate descentmethod.     

Enhancing network lifespan in wireless sensor networks using deep learning based Graph Neural Network

Inadequate energy of sensors is one of the most significant challenges in the development of a reliable wireless sensor network (WSN) that can withstand the demands of growing WSN applications. Implementing a sleep-wake scheduling scheme while assigning data collection and sensing chores to a dominant group of awake sensors while all other nodes are in a sleep state seems to be a potential way for preserving the energy of these sensor nodes. When the starting energy of the nodes changes from one node to another, this issue becomes more difficult to solve. The notion of a dominant set-in graph has been used in a variety of situations. The search for the smallest dominant set in a big graph might be time-consuming. Specifically, we address two issues: first, identifying the smallest possible dominant set, and second, extending the network lifespan by saving the energy of the sensors. To overcome the first problem, we design and develop a deep learning-based Graph Neural Network (DL-GNN). The GNN training method and back-propagation approach were used to train a GNN consisting of three networks such as transition network, bias network, and output network, to determine the minimal dominant set in the created graph. As a second step, we proposed a hybrid fixed-variant search (HFVS) method that considers minimal dominant sets as input and improves overall network lifespan by swapping nodes of minimal dominating sets. We prepared simulated networks with various network configurations and modeled different WSNs as undirected graphs. To get better convergence, the different values of state vector dimensions of the input vectors are investigated. When the state vector dimension is 3 or 4, minimum dominant set is recognized with high accuracy. The paper also presents comparative analyses between the proposed HFVS algorithm and other existing algorithms for extending network lifespan and discusses the trade-offs that exist between them. Lifespan of wireless sensor network, which is based on the dominant set method, is greatly increased by the techniques we have proposed.     

结构综合的曲线寻优近似解析方法

本文首次在结构优化领域应用曲线寻优近似解析方法，数值实验表明本文方法的效率较高     

顶空气相色谱-质谱联用结合同位素峰形校正检索技术鉴别芝麻油风味成分

采用顶空气相色谱-质谱联用(GC-MS)仪结合同位素峰形校正检索技术鉴别了市售芝麻油风味成分中的71种化合物,占总检出化合物的90.2%。检出化合物可分为吡嗪、吡咯、吡啶、噻唑、噻吩、吲哚、唑、呋喃、醛类和酚类等,其中醛、酚、吡嗪和呋喃类化合物的含量较高,分别占风味成分含量的37.4%,20.1%,10.0%和6.7%。同位素峰形校正检索技术在低分辨率质谱上可对化合物的相对分子质量实现精确测量,从而为低分辨率四极杆质谱确定化合物的元素组成和解析化合物结构提供了重要依据,同时也为芝麻油的成分分析提供了新的技术手段。     

Flexible and powerful strategy for qualitative and quantitative analysis of valepotriates in Valeriana jatamansi Jones using high‐performance liquid chromatography with linear ion trap Orbitrap mass spectrometry

Valeriana jatamansi Jones is an important medicinal plant and its quality is closely related to its region of origin. In the current study, we utilized a flexible and powerful strategy for comprehensive evaluation of the quality diversity for 15 regions in China. The method was based on a hybrid linear ion trap‐Orbitrap mass spectrometry platform. For structure characterization, fragmentation patterns were detected by analyzing a series of standard compounds using data dependent multistage mass spectrometry acquisition. A fragment ion database for valepotriates was established, and the acquired data were high throughput filtered by fragment ion search for compound identification. For quantitative purposes, we normalized the mass spectrometry data of 15 samples using SIEVE 2.0 and the differences in composition were analyzed using principal component analysis combined with hierarchical clustering analysis. The results identified a total of 92 compounds from Valeriana jatamansi Jones. Samples from Dali, Kunming, and Baoshan have better qualities and concentrations of the main active constituents. To verify our strategy, we compared the valtrate, acevaltrate, and baldrinal contents using high‐performance liquid chromatography with diode array detector. We developed and validated a comprehensive qualitative and quantitative analytical method to achieve quality control of Valeriana jatamansi Jones.