An efficient gradient forecasting search method utilizing the discrete difference equation prediction model

Authors
Citation
Cm. Chen et Hm. Lee, An efficient gradient forecasting search method utilizing the discrete difference equation prediction model, APPL INTELL, 16(1), 2001, pp. 43-58
Citations number
27
Language
INGLESE
art.tipo
Article
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
APPLIED INTELLIGENCE
ISSN journal
0924-669X → ACNP
Volume
16
Issue
1
Year of publication
2001
Pages
43 - 58
Database
ISI
SICI code
0924-669X(2001)16:1<43:AEGFSM>2.0.ZU;2-V
Abstract
Optimization theory and method profoundly impact numerous engineering desig ns and applications. The gradient descent method is simpler and more extens ively used to solve numerous optimization problems than other search method s. However, the gradient descent method is easily trapped into a local mini mum and slowly converges. This work presents a Gradient Forecasting Search Method (GFSM) for enhancing the performance of the gradient descent method in order to resolve optimization problems. GFSM is based on the gradient descent method and on the universal Discrete Difference Equation Prediction Model (DDEPM) proposed herein. In addition, the concept of the universal DDEPM is derived from the grey prediction mode l. The original grey prediction model uses a mathematical hypothesis and ap proximation to transform a continuous differential equation into a discrete difference equation. This is not a logical approach because the forecastin g sequence data is invariably discrete. To construct a more precise predict ion model, this work adopts a discrete difference equation. GFSM proposed h erein can accurately predict the precise searching direction and trend of t he gradient descent method via the universal DDEPM and can adjust predictio n steps dynamically using the golden section search algorithm. Experimental results indicate that the proposed method can accelerate the s earching speed of gradient descent method as well as help the gradient desc ent method escape from local minima. Our results further demonstrate that a pplying the golden section search method to achieve dynamic prediction step s of the DDEPM is an efficient approach for this search algorithm.