scholarly journals Generalized Fibonacci Search Method in One-Dimensional Unconstrained Non-Linear Optimization

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
Chin Yoon Chong ◽  
Soo Kar Leow ◽  
Hong Seng Sim
Keyword(s):  
Golden Section ◽  
Linear Optimization ◽  
Fibonacci Numbers ◽  
Search Method ◽  
Initial Ratio ◽  
Microsoft Excel ◽  
One Dimensional ◽  
Golden Section Search ◽  
Non Linear ◽  
Number Of Iterations

In this paper, we develop a generalized Fibonacci search method for one-dimensional unconstrained non-linear optimization of unimodal functions. This method uses the idea of the “ratio length of 1” from the golden section search. Our method takes successive lower Fibonacci numbers as the initial ratio and does not specify beforehand, the number of iterations to be used. We evaluated the method using Microsoft Excel with nine one-dimensional benchmark functions. We found that our generalized Fibonacci search method out-performed the golden section and other Fibonacci-type search methods such as the Fibonacci, Lucas and Pell approaches.

Numerical Investigation of Some Potential Problems of Univariate Minimization Methods

1979 ◽  
Vol 101 (4) ◽  
pp. 663-666 ◽  
Author(s):  
G. E. Johnson ◽  
M. A. Townsend
Keyword(s):  
Golden Section ◽  
Step Length ◽  
Companion Paper ◽  
Test Functions ◽  
Convergence Criteria ◽  
One Dimensional ◽  
Exact Arithmetic ◽  
Golden Section Search ◽  
Minimization Methods ◽  
Programming Algorithms

Many nonlinear programming algorithms employ a univariate subprocedure to determine the step length at each multivariate iteration. In this note, a popular polynomial approximation-interpolation univariate algorithm (DSC-P) is compared to two versions of the golden section search. One-dimensional test functions which model the behavior of barrier and penalty functions are used for the comparison. In general, the polynominal method indicates convergence in fewer function evaluations than the golden section search. However, it is significantly less reliable. Tight convergence criteria do not necessarily lead to accurate results with the polynomial-based univariate strategy. A companion paper provides a theoretical basis for the observations and gives conditions underwhich DSC-P will fail—even for strictly convex, unimodal functions and exact arithmetic.

scholarly journals Optimized designing of a patch phased array with a MoM-solver

2014 ◽  
Vol 33 (6) ◽  
pp. 1847-1862 ◽  
Author(s):  
Yuanhao Wang ◽  
Michael Berens ◽  
Alexander Nietsch ◽  
Werner John ◽  
Wolfgang Mathis
Keyword(s):  
Design Process ◽  
Patch Antenna ◽  
Phased Array ◽  
Golden Section ◽  
Search Method ◽  
Optimization Process ◽  
Field Pattern ◽  
Uhf Rfid ◽  
Content Type ◽  
Golden Section Search

Purpose – The purpose of this paper is to present an optimization process for the design of a 2×2 patch antenna phased array with application for an UHF RFID system. Design/methodology/approach – The optimization process is based on a method of moment (MoM)-solver, which was individually made to create such patch antenna phased arrays and simulate the radiated field pattern. In combination with this MoM-solver, a GUI, which gives the opportunity to change every physical antenna factor and create the antenna structure within a few minutes is presented. Furthermore the golden section search method is used to produce an even better solution in a more efficient way compared to the first attempt. After the simulation, different types of presentation of results can be chosen for a fast and easy optimization. Findings – The design process is discussed while the authors try to optimize the distance between the elements and the difference of input phase for each patch element. The final goal is to create an antenna with maximum directivity and coverage of field pattern. Practical implications – A physical implementation of an optimized patch antenna phased array and the results of measurement are presented in the end. Originality/value – An optimization process for the design of a 2×2 patch antenna phased array with application for an UHF RFID system is presented. Furthermore the golden section search method is combined with the design process to increase the accuracy of the solution and decrease the time effort.

scholarly journals Moth Flame Optimization Based on Golden Section Search and its Application for Link Prediction Problem

2018 ◽  
Vol 13 (1) ◽  
pp. 10 ◽  
Author(s):  
Reham Barham ◽  
Ahmad Sharieh ◽  
Azzam Sleit
Keyword(s):  
Present State ◽  
Link Prediction ◽  
Heuristic Algorithms ◽  
Golden Section ◽  
Search Space ◽  
Natural World ◽  
Search Method ◽  
Transverse Orientation ◽  
Prediction Problem ◽  
Golden Section Search

Moth Flame Optimization (MFO) is one of the meta-heuristic algorithms that recently proposed. MFO is inspired from the method of moths' navigation in natural world which is called transverse orientation. This paper presents an improvement of MFO algorithm based on Golden Section Search method (GSS), namely GMFO. GSS is a search method aims at locating the best maximum or minimum point in the problem search space by narrowing the interval that containing this point iteratively until a particular accuracy is reached. In this paper, the GMFO algorithm is tested on fifteen benchmark functions. Then, GMFO is applied for link prediction problem on five datasets and compared with other well-regarded meta- heuristic algorithms. Link prediction problem interests in predicting the possibility of appearing a connection between two nodes of a network, while there is no connection between these nodes in the present state of the network. Based on the experimental results, GMFO algorithm significantly improves the original MFO in solving most of benchmark functions and providing more accurate prediction results for link prediction problem for major datasets.

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