A Fibonacci Search technique for a class of multivariable functions and ODEs

Omolehin, J. O.; Ibiejugba, M. A.; Onachi, A. E.; Evans, David

doi:10.1080/0020716031000087104

Cited by 8 publications

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, it is necessary to reduce the initial box of range to a sufficiently small box region including the minimum solution of f (x) (through an iteration process) for the interval that can be narrowed down provided that the function values are known at two different points in the range. The implementation of the classical Fibonacci serial optimization algorithm can be found in [22], and we will not go into further details here.…”

Section: The Standard Principle Of Fibonacci Sequence Methodsmentioning

confidence: 99%

A Beamformer Design Based on Fibonacci Branch Search

Dong¹,

Zhang²,

Zeng³

2020

PIER B

View full text Add to dashboard Cite

An approach towards beamforming for a uniform linear array (ULA) based on a novel optimization algorithm, designated as Fibonacci branch search (FBS) is presented in this paper. The proposed FBS search strategy was inspired from Fibonacci sequence principle and uses a fundamental branch structure and interactive searching rules to obtain the global optimal solution in the search space. The structure of FBS is established by two types of multidimensional points on the basis of shortening fraction formed by the Fibonacci sequence, and in this mode, interactive global searching and local optimization rules are implemented alternately to reach global optima, avoiding stagnating in local optimum. At the same time, the rigorous mathematical proof for the accessibility and convergence of FBS towards the global optimum is presented to further verify the validity of our theory and support our claim. Taking advantage of the global search ability and high convergence rate of this technique, a robust adaptive beamformer technique is also constructed here by FBS as a real time implementation to improve the beamforming performance by preventing the loss of optimal trajectory. The performance of the FBS is compared with five typical heuristic optimization algorithms, and the reported simulation results demonstrate the superiority of the proposed FBS algorithm in locating the optimal solution with higher precision and reveal the further improvement in adaptive beamforming performance.

show abstract

Section: The Standard Principle Of Fibonacci Sequence Methodsmentioning

confidence: 99%

A Beamformer Design Based on Fibonacci Branch Search

Dong¹,

Zhang²,

Zeng³

2020

PIER B

View full text Add to dashboard Cite

show abstract

“…The smallest lie can be reduced by providing the function value known in two different ranges of points. The realization of the classic Fibonacci sequence optimization algorithm was given in [36], and no further detailed description is given here.…”

Section: Fibonacci Branch Search Algorithmmentioning

confidence: 99%

Jammer Location‐Aware Method in Wireless Sensor Networks Based on Fibonacci Branch Search

Yang

Shu

et al. 2023

Journal of Sensors

View full text Add to dashboard Cite

Due to the sharing and open-access characteristics of the wireless medium, wireless sensor networks (WSNs) can be easily attacked by jammers. To mitigate the effects of a jamming attack, one reliable solution is to locate and remove the jammer from the deployed area within the WSN. To realize the jammer’s localization in the WSN, many range-free methods have been proposed. However, most of these methods are sensitive to the distribution of nodes and the parameters of the jammer. For this reason, a jammer location-aware method based on Fibonacci branch search (FBS) is proposed in this article. First, the interference region is estimated by using the interference region mapping service of sensors in wireless sensor networks. Then, the search point is selected in the jamming area and the fitness function is designed according to the average distance from the search point to the boundary sensor. According to the basic branch structure and interactive search rules, the global optimal solution is obtained in the jamming area. Finally, the position of the search point with the best fitness value is used as the estimation of the jammer position. Compared with the existing typical range-free methods, rich simulation experiments demonstrate that the FBS algorithm is superior in the location-aware method for jammers with a higher precision and a lower sensitivity to the distribution of nodes and the parameters of the jammer, respectively.

show abstract

“…Initially, the technique starts a choice of two feasible points and , in the given range for the first iteration. Then, it is necessary to reduce the initial box of range to a sufficiently small box region including the minimum solution of (through an iteration process) for the interval in which the minimum lies can be narrowed down provided the function values are known at two different points in the range [22].…”

Section: Proposed Fbs Algorithmmentioning

confidence: 99%

Implementation of a novel Fibonacci branch search optimizer for the design of the low sidelobe and deep nulling adaptive beamformer

Zhang

Zeng

2020

Int. J. Microw. Wireless Technol.

View full text Add to dashboard Cite

In this work, we proposed an adaptive beamformer based on a novel heuristic optimization algorithm. The novel optimization technique inspired from Fibonacci sequence principle, designated as Fibonacci branch search (FBS), used new tree's branches fundamental structure and interactive searching rules to obtain the global optimal solution in the search space. The branch structure of FBS is selected using two types of multidimensional points on the basis of shortening fraction formed by Fibonacci sequence; in this mode, interactive global and local searching rules are implemented alternately to obtain the optimal solutions, avoiding stagnating in local optimum. The proposed FBS is also used here to construct an adaptive beamforming (ABF) technique as a real-time implementation to achieve near-optimal performance for its simplicity and high convergence rate, then, the performance of the FBS is compared with the five typical heuristic optimization algorithms. Simulation results demonstrate the superiority of the proposed FBS approach in locating the optimal solution with higher precision and reveal further improvement in the ABF performance.

show abstract

A Fibonacci Search technique for a class of multivariable functions and ODEs

Cited by 8 publications

References 2 publications

A Beamformer Design Based on Fibonacci Branch Search

A Beamformer Design Based on Fibonacci Branch Search

Jammer Location‐Aware Method in Wireless Sensor Networks Based on Fibonacci Branch Search

Implementation of a novel Fibonacci branch search optimizer for the design of the low sidelobe and deep nulling adaptive beamformer

Contact Info

Product

Resources

About