An improvement on Fibonacci search method in optimization theory

Subaşi, Murat; Yıldırım, Necmettin; Yıldız, Bünyamin

doi:10.1016/s0096-3003(02)00828-7

Cited by 32 publications

(16 citation statements)

References 2 publications

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“…The famous Fibonacci sequence was proposed initially by Etminaniesfahani et al [19], and the recurrence formula of the general sequence term is given by [20]…”

Section: The Standard Principle Of Fibonacci Sequence Methodsmentioning

confidence: 99%

A Beamformer Design Based on Fibonacci Branch Search

Dong¹,

Zhang²,

Zeng³

2020

PIER B

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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.

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“…The famous Fibonacci sequence was proposed initially by Etminaniesfahani et al [19], and the recurrence formula of the general sequence term is given by [20]…”

Section: The Standard Principle Of Fibonacci Sequence Methodsmentioning

confidence: 99%

A Beamformer Design Based on Fibonacci Branch Search

Dong¹,

Zhang²,

Zeng³

2020

PIER B

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“…The famous Fibonacci sequence was proposed by Leonardoda [19], the recurrence formula sequence term is given by [20]…”

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.

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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.

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“…The famous Fibonacci sequence was first proposed by Italian mathematician Leonardoda in the 12-13th century, and the recursion formula is given by [23], [24]…”

Section: Fibonacci Branch Search Algorithm a The Standard Princmentioning

confidence: 99%

A Fibonacci Branch Search (FBS)-Based Optimization Algorithm for Enhanced Nulling Level Control Adaptive Beamforming Techinique

Zhang

Zeng

2019

IEEE Access

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The present work introduced an adaptive beamformer based on a Fibonacci branch search (FBS) based heuristic algorithm is proposed for uniform linear arrays. The proposed optimization technique inspired by the Fibonacci sequence principle, designated Fibonacci branch search (FBS), used the new tree's fundamental branch structure and interactive searching rules to obtain the global optimal solution in the search space. The branch structure of FBS is selected by two types of multidimensional points on the basis of the shortening fraction formed by the Fibonacci sequence; in this mode, interactive global and local searching rules are implemented alternately to reach optimal solutions, avoiding stagnating in local optima. The proposed FBS is also used to construct an adaptive beamforming technique as a real-time implementation to achieve near-optimal performance due to its simplicity and high convergence; the performance of FBS is compared with that of five typical heuristic optimization algorithms. Simulation results demonstrate the superiority of the proposed FBS approach in locating the optimal solution with higher precision and further improvement in the adaptive beamforming performance. INDEX TERMS Adaptive beamformer, uniform linear arrays, shortening fraction, Fibonacci branch search, interactive searching rule.

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An improvement on Fibonacci search method in optimization theory

Cited by 32 publications

References 2 publications

A Beamformer Design Based on Fibonacci Branch Search

A Beamformer Design 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

A Fibonacci Branch Search (FBS)-Based Optimization Algorithm for Enhanced Nulling Level Control Adaptive Beamforming Techinique

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