A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems

In this paper, a new deterministic method is proposed. This method depends on presenting (suggesting) some modifications to existing parameters of some conjugate gradient methods. The parameters of our suggested method contain a mix of deterministic and stochastic parameters. The proposed method is...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Mathematics (Basel) Ročník 10; číslo 17; s. 3032
Hlavní autori: Alshamrani, Ahmad M., Alrasheedi, Adel Fahad, Alnowibet, Khalid Abdulaziz, Mahdi, Salem, Mohamed, Ali Wagdy
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.09.2022
Predmet:
Algorithms
Approximation
Conjugate gradient method
conjugate gradient methods
Convergence
derivative-free optimization
Finite difference method
Food science
global optimization
Mathematical functions
Mathematical optimization
Mathematical research
meta-heuristics
Methods
Optimization
Optimization algorithms
Parameter modification
Search algorithms
stochastic methods
Stochastic processes
unconstrained minimization
United States
ISSN:2227-7390, 2227-7390
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:In this paper, a new deterministic method is proposed. This method depends on presenting (suggesting) some modifications to existing parameters of some conjugate gradient methods. The parameters of our suggested method contain a mix of deterministic and stochastic parameters. The proposed method is added to a line search algorithm to make it a globally convergent method. The convergence analysis of the method is established. The gradient vector is estimated by a finite difference approximation approach, and a new step-size h of this approach is generated randomly. In addition, a set of stochastic parameter formulas is constructed from which some solutions are generated randomly for an unconstrained problem. This stochastic technique is hybridized with the new deterministic method to obtain a new hybrid algorithm that finds an approximate solution for the global minimization problem. The performance of the suggested hybrid algorithm is tested in two sets of benchmark optimization test problems containing convex and non-convex functions. Comprehensive comparisons versus four other hybrid algorithms are listed in this study. The performance profiles are utilized to evaluate and compare the performance of the five hybrid algorithms. The numerical results show that our proposed hybrid algorithm is promising and competitive for finding the global optimum point. The comparison results between the performance of our suggested hybrid algorithm and the other four hybrid algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math10173032