Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribiere-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.
Conjugate Gradient (CG) method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we proposed a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our CG method new present an efficient numerical result when it compared with well-known formulas. Keywords—Conjugate gradient method, conj...
The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit lowdimensional deterministic-chaotic activities. However, the influences of the nest, ants’ physical abilities, and ants’ knowledge (or experience) on foraging behavior have received relatively little attention in studies of the colle...
#1Miao Wan(Beijing University of Posts and Telecommunications)H-Index: 5
#2Cong Wang(Beijing University of Posts and Telecommunications)H-Index: 9
Last. Yixian Yang(Beijing University of Posts and Telecommunications)H-Index: 44
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Clustering divides data into meaningful or useful groups (clusters) without any prior knowledge. It is a key technique in data mining and has become an important issue in many fields. This article presents a new clustering algorithm based on the mechanism analysis of chaotic ant swarm (CAS). It is an optimization methodology for clustering problem which aims to obtain global optimal assignment by minimizing the objective function. The proposed algorithm combines three advantages into one: findin...
#1Mohd Rivaie(UiTM: Universiti Teknologi MARA)H-Index: 7
#2Mustafa Mamat(UMT: Universiti Malaysia Terengganu)H-Index: 15
Last. Ismail Mohd(UMT: Universiti Malaysia Terengganu)H-Index: 8
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Abstract Nonlinear conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. Their wide application in many fields is due to their low memory requirements and global convergence properties. Numerous studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients ( β k ) that possess global convergence properties is presented. The global convergence result is establi...
#1Miao Wan(Beijing University of Posts and Telecommunications)H-Index: 5
#2Lixiang Li(Beijing University of Posts and Telecommunications)H-Index: 41
Last. Yixian Yang(Beijing University of Posts and Telecommunications)H-Index: 16
view all 5 authors...
Clustering divides data into meaningful or useful groups (clusters) without any prior knowledge. It is a key technique in data mining and has become an important issue in many fields. This article presents a new clustering algorithm based on the mechanism analysis of Bacterial Foraging (BF). It is an optimization methodology for clustering problem in which a group of bacteria forage to converge to certain positions as final cluster centers by minimizing the fitness function. The quality of this ...
#1Zhifeng Dai(CSUST: Changsha University of Science and Technology)H-Index: 10
#2Fenghua Wen(CSUST: Changsha University of Science and Technology)H-Index: 28
Abstract Recently, Zhang [13] take a little modification to the Wei–Yao–Liu nonlinear conjugate gradient method proposed by Wei et al. [10] such that the modified method (called NPRP method in Zhang [13] ) satisfies sufficient descent condition with greater parameter σ ∈ 0 , 1 2 in the strong Wolfe line search and converges globally for nonconvex minimization with the strong Wolfe line search. In this paper, we take a little modification to the NPRP method such that the modified NPRP method poss...
Clustering divides data into meaningful or useful groups (clusters) without any prior knowledge. It is a key technique in data mining and has become an important issue in many fields. This article presents a new clustering algorithm based on the mechanism analysis of chaotic ant swarm (CAS). It is an optimization methodology for clustering problem which aims to obtain global optimal assignment by minimizing the objective function. The proposed algorithm combines three advantages into one: findin...
#1Jiejin Cai(SYSU: Sun Yat-sen University)H-Index: 16
#2Qiong Li(SCUT: South China University of Technology)H-Index: 12
Last. Yixian Yang(Beijing University of Posts and Telecommunications)H-Index: 44
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Abstract This paper developed a fuzzy adaptive chaotic ant swarm optimization (FCASO) algorithm for solving the economic dispatch (ED) problems of thermal generators in power systems. The FCASO algorithm introduces a fuzzy system to dynamically tune the characteristic parameters ψ d and r i of chaotic swarm optimization (CASO). The proposed method was applied to two cases of power systems. The simulation results demonstrate the applicability and effectiveness of the proposed algorithm to the pra...
#1Li Zhang(CSUST: Changsha University of Science and Technology)H-Index: 3
In this paper, we take a little modification to the Wei-Yao-Liu nonlinear conjugate gradient method proposed by Wei et al. [Z. Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006) 1341-1350] such that the modified method possesses better convergence properties. In fact, we prove that the modified method satisfies sufficient descent condition with greater parameter @[email protected]?0,12 in the strong Wolfe line search and converg...
A collection of unconstrained optimization test functions is presented. The purpose of this collection is to give to the optimization community a large number of general test functions to be used in testing the unconstrained optimization algorithms and comparisons studies. For each function we give its algebraic expression and the standard initial point. Some of the test fnctions are from the CUTE collection established by Bongartz, Conn, Gould and Toint, (1995), others are from More, Garbow and...
Abstract In this paper, a new hybrid conjugate gradient method for solving unconstrained optimization problems is proposed. The proposed method inherits the features of the PRP, FR and NPRP conjugate gradient methods. The method satisfies the sufficient descent property independent of any line search and its global convergence is established under the strong Wolfe-Powell line search conditions. Numerical results show that the new algorithm is very competitive.
AbstractConjugate gradient algorithm (method) is a very simple and powerful technique for solving large scale unconstrained optimization problems. In this paper a new modified hybrid conjugate grad...
This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees glo...
: Dynamic magnetic resonance imaging (DMRI) is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel D...
A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribiere-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-t...
Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line sear...
#1Zabidin Salleh(UMT: Universiti Malaysia Terengganu)H-Index: 8
#2Ahmad Alhawarat(UMT: Universiti Malaysia Terengganu)H-Index: 5
The conjugate gradient (CG) method is one of the most popular methods to solve nonlinear unconstrained optimization problems. The Hestenes-Stiefel (HS) CG formula is considered one of the most efficient methods developed in this century. In addition, the HS coefficient is related to the conjugacy condition regardless of the line search method used. However, the HS parameter may not satisfy the global convergence properties of the CG method with the Wolfe-Powell line search if the descent conditi...
