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Hybrid Particle Swarm optimization with a Modified Arithmetical Crossover for Solving unconstrained optimization problems

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INFOR 2015年第3期53卷 125-141页

作者： Ali, Ahmed F. Tawhid, Mohamed A. Suez Canal Univ Fac Comp & Informat Dept Comp Sci Ismailia Egypt Thompson Rivers Univ Fac Sci Dept Math & Stat Kamloops BC V2C 0C8 Canada Univ Alexandria Fac Sci Dept Math & Comp Sci Alexandria 21511 Egypt

In this article, we propose a new hybrid algorithm by combining the particle swarm optimization and genetic arithmetical crossover operator. We adjust the proposed algorithm in order to avoid the problem of stagnation and premature convergence of the population. Invoking the modified arithmetical crossover operator improves the exploration process of the proposed algorithm. We call the new proposed algorithm hybrid particle swarm optimization with a modified arithmetical crossover (HPSOAC). Also, we test HPSOAC on 26 functions (16 unconstrained optimization benchmark functions and 10 CEC05 special session functions). Furthermore, we compare the general performance of the proposed algorithm against 6 various particle swarm optimization algorithms. Moreover, we show the efficiency of the proposed algorithm and its ability to solve unconstrained optimization problems by giving several computational results.

关键词： Particle swarm optimization arithmetical crossover unconstrained optimization problems global optimization

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Solving nonlinear systems and unconstrained optimization problems by hybridizing whale optimization algorithm and flower pollination algorithm

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MATHEMATICS AND COMPUTERS IN SIMULATION 2021年 190卷 1342-1369页

作者： Tawhid, M. A. Ibrahim, A. M. Thompson Rivers Univ Fac Sci Dept Math & Stat Kamloops BC V2C 0C8 Canada Al Azhar Univ Fac Sci Dept Math Assiut Branch Assiut Egypt

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA;WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Hybridization algorithm Metaheuristics Whale optimization algorithm Flower pollination algorithm unconstrained optimization problems System of nonlinear equations

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A two-step improved Newton method to solve convex unconstrained optimization problems

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2020年第1-2期62卷 37-53页

作者： Niri, T. Dehghan Fazeli, S. A. Shahzadeh Heydari, M. Yazd Univ Dept Math Yazd Iran

In this investigation, a new two-step Newton method to solve convex unconstrained optimization problems is developed. This proposed method is based on Traub's iterative scheme (Iterative methods for the solution of equations, Prentice Hall, Englewood Cliffs, 1964) which is extended to n-variable. The presented two-step algorithm is a modification of Newton method for solving unconstrained optimization problems. The convergence analysis for this iterative algorithm is established under suitable conditions. Various numerical examples are given to illustrate the efficiency and performance of the newly suggested method.

关键词： Newton method unconstrained optimization problems Convergence analysis

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A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING unconstrained optimization problems

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Journal of Computational Mathematics 2014年第4期32卷 476-490页

作者： Jinghui Liu Changfeng Ma School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China

Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

关键词： unconstrained optimization problems Nonmonotone trust region method Global convergence Superlinear convergence.

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On large-scale unconstrained optimization problems and higher order methods

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optimization METHODS & SOFTWARE 2010年第3期25卷 337-358页

作者： Gundersen, Geir Steihaug, Trond Univ Bergen Dept Informat Ctr High Technol N-5020 Bergen Norway

Third-order methods will, in most cases, use fewer iterations than a second-order method to reach the same accuracy. However, the number of arithmetic operations per iteration is higher for third-order methods than for a second-order method. Newton's method is the most commonly used second order method and Halley's method is the most well-known third-order method. Newton's method is more used in practical applications than any third-order method. We will show that for a large class of problems, the ratio of the number of arithmetic operations of Halley's method and Newton's method is constant per iteration. It is shown that [image omitted] We show that the zero elements in the Hessian matrix induce zero elements in the tensor (third derivative). The sparsity structure in the Hessian matrix we consider is the skyline or envelope structure. This is a very convenient structure for solving linear systems of equations with a direct method. The class of matrices that have a skyline structure includes banded and dense matrices. Numerical testing confirms that the ratio of the number of arithmetic operations of a third-order method and Newton's method is constant per iteration, and is independent of the number of unknowns.

关键词： unconstrained optimization problems induced sparsity higher order methods tensor computations

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Application of Newton-4EGSOR Iteration for Solving Large Scale unconstrained optimization problems with a Tridiagonal Hessian Matrix 5th

Application of Newton-4EGSOR Iteration for Solving Large Sca...

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5th International Conference on Computational Science and Technology (ICCST)

作者： Ghazali, Khadizah Sulaiman, Jumat Dasril, Yosza Gabda, Darmesah Univ Malaysia Sabah Math Econ Programme Kota Kinabalu 88400 Sabah Malaysia Univ Tekn Malaysia Melaka Fac Elect & Comp Engn Melaka 76100 Malaysia

ISBN: (纸本)9789811326226;9789811326219

Solving the unconstrained optimization problems using Newton method will lead to the need to solve linear system. Further, the Explicit Group iteration is one of the numerical methods that has an advantage of the efficient block iterative method for solving any linear system. Thus, in this paper to reduce the cost of solving large linear system, we proposed a combination between Newton method with four-point Explicit Group (4-point EG) block iterative method for solving large scale unconstrained optimization problems where the Hessian of the Newton direction is tridiagonal matrices. For the purpose of comparison, we used combination of Newton method with basic iterative method namely successive-over relaxation (SOR) point iteration and Newton method with two-point Explicit Group (2-point EG) block iterative method as reference method. The proposed method shows that the numerical results were more superior compared to the reference methods in term of execution time and number of iteration.

关键词： Explicit Group iteration Newton method unconstrained optimization problems

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A PRP-HS Type Hybrid Nonlinear Conjugate Gradient Method for Solving unconstrained optimization problems 1

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3rd Conference on Computational Methods in Systems and Software (CoMeSySo)

作者： Adeleke, Olawale J. Olusanya, Micheal O. Osinuga, Idowu A. Covenant Univ Coll Sci & Technol Dept Math Ota Nigeria Durban Univ Technol Fac Accounting & Informat Dept Informat Technol Durban South Africa Fed Univ Agr Dept Math Coll Phys Sci Abeokuta Nigeria

ISBN: (数字)9783030303297

ISBN: (纸本)9783030303297;9783030303280

Many engineering problems that occur in real-life are usually constrained by one or more factors which constitute the basis for the complexity of obtaining optimal solutions. While some of these problems may be transformed to the unconstrained forms, there is a large pool of purely unconstrained optimization problems in engineering which have practical applications in the industry. One effective approach for solving this latter category of problems is the nonlinear conjugate gradient method (NCGM). Particularly, the NCGM uses an efficient recursive scheme to solve unconstrained optimization problems with very large dimensions. In this paper, a new hybrid NCGM is proposed based on the recent modifications of the Polak-Ribiere-Polyak (PRP) and Hestenes-Stiefel (HS) methods. Theoretical analyses and numerical computations using standard benchmark functions, as well as comparison with existing NCGM schemes show that the proposed PRP-HS type hybrid scheme is globally convergent and computationally efficient.

关键词： Hybrid methods Nonlinear conjugate gradient method unconstrained optimization problems Descent property Global convergence Line search

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Some Quadrature-Based Versions of the Generalized Newton Method for Solving unconstrained optimization problems 6th

Some Quadrature-Based Versions of the Generalized Newton Met...

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6th International Conference on Numerical Analysis and Applications (NAA)

作者： Smietanski, Marek J. Univ Lodz Fac Math & Comp Sci Lodz Poland

ISBN: (纸本)9783319570990;9783319570983

Many practical problems require solving system of nonlinear equations. A lot of optimization problems can be transformed to the equation F(x) = 0, where the function F is nonsmooth, i.e. nonlinear complementarity problem or variational inequality problem. We propose a modifications of a generalized Newton method based on some rules of quadrature. We consider these algorithms for solving unconstrained optimization problems, in which the objective function is only LC1, i.e. has not differentiable gradient. Such problems often appear in nonlinear programming, usually as subproblems. The methods considered are Newton-like iterative schemes, however they use combination of elements of some subdifferential. The methods are locally and at least superlinearly convergent under mild conditions imposed on the gradient of the objective function. Finally, results of numerical tests are presented.

关键词： unconstrained optimization problems Generalized Newton method B-differential Superlinear convergence

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Multi-directional bat algorithm for solving unconstrained optimization problems

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OPSEARCH 2017年第4期54卷 684-705页

作者： Tawhid, Mohamed A. Ali, Ahmed F. Thompson Rivers Univ Dept Math & Stat Fac Sci Kamloops BC V2C 0C8 Canada Alexandria Univ Dept Math & Comp Sci Fac Sci Alexandria 21511 Egypt Suez Canal Univ Fac Comp & Informat Dept Comp Sci Ismailia Egypt Thompson Rivers Univ Dept Math & Stat Fac Sci Kamloops BC V2C 0C8 Canada

In this paper, we propose a new hybrid algorithm for solving unconstrained global optimization problems by hybridizing the bat algorithm with multi-directional search algorithm (MDS). We call the proposed algorithm by multi-directional bat algorithm (MDBAT). In MDBAT algorithm, we try to overcome the slow convergence of the bat algorithm as a metaheuristic algorithm by invoking one of the promising direct search algorithm which is called MDS algorithm. The bat algorithm has a good ability to make exploration and exploitation search while the MDS has a good ability for accelerating convergence on the region of optimal response. In the beginning, the standard bat algorithm starts the search for number of iterations then the MDS algorithm starts its search from bat algorithm found so far. The combination between the standard bat algorithm and the MDS algorithm helps the MDS algorithm to start the search from a good solution instead of the random initial solution. The MDS algorithm can accelerate the search of the proposed algorithm instead of letting the algorithm running for more iterations without any improvement. We investigate the general performance of the MDBAT algorithm by applying it on 16 unconstrained global optimization problems and comparing it against 8 benchmark algorithms. The experimental results indicate that MDBAT is a promising algorithm and outperforms the other algorithms in most cases.

关键词： Bat algorithm Multi-directional search algorithm Global optimization unconstrained optimization problems

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A new CG algorithm based on a scaled memoryless BFGS update with adaptive search strategy, and its application to large-scale unconstrained optimization problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021年 398卷 113670-113670页

作者： Li, Xiangli Zhao, Wenjuan Dong, Xiaoliang Guilin Univ Elect Technol Sch Math & Comp Sci Guilin 541004 Peoples R China Guilin Univ Elect Technol Guangxi Key Lab Automat Testing Technol & Instrum Guilin 541004 Peoples R China Xi An Jiao Tong Univ Binzhou City Sunshine High Sch Fan Gong Middle Sch Binzhou City Xianyang 712000 Peoples R China Beifang Univ Nationalities Sch Math & Informat Yinchuan 710021 Ningxia Peoples R China

Conjugate gradient method is an effective method for solving large-scale unconstrained optimization problems. This paper proposes a new conjugate gradient algorithm based on the self-scaling memoryless BFGS update, which uses the Wolfe line search. The descent and global convergence of the method are given under mild conditions. Numerical experiments show that our new conjugate gradient method is effective. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Conjugate gradient method unconstrained optimization problems Wolfe line search Global convergence

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