An Efficient Algorithm for Unconstrained Optimization

This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1) stabilization, (2) breadth-first search, and (3) depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.

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A Three Particles Algorithm for Solving Some Very High Dimensional Benchmark Unconstrained Optimization Problems Using a Fuzzy Fitness Criterium

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488518400068 ◽

2018 ◽

Vol 26 (Suppl. 1) ◽

pp. 93-119

Author(s):

Sergio G. De-Los-Cobos-Silva ◽

Roman A. Mora-Gutiérrez ◽

Eric A. Rincón-García ◽

Pedro Lara-Velázquez ◽

Miguel A. Gutiérrez-Andrade ◽

...

Keyword(s):

Unconstrained Optimization ◽

Optimization Problems ◽

Global Optimum ◽

Numerical Results ◽

High Dimensional ◽

Benchmark Problems ◽

Benchmark Problem ◽

Original Algorithm ◽

Unconstrained Optimization Problems ◽

Very High

This work focuses predominantly on unconstrained optimization problems and presents an original algorithm (the code can be downloaded from Ref. 1), which is used for solving a variety of benchmark problems whose dimensions range from 2 to 2.5 millions, using only 3 particles. The algorithm was tested in 36 benchmark continuous unconstrained optimization problems, on a total of 312 instances. The results are presented comparing two fitness criteria: crisp and a fuzzy. The numerical results show that the proposed algorithm is able to reach the global optimum in every benchmark problem.

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SC: A NOVEL FUZZY CRITERION FOR SOLVING ENGINEERING AND CONSTRAINED OPTIMIZATION PROBLEMS

Revista de Matemática Teoría y Aplicaciones ◽

10.15517/rmta.v23i1.22353 ◽

2017 ◽

Vol 23 (1) ◽

pp. 111-142

Author(s):

Sergio G. De los Cobos Silva ◽

Miguel A. Gutiérrez Andrade ◽

Eric A. Rincón García ◽

Pedro Lara Velázquez ◽

Roman A. Mora Gutiérrez ◽

...

Keyword(s):

Constrained Optimization ◽

Optimization Problems ◽

Pso Algorithm ◽

Breadth First Search ◽

Constrained Optimization Problems ◽

Engineering Problems ◽

Convergence System ◽

Fuzzy Convergence ◽

Three Phases

In this paper a novel fuzzy convergence system (SC) and its fundamentals are presented. The model was implemented on a monoobjetive PSO algorithm with three phases: 1) Stabilization, 2) generation and breadth-first search, and 3) generation and depth-first. The system SC-PSO-3P was tested with several benchmark engineering problems and with several CEC2006 problems. The computing experience and comparison with previously reported results is presented. In some cases the results reported in the literature are improved.

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A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems

Algorithms ◽

10.3390/a14080227 ◽

2021 ◽

Vol 14 (8) ◽

pp. 227

Author(s):

Zabidin Salleh ◽

Ghaliah Alhamzi ◽

Ibitsam Masmali ◽

Ahmad Alhawarat

Keyword(s):

Unconstrained Optimization ◽

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Large Scale ◽

Optimization Problems ◽

Numerical Results ◽

New Method ◽

Unconstrained Optimization Problems ◽

Large Scale Unconstrained Optimization

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.

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A New Method with Sufficient Descent Property for Unconstrained Optimization

Abstract and Applied Analysis ◽

10.1155/2014/940120 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Weiyi Qian ◽

Haijuan Cui

Keyword(s):

Global Convergence ◽

Unconstrained Optimization ◽

Optimization Problems ◽

Numerical Results ◽

Sufficient Descent Property ◽

Unconstrained Optimization Problems ◽

Descent Property ◽

Sufficient Descent ◽

New Iterative Method ◽

Methods Numerical

Recently, sufficient descent property plays an important role in the global convergence analysis of some iterative methods. In this paper, we propose a new iterative method for solving unconstrained optimization problems. This method provides a sufficient descent direction for objective function. Moreover, the global convergence of the proposed method is established under some appropriate conditions. We also report some numerical results and compare the performance of the proposed method with some existing methods. Numerical results indicate that the presented method is efficient.

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A Modified Spectral Methods for Large-Scale UnconStrained

Al-Mustansiriyah Journal of Science ◽

10.23851/mjs.v29i1.576 ◽

2018 ◽

Vol 29 (1) ◽

pp. 127

Author(s):

Basim A. Hassan ◽

Haneen A. Alashoor

Keyword(s):

Unconstrained Optimization ◽

Spectral Methods ◽

Large Scale ◽

Optimization Problems ◽

Numerical Results ◽

Unconstrained Optimization Problems ◽

Globally Convergent ◽

Descent Condition

A modified spectral methods for solving unconstrained optimization problems based on the formulae are derived which are given in [4, 5]. The proposed methods satisfied the descent condition. Moreover, we prove that the new spectral methods are globally convergent. The Numerical results show that the proposed methods effective by comparing with the FR-method.

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A MODIFIED BFGS METHOD VIA NEW RATIONAL APPROXIMATION MODEL FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS AND ITS APPLICATION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.12.61 ◽

2020 ◽

Vol 9 (12) ◽

pp. 10771-10786

Author(s):

K. Kamfa ◽

S. Ibrahim ◽

S. F. Sufahani ◽

R. B. Yunus ◽

M. Mamat

Keyword(s):

Unconstrained Optimization ◽

Rational Approximation ◽

Optimization Problems ◽

Bfgs Method ◽

Approximation Model ◽

Unconstrained Optimization Problems

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A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

The Open Electrical & Electronic Engineering Journal ◽

10.2174/1874129001408010218 ◽

2014 ◽

Vol 8 (1) ◽

pp. 218-221 ◽

Cited By ~ 2

Author(s):

Ping Hu ◽

Zong-yao Wang

Keyword(s):

Global Convergence ◽

Unconstrained Optimization ◽

Numerical Experiments ◽

Line Search ◽

Optimization Problems ◽

Search Algorithm ◽

New Combination ◽

Combination Rule ◽

Combination Technique ◽

Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

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