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Journal articles on the topic 'Global function optimization'

Author: Grafiati

Published: 16 July 2024

Last updated: 31 July 2025

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1

Şahiner, Ahmet, Temel Ermiş, and Muhammad Wasim Awan. "A New Filled Function for Global Optimization." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 3 (2023): 207–20. https://doi.org/10.2478/auom-2023-0039.

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Abstract The filled function method has recently become very popular in optimization theory, as it is an e cient and e ective method for finding the global minimizer of multimodal functions. However, the fact that the existing filled functions in the literature generally have exponential or logarithmic terms and/or parameter sensitivity reduces the e ectiveness of this method. In this study, we propose a new non parameter and without exponential/logarithmic terms filled function, which is numerically stable, and is successfully used to solve global optimization problems. Furthermore, we have d

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2

Liu, Y., and K. L. Teo. "A bridging method for global optimization." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 41, no. 1 (1999): 41–57. http://dx.doi.org/10.1017/s0334270000011024.

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AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

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3

Norkin, Vladimir. "A Stochastic Smoothing Method for Nonsmooth Global Optimization." Cybernetics and Computer Technologies, no. 1 (March 31, 2020): 5–14. http://dx.doi.org/10.34229/2707-451x.20.1.1.

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The paper presents the results of testing the stochastic smoothing method for global optimization of a multiextremal function in a convex feasible subset of Euclidean space. Preliminarily, the objective function is extended outside the admissible region so that its global minimum does not change, and it becomes coercive. The smoothing of a function at any point is carried out by averaging the values of the function over some neighborhood of this point. The size of the neighborhood is a smoothing parameter. Smoothing eliminates small local extrema of the original function. With a sufficiently l

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4

Zhu, Jinghao, Jiani Zhou, and David Gao. "Global optimization by canonical dual function." Journal of Computational and Applied Mathematics 234, no. 2 (2010): 538–44. http://dx.doi.org/10.1016/j.cam.2009.12.045.

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5

Wang, Wei, Xiaoshan Zhang, and Min Li. "A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization." Journal of Applied Mathematics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/245427.

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This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end.

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6

Satapathy, Suresh Chandra. "Improved teaching learning based optimization for global function optimization." Decision Science Letters 2, no. 1 (2013): 23–34. http://dx.doi.org/10.5267/j.dsl.2012.10.005.

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7

Satapathy, Suresh Chandra, Anima Naik, and K. Parvathi. "Weighted Teaching-Learning-Based Optimization for Global Function Optimization." Applied Mathematics 04, no. 03 (2013): 429–39. http://dx.doi.org/10.4236/am.2013.43064.

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8

DJALIL, BOUDJEHEM, BOUDJEHEM BADREDDINE, and BOUKAACHE ABDENOUR. "REDUCING DIMENSION IN GLOBAL OPTIMIZATION." International Journal of Computational Methods 08, no. 03 (2011): 535–44. http://dx.doi.org/10.1142/s0219876211002460.

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In this paper, we propose a very interesting idea in global optimization making it easer and a low-cost task. The main idea is to reduce the dimension of the optimization problem in hand to a mono-dimensional one using variables coding. At this level, the algorithm will look for the global optimum of a mono-dimensional cost function. The new algorithm has the ability to avoid local optima, reduces the number of evaluations, and improves the speed of the algorithm convergence. This method is suitable for functions that have many extremes. Our algorithm can determine a narrow space around the gl

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9

Bermudez, Dalton H. "Plane Based Optimization Method: A Method for Better Global Minimum Cost Function Localization." Journal of Biomedical and Engineering Research 3, no. 1 (2025): 01–05. https://doi.org/10.64030/3065-8780.03.01.03.

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Background: As a popular optimization algorithm, gradient descent is more prone to converge at a local minimum rather than a global one since it is highly dependent on how initial values are instantiated and an iterative process of updates, reducing its efficiency for non-convex cost functions. This limitation is of utmost importance in domains such as medical physics, where there exist many treatment parameters that need to be optimized. Purpose: We introduce the flat plane with maximum perpendicular distance method, a new optimization algorithm which identifies global minima robustly and eff

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10

Bemporad, Alberto. "Global optimization via inverse distance weighting and radial basis functions." Computational Optimization and Applications 77, no. 2 (2020): 571–95. http://dx.doi.org/10.1007/s10589-020-00215-w.

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Abstract Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new glob

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11

Pandiya, Ridwan, Atina Ahdika, Siti Khomsah, and Rima Dias Ramadhani. "A New Integral Function Algorithm for Global Optimization and Its Application to the Data Clustering Problem." MENDEL 29, no. 2 (2023): 162–68. http://dx.doi.org/10.13164/mendel.2023.2.162.

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The filled function method is an approach to finding global minimum points of multidimensional unconstrained global optimization problems. The conventional parametric filled functions have computational weaknesses when they are employed in some benchmark optimization functions. This paper proposes a new integral function algorithm based on the auxiliary function approach. The proposed method can successfully be used to find the global minimum point of a function of several variables. Some testing global optimization problems have been used to show the ability of this recommended method. The in

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12

Xiao, Jin-ke, Wei-min Li, Wei Li, and Xin-rong Xiao. "Optimization on Black Box Function Optimization Problem." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/647234.

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There are a large number of engineering optimization problems in real world, whose input-output relationships are vague and indistinct. Here, they are called black box function optimization problem (BBFOP). Then, inspired by the mechanism of neuroendocrine system regulating immune system, BP neural network modified immune optimization algorithm (NN-MIA) is proposed. NN-MIA consists of two phases: the first phase is training BP neural network with expected precision to confirm input-output relationship and the other phase is immune optimization phase, whose aim is to search global optima. BP ne

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13

Aaid, Djamel, and Özen Özer. "New technique for solving multivariate global optimization." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (2023): 3–16. http://dx.doi.org/10.33993/jnaat521-1287.

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In this paper, we propose an algorithm based on branch and bound method to underestimate the objective function and reductive transformation which is transformed the all multivariable functions on univariable functions. We also demonstrate several quadratic lower bound functions are proposed which they are better/preferable than the others well-known in literature. We obtain that our experimental results are more effective when we face different nonconvex functions.

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14

Mou-Yan Zou and Xi Zou. "Global optimization: an auxiliary cost function approach." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 30, no. 3 (2000): 347–54. http://dx.doi.org/10.1109/3468.844358.

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15

Han, Qiaoming, and Jiye Han. "Revised filled function methods for global optimization." Applied Mathematics and Computation 119, no. 2-3 (2001): 217–28. http://dx.doi.org/10.1016/s0096-3003(99)00266-0.

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16

Wu, Z. Y., L. S. Zhang, K. L. Teo, and F. S. Bai. "New Modified Function Method for Global Optimization." Journal of Optimization Theory and Applications 125, no. 1 (2005): 181–203. http://dx.doi.org/10.1007/s10957-004-1718-2.

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17

Liang, Y. M., L. S. Zhang, M. M. Li, and B. S. Han. "A filled function method for global optimization." Journal of Computational and Applied Mathematics 205, no. 1 (2007): 16–31. http://dx.doi.org/10.1016/j.cam.2006.04.038.

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18

Isshiki, Masaki, Hiroki Ono, Kouichi Hiraga, Jun Ishikawa, and Suezou Nakadate. "Lens Design: Global Optimization with Escape Function." Optical Review 2, no. 6 (1995): 463–70. http://dx.doi.org/10.1007/s10043-995-0463-6.

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19

Pandiya, Ridwan, Widodo Widodo, Salmah, and Irwan Endrayanto. "Non parameter-filled function for global optimization." Applied Mathematics and Computation 391 (February 2021): 125642. http://dx.doi.org/10.1016/j.amc.2020.125642.

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20

Wang, Weixiang, Youlin Shang, and Ying Zhang. "Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization." Discrete Dynamics in Nature and Society 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/843609.

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A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

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21

Horai, Mio, Hideo Kobayashi, and Takashi G. Nitta. "Global Optimization for the Sum of Certain Nonlinear Functions." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/408918.

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We extend work by Pei-Ping and Gui-Xia, 2007, to a global optimization problem for more general functions. Pei-Ping and Gui-Xia treat the optimization problem for the linear sum of polynomial fractional functions, using a branch and bound approach. We prove that this extension makes possible to solve the following nonconvex optimization problems which Pei-Ping and Gui-Xia, 2007, cannot solve, that the sum of the positive (or negative) first and second derivatives function with the variable defined by sum of polynomial fractional function by using branch and bound algorithm.

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22

Wang, Wei-xiang, You-lin Shang, and Ying Zhang. "Global Minimization of Nonsmooth Constrained Global Optimization with Filled Function." Mathematical Problems in Engineering 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/563860.

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A novel filled function is constructed to locate a global optimizer or an approximate global optimizer of smooth or nonsmooth constrained global minimization problems. The constructed filled function contains only one parameter which can be easily adjusted during the minimization. The theoretical properties of the filled function are discussed and a corresponding solution algorithm is proposed. The solution algorithm comprises two phases: local minimization and filling. The first phase minimizes the original problem and obtains one of its local optimizers, while the second phase minimizes the

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23

Zhang, Laiyong, Chunming Tu, Fan Xiao, Bei Liu, and Peiqiang Li. "Intrinsic Regularity Analysis and Optimization Control of Current Stress and RMS for Dual-Active Bridge Converter." Electronics 13, no. 23 (2024): 4802. https://doi.org/10.3390/electronics13234802.

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Currently, current stress optimization control and current effective value optimization control have become the mainstream methods for real-time optimization control of dual-active bridge converters. However, there is still a lack of systematic research on the internal optimization regularities between the two and their respective internal optimization regularities, as well as problems such as the complex derivation of the effective value optimization control variable function. To address these issues, this paper analyzes the optimization results of stress optimization, effective value optimiz

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24

Weixiang Wang, Youlin Shang, and Shenhua Gui. "Application of Global Descent Function Method to Discrete Global Optimization." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 5, no. 7 (2013): 684–91. http://dx.doi.org/10.4156/aiss.vol5.issue7.80.

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25

Tsoulos, Ioannis G., Alexandros Tzallas, Evangelos Karvounis, and Dimitrios Tsalikakis. "NeuralMinimizer: A Novel Method for Global Optimization." Information 14, no. 2 (2023): 66. http://dx.doi.org/10.3390/info14020066.

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The problem of finding the global minimum of multidimensional functions is often applied to a wide range of problems. An innovative method of finding the global minimum of multidimensional functions is presented here. This method first generates an approximation of the objective function using only a few real samples from it. These samples construct the approach using a machine learning model. Next, the required sampling is performed by the approximation function. Furthermore, the approach is improved on each sample by using found local minima as samples for the training set of the machine lea

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26

Angeles, J., and A. Bernier. "The Global Least-Square Optimization of Function-Generating Linkages." Journal of Mechanisms, Transmissions, and Automation in Design 109, no. 2 (1987): 204–9. http://dx.doi.org/10.1115/1.3267439.

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As shown elsewhere, the approximate least-square synthesis of function-generating linkages can be formulated in terms of one single decision variable. Hence, functions representing global properties of linkages such as accuracy and transmission quality, which are terms precisely defined in this paper, as well as mobility type, are all functions of one single variable. The optimization procedure presented here is aimed at the synthesis of function-generating linkages with a minimum least-square design error and a maximum transmission quality, while meeting conditions prescribed on the type of m

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27

Wang, Wei, Yong-jian Yang, and Lian-sheng Zhang. "Unification of Filled Function and Tunnelling Function in Global Optimization." Acta Mathematicae Applicatae Sinica, English Series 23, no. 1 (2007): 59–66. http://dx.doi.org/10.1007/s10255-006-0349-9.

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28

Zhou, Heng Jun, Ming Yan Jiang, and Xian Ye Ben. "Niche Brain Storm Optimization Algorithm for Multi-Peak Function Optimization." Advanced Materials Research 989-994 (July 2014): 1626–30. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1626.

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Brain Storm Optimization (BSO) is a novel proposed swarm intelligence optimization algorithm which has a fast convergent speed. However, it is easy to trap into local optimal. In this paper, a new model based on niche technology, which is named Niche Brain Storm Optimization (NBSO), is proposed to overcome the shortcoming of BSO. Niche technology effectively prevents premature and maintains population diversity during the evolution process. NBSO shows excellent performance in searching global value and finding multiple global and local optimal solutions for the multi-peak problems. Several ben

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29

Fateen, Seif-Eddeen K., and Adrián Bonilla-Petriciolet. "Gradient-Based Cuckoo Search for Global Optimization." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/493740.

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One of the major advantages of stochastic global optimization methods is the lack of the need of the gradient of the objective function. However, in some cases, this gradient is readily available and can be used to improve the numerical performance of stochastic optimization methods specially the quality and precision of global optimal solution. In this study, we proposed a gradient-based modification to the cuckoo search algorithm, which is a nature-inspired swarm-based stochastic global optimization method. We introduced the gradient-based cuckoo search (GBCS) and evaluated its performance v

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30

Zabotin,, Vladislav I., and Pavel A. Chernyshevskij. "Extension of Strongins Global Optimization Algorithm to a Function Continuous on a Compact Interval." Computer Research and Modeling 11, no. 6 (2019): 1111–19. http://dx.doi.org/10.20537/2076-7633-2019-11-6-1111-1119.

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31

Li, Jia, Yuelin Gao, Tiantian Chen, and Xiaohua Ma. "A new filled function method based on global search for solving unconstrained optimization problems." AIMS Mathematics 9, no. 7 (2024): 18475–505. http://dx.doi.org/10.3934/math.2024900.

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<abstract><p>The filled function method is a deterministic algorithm for finding a global minimizer of global optimization problems, and its effectiveness is closely related to the form of the constructed filled function. Currently, the filled functions mainly have three drawbacks in form, namely, parameter adjustment and control (if any), inclusion of exponential or logarithmic functions, and properties that are discontinuous and non-differentiable. In order to overcome these limitations, this paper proposed a parameter-free filled function that does not include exponential or log

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32

Wei, Fei, and Yuping Wang. "A New Filled Function Method with One Parameter for Global Optimization." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/532325.

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The filled function method is an effective approach to find the global minimizer of multidimensional multimodal functions. The conventional filled functions are numerically unstable due to exponential or logarithmic term and sensitive to parameters. In this paper, a new filled function with only one parameter is proposed, which is continuously differentiable and proved to satisfy all conditions of the filled function definition. Moreover, this filled function is not sensitive to parameter, and the overflow can not happen for this function. Based on these, a new filled function method is propos

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33

Wang, Weixiang, Youlin Shang, and Ying Zhang. "A Filled Function Approach for Nonsmooth Constrained Global Optimization." Mathematical Problems in Engineering 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/310391.

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A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising.

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34

Zhao, Ruxin, Qifang Luo, and Yongquan Zhou. "Elite Opposition-Based Social Spider Optimization Algorithm for Global Function Optimization." Algorithms 10, no. 1 (2017): 9. http://dx.doi.org/10.3390/a10010009.

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35

Goitom, Simret, Tibor Nagy, and Tamás Turányi. "Testing various numerical optimization methods on a series of artificial test functions." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 53 (2022): 175–99. https://doi.org/10.71352/ac.53.175.

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Features of several well-known global and local optimization methods were discussed and their robustness and efficiency were tested on several artificial test functions in Matlab environment. The tested local methods were the interior-point, the quasi-Newton method, Nelder–Mead simplex, the pattern search, the NEWUOA and the BOBYQA methods. The global methods were the genetic algorithm (GA), the simulated annealing (SA), the particle swarm optimization (PSO), and the covariance matrix adaptation evolutionary strategy (CMA-ES) methods (see subsections 2.2 and 2.3 for their details). Furthermore

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36

Wu, Xiuli, Yongquan Zhou, and Yuting Lu. "Elite Opposition-Based Water Wave Optimization Algorithm for Global Optimization." Mathematical Problems in Engineering 2017 (2017): 1–25. http://dx.doi.org/10.1155/2017/3498363.

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Water wave optimization (WWO) is a novel metaheuristic method that is based on shallow water wave theory, which has simple structure, easy realization, and good performance even with a small population. To improve the convergence speed and calculation precision even further, this paper on elite opposition-based strategy water wave optimization (EOBWWO) is proposed, and it has been applied for function optimization and structure engineering design problems. There are three major optimization strategies in the improvement: elite opposition-based (EOB) learning strategy enhances the diversity of

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37

Ikponmwoba, Eloghosa, and Opeoluwa Owoyele. "Deephive: A Reinforcement Learning Approach for Automated Discovery of Swarm-Based Optimization Policies." Algorithms 17, no. 11 (2024): 500. http://dx.doi.org/10.3390/a17110500.

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We present an approach for designing swarm-based optimizers for the global optimization of expensive black-box functions. In the proposed approach, the problem of finding efficient optimizers is framed as a reinforcement learning problem, where the goal is to find optimization policies that require a few function evaluations to converge to the global optimum. The state of each particle within the swarm is defined as its current position and function value within a design space, and the particles learn to take favorable actions that maximize the reward, which is based on the final value of the

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38

Lin, Youjiang, Yongjian Yang, and Liansheng Zhang. "A NOVEL FILLED FUNCTION METHOD FOR GLOBAL OPTIMIZATION." Journal of the Korean Mathematical Society 47, no. 6 (2010): 1253–67. http://dx.doi.org/10.4134/jkms.2010.47.6.1253.

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39

Zhang, Lian-Sheng, Chi-Kong Ng, Duan Li, and Wei-Wen Tian. "A New Filled Function Method for Global Optimization." Journal of Global Optimization 28, no. 1 (2004): 17–43. http://dx.doi.org/10.1023/b:jogo.0000006653.60256.f6.

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40

Sun, X. L., and D. Li. "Value-Estimation Function Method for Constrained Global Optimization." Journal of Optimization Theory and Applications 102, no. 2 (1999): 385–409. http://dx.doi.org/10.1023/a:1021736608968.

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41

Liu, Xian. "The impelling function method applied to global optimization." Applied Mathematics and Computation 151, no. 3 (2004): 745–54. http://dx.doi.org/10.1016/s0096-3003(03)00525-3.

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Wang, Yuncheng, Weiwu Fang, and Tianjiao Wu. "A cut-peak function method for global optimization." Journal of Computational and Applied Mathematics 230, no. 1 (2009): 135–42. http://dx.doi.org/10.1016/j.cam.2008.10.069.

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43

Liu, Xian, and Wilsun Xu. "A new filled function applied to global optimization." Computers & Operations Research 31, no. 1 (2004): 61–80. http://dx.doi.org/10.1016/s0305-0548(02)00154-5.

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Wang, Xiaoli, and Guobiao Zhou. "A new filled function for unconstrained global optimization." Applied Mathematics and Computation 174, no. 1 (2006): 419–29. http://dx.doi.org/10.1016/j.amc.2005.05.009.

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Ruan, Zhao-Hui, Yuan Yuan, Qi-Xiang Chen, Chuan-Xin Zhang, Yong Shuai, and He-Ping Tan. "A new multi-function global particle swarm optimization." Applied Soft Computing 49 (December 2016): 279–91. http://dx.doi.org/10.1016/j.asoc.2016.07.034.

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46

Schnabel, Robert B. "Concurrent function evaluations in local and global optimization." Computer Methods in Applied Mechanics and Engineering 64, no. 1-3 (1987): 537–52. http://dx.doi.org/10.1016/0045-7825(87)90055-7.

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47

Gao, Yuelin, Yongjian Yang, and Mi You. "A new filled function method for global optimization." Applied Mathematics and Computation 268 (October 2015): 685–95. http://dx.doi.org/10.1016/j.amc.2015.06.090.

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Wu, Z. Y., F. S. Bai, H. W. J. Lee, and Y. J. Yang. "A filled function method for constrained global optimization." Journal of Global Optimization 39, no. 4 (2007): 495–507. http://dx.doi.org/10.1007/s10898-007-9152-2.

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Ng, Chi-Kong, Lian-Sheng Zhang, Duan Li, and Wei-Wen Tian. "Discrete Filled Function Method for Discrete Global Optimization." Computational Optimization and Applications 31, no. 1 (2005): 87–115. http://dx.doi.org/10.1007/s10589-005-0985-7.

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Lampariello, F., and G. Liuzzi. "A filling function method for unconstrained global optimization." Computational Optimization and Applications 61, no. 3 (2015): 713–29. http://dx.doi.org/10.1007/s10589-015-9728-6.

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