• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.2
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• pp.8-18
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• 2020

An Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS) was developed to enhance the performance of a Harmony Search (HS). EBHS-CGS added two methods to improve the performance of HS. The first method is an improvement of bandwidth (bw) that enhances the local search. This method replaces the existing bw with an exponential bw and reduces the bw value as the iteration proceeds. This form of bw allows for an accurate local search, which enables the algorithm to obtain more accurate values. The second method is to reduce the search range for an efficient global search. This method reduces the search space by considering the best decision variable in Harmony Memory (HM). This process is carried out separately from the global search of the HS by the new parameter, Centralized Global Search Rate (CGSR). The reduced search space enables an effective global search, which improves the performance of the algorithm. The proposed algorithm was applied to a representative optimization problem (math and engineering), and the results of the application were compared with the HS and better Improved Harmony Search (IHS).

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.101.4-101
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• 2001

Evolutionary algorithm has been receiving a remarkable attention due to the model-free and population-based parallel search attributes and much successful results are coming out. However, there are some problems in most of the evolutionary algorithms. The critical one is that it takes much time or large generations to search the global optimum in case of the objective function with multimodality. Another problem is that it usually cannot search all the local optima because it pays great attention to the search of the global optimum. In addition, if the objective function has several global optima, it may be very difficult to search all the global optima due to the global characteristics of the selection methods. To cope with these problems, at first we propose a preprocessing process, grid-filtering algorithm(GFA), and propose a new distributed evolutionary ...

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.857-862
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• 2004

This paper analyzes properties of the recently developed nonlinear optimization method, Dynamic Encoding Algorithm for Searches (DEAS) [1]. DEAS locates local minima with binary strings (or binary matrices for multi-dimensional problems) by iterating the two operators; bisectional search (BSS) and unidirectional search (UDS). BSS increases binary strings by one digit (i.e., zero or one), while UDS performs increment or decrement to binary strings with no change of string length. Owing to these search routines, DEAS retains the optimization capability that combines the special features of several conventional optimization methods. In this paper, a special feature of BSS and UDS in DEAS is analyzed. In addition, a effective global search strategy is established by using information of DEAS. Effectiveness of the proposed global search strategy is validated through the well-known benchmark functions.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.571-582
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• 2008

This paper analyzes global convergence of the univariate dynamic encoding algorithm for searches (uDEAS) and provides an application result to function optimization. uDEAS is a more advanced optimization method than its predecessor in terms of the number of neighborhood points. This improvement should be validated through mathematical analysis for further research and application. Since uDEAS can be categorized into the generating set search method also established recently, the global convergence property of uDEAS is proved in the context of the direct search method. To show the strong performance of uDEAS, the global minima of four 30 dimensional benchmark functions are attempted to be located by uDEAS and the other direct search methods. The proof of global convergence and the successful optimization result guarantee that uDEAS is a reliable and effective global optimization method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.488-491
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• 1995

The paper presents a new global maximum search method for multimodal unknown functions of two variables. The search method is composed of two stages and sequentially samples the candidate point in a subdomain selected using a priority function in each stage. The search domain is auto-similarly divided into triangular subdomains, or cells, during the search process. A measure of accuracy of local maximum search is introduced to check if a local search has converged to a specified accuracy or the maximum of a local peak cannot be the global maximum. A criterion for switching from the first to the second stage, is proposed using a ratio of the observed peak width to the largest cell in the domain. By numerical simulations, the required number of trials is evaluated for some function models with different peak parameters, and the switching criterion is optimally determined. The results show that the proposed method obtains global maximum points with certainty and saves largely computation time even for functions with extremely steep peaks.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.157-165
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• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.373-378
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• 2013

In this paper, we consider two kinds of the Levenberg-Marquardt method for solve a system of nonlinear equations. We use line search on every iteration to guarantee that the Levenberg-Marquardt methods are globally convergent. Under mild conditions, we prove that while the de- scent condition can be satisfied at the iteration of the Levenberg-Marquardt method, the global convergence of the method can be established.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.239-254
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• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.38-46
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• 2003

Aim of this article is to propose Micro-Genetic Simulated Annealing (${\mu}GSA$) as a hybrid metaheuristics approach to find the global optimum of nonlinear optimisation problems. This approach combines the features of modern metaheuristics such as micro-genetic algorithm (${\mu}GAs$) and simulated annealing (SA) with the general robustness of parallel exploration and asymptotic convergence, respectively. Therefore, ${\mu}GSA$ approach can help in avoiding the premature convergence and can search for better global solution, because of its wide spread applicability, global perspective and inherent parallelism. For the superior performance of the ${\mu}GSA$, the five well-know benchmark test functions that were tested and compared with the two global optimisation approaches: scatter search (SS) and hybrid scatter genetic tabu (HSGT) approach. A practical application to structural sandwich panel is also examined by optimism the weight function. From the simulation results, it has been concluded that the proposed ${\mu}GSA$ approach is an effective optimisation tool for soloing continuous nonlinear global optimisation problems in suitable computational time frame.