• Journal of the Korea Convergence Society
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• v.12 no.11
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• pp.81-90
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• 2021

There are various optimization problems in real world and research continues to solve them. An optimization problem is the problem of finding a combination of parameters that maximizes or minimizes the objective function. Harmony search is a population-based metaheuristic algorithm for solving optimization problems and it is designed to mimic the improvisation of jazz music. Harmony search has been actively applied to optimization problems in various fields such as civil engineering, computer science, energy, medical science, and water quality engineering. Harmony search has a simple working principle and it has the advantage of finding good solutions quickly in constrained optimization problems. Especially there are various application cases showing high accuracy with a low number of iterations by improving the solution through the empirical derivative. In this paper, we explain working principle of Harmony search and classify the leading research in recent 3 years, review them according to category, and suggest future research directions. The research is divided into review by field, algorithmic analysis and theory, and application to real world problems. Application to real world problems is classified according to the purpose of optimization and whether or not they are hybridized with other metaheuristic algorithms.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.351-368
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• 2014

This study presents a hunting search based optimum design algorithm for engineering optimization problems. Hunting search algorithm is an optimum design method inspired by group hunting of animals such as wolves, lions, and dolphins. Each of these hunters employs hunting in a different way. However, they are common in that all of them search for a prey in a group. Hunters encircle the prey and the ring of siege is tightened gradually until it is caught. Hunting search algorithm is employed for the automation of optimum design process, during which the design variables are selected for the minimum objective function value controlled by the design restrictions. Three different examples, namely welded beam, cellular beam and moment resisting steel frame are selected as numerical design problems and solved for the optimum solution. Each example differs in the following ways: Unlike welded beam design problem having continuous design variables, steel frame and cellular beam design problems include discrete design variables. Moreover, while the cellular beam is designed under the provisions of BS 5960, LRFD-AISC (Load and Resistant Factor Design-American Institute of Steel Construction) is considered for the formulation of moment resisting steel frame. Levy Flights is adapted to the simple hunting search algorithm for better search. For comparison, same design examples are also solved by using some other well-known search methods in the literature. Results reveal that hunting search shows good performance in finding optimum solutions for each design problem.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.3
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• pp.17-28
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• 2008

The Steiner arborescence problem is known to be NP-hard. The objective of this problem is to find a minimal Steiner tree which starts from a designated node and spans all given terminal nodes. This paper proposes a method based on a two-step procedure to solve this problem efficiently. In the first step, graph reduction rules eliminate useless nodes and arcs which do not contribute to make an optimal solution. In the second step. ant colony algorithm with use of Prim's algorithm is used to solve the Steiner arborescence problem in the reduced graph. The proposed method based on a two-step procedure is tested in the five test problems. The results show that this method finds the optimal solutions to the tested problems within 50 seconds. The algorithm can be applied to undirected Steiner tree problems with minor changes. 18 problems taken from Beasley are used to compare the performances of the proposed algorithm and Singh et al.'s algorithm. The results show that the proposed algorithm generates better solutions than the algorithm compared.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.369-379
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• 2023

Reliability-Based Design Optimization (RBDO) is an appropriate framework for obtaining optimal designs by taking uncertainties into account. Large-scale problems with implicit limit state functions and problems with discrete design variables are two significant challenges to traditional RBDO methods. To overcome these challenges, this paper proposes a hybrid method to perform RBDO of structures that links Firefly Algorithm (FA) as an optimization tool to advanced (finite element) reliability methods. Furthermore, the Genetic Algorithm (GA) and the FA are compared based on the design cost (objective function) they achieve. In the proposed method, Weighted Simulation Method (WSM) is utilized to assess reliability constraints in the RBDO problems with explicit limit state functions. WSM is selected to reduce computational costs. To performing RBDO of structures with finite element modeling and implicit limit state functions, a First-Order Reliability Method (FORM) based on the Direct Differentiation Method (DDM) is utilized. Four numerical examples are considered to assess the effectiveness of the proposed method. The findings illustrate that the proposed RBDO method is applicable and efficient for RBDO problems with discrete and continuous design variables and finite element modeling.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.7
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• pp.28-34
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• 2006

In general engineering problems, the purpose of an optimization is to get optimal design variables. It is the same problem to fix the total amount of the design variables and to judge the optimal mixing proportions of the design variables. That is to say, we can recompose the engineering problems in the concepts of the mixture amount experiments. The goal of mixture amount method is to get the response surfaces of varying both the mixing proportion of component and the total amount of the mixture. The solution of the aircraft fuselage optimization problem is obtained by the mixture amount method and genetic algorithm. In this study, it is shown that the mixture amount method can be utilized for the aircraft structural optimization problem. Also, this method in this study can be applied for the optimization problems over 12 design variables which is impossible for D-optimal design.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.19-28
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• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.4
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• pp.407-417
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• 2003

Enen though several GA-based optimization algorithms have been successfully applied to complex optimization problems in various engineering fields, GA-based optimization methods are computationally too expensive for practical use in the field of structural optimization, particularly for large- scale problems. Furthermore, a successful implementation of GA-based optimization algorithm requires a cumbersome and trial-and-error routine related to setting of parameters dependent on a optimization problem. Therefore, to overcome these disadvantages, a high-performance GA is developed in the form of distributed hybrid genetic algorithm for structural optimization on a cluster of personal computers. The distributed hybrid genetic algorithm proposed in this paper consist of a simple GA running on a master computer and multiple μ-GAs running on slave computers. The algorithm is implemented on a PC cluster and applied to the minimum weight design of steel structures. The results show that the computational time required for structural optimization process can be drastically reduced and the dependency on the parameters can be avoided.

• 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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.697-708
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• 1995

For many practical optimization problems where the system components are stochastic, the objective functions can not be represented analytically. Furthermore, many of these problems are characterized by the presence of multiple and conflicting objectives. In this research, we introduce a new algorithm through an interactive cutting plane method for solving this multi-criteria simulation optimization problem. Then a turning process is evaluated through the proposed algorithm.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1639-1650
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• 2013

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.