• IE interfaces
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• v.25 no.2
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• pp.153-162
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• 2012

The reliability is defined as a probability that a system will operate properly for a specified period of time under the design operating conditions without failure and it has been considered as one of the major design parameters in the field of industries. Reliability-Redundancy Optimization Problem(RROP) involves selec tion of components with multiple choices and redundancy levels for maximizing system reliability with constraints such as cost, weight, etc. However, in practice both active and cold standby redundancies may be used within a particular system design. Therefore, a redundancy strategy(active, cold standby) for each subsystem in order to maximize system reliability is considered in this study. Due to the nature of RROP, i.e. NP-hard problem, A Parallel Particle Swarm Optimization(PPSO) algorithm is proposed to solve the mathematical programming model and it gives consistently better quality solutions than existing studies for benchmark problems.

• Journal of Korean Institute of Industrial Engineers
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• v.43 no.2
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• pp.135-146
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• 2017

This paper considers redundancy optimization problems of multi-level systems and reviews existing papers which proposed various optimization models and used different algorithms in this research area. Three different mathematical models are studied: Multi-level redundancy allocation (MRAP), multiple multi-level redundancy allocation, and availability-based MRAP models. Many meta-heuristics are applied to find optimal solutions in the several optimization problems. We summarized key idea of meta-heuristics applied to the existing MARP problems. Two extended models (MRAP with interval reliability of units and an integrated optimization problem of MRAP and preventive maintenance) are studied and further research ideas are discussed.

• Proceedings of the Korea Society for Simulation Conference
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• 1997.04a
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• pp.3-7
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• 1997

Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. "Simulation Optimization" technique is used to optimize the expressed in analytical of mathematical models. In this research, we will study Reverse-Simulation optimization method which is quite different from current simulation optimization methods in literature. We will focus on the on-line determination of steady-state method which is very important issue in Reverse-Simulation optimization, and the construction of Reverse-Simulation algorithm with expert systems. Especially, in the case of multiple objectives because of the dependency of simulation model, all objectives do not satisfied simulataneously. In this paper, therefore, we process simulation optimization using objectives with priority to optimize multiple objectives under single run.ingle run.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1169-1182
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• 2006

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.95-111
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• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• Structural Engineering and Mechanics
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• v.50 no.3
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• pp.257-273
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• 2014

This paper introduces a novel optimization technique based on gravitational search algorithm (GSA) for numerical optimization and multi-objective optimization of foundation. In the proposed method, a chaotic time varying system is applied into the position updating equation to increase the global exploration ability and accurate local exploitation of the original algorithm. The new algorithm called global-local GSA (GLGSA) is applied for optimization of some well-known mathematical benchmark functions as well as two design examples of spread foundation. In the foundation optimization, two objective functions include total cost and $CO_2$ emissions of the foundation subjected to geotechnical and structural requirements are considered. From environmental point of view, minimization of embedded $CO_2$ emissions that quantifies the total amount of carbon dioxide emissions resulting from the use of materials seems necessary to include in the design criteria. The experimental results demonstrate that, the proposed GLGSA remarkably improves the accuracy, stability and efficiency of the original algorithm.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1590-1603
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• 2004

In this study the optimization of plate-fin type heat sink with vortex generator for the thermal stability is performed numerically. The optimum solutions in the heat sink are obtained when the temperature rise and the pressure drop are minimized simultaneously. Thermal performance of heat sink is influenced by the heat sink shape such as the base-part fin width, lower-part fin width, and basement thickness. To acquire the optimal design variables automatically, CFD and mathematical optimization are integrated. The flow and thermal fields are predicted using the finite volume method. The optimization is carried out by means of the sequential quadratic programming (SQP) method which is widely used for the constrained nonlinear optimization problem. The results show that the optimal design variables are as follows; B$_1$=2.584 mm, B$_2$=1.741 mm, and t=7.914 mm when the temperature rise is less than 40 K. Comparing with the initial design, the temperature rise is reduced by 4.2 K, while the pressure drop is increased by 9.43 Pa. The relationship between the pressure drop and the temperature rise is also presented to select the heat sink shape for the designers.

• Journal of Korean Society for Quality Management
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• v.47 no.4
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• pp.701-711
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• 2019

Purpose: The problem of optimizing redundancy allocation in multi-level systems is considered when each item in a multi-level system has alternative items with the same function. The number of redundancy of multi-level system is allocated to maximize the reliability of the system under path set and cost limitation constraints. Methods: Based on cost limitation and path set constraints, a mathematical model is established to maximize system reliability. Particle swarm optimization is employed for redundant allocation and verified by numerical experiments. Results: Comparing the particle swarm optimization method and the memetic algorithm for the 3 and 4 level systems, the particle swarm optimization method showed better performance for solution quality and search time. Particularly, the particle swarm optimization showed much less than the memetic algorithm for variation of results. Conclusion: The proposed particle swarm optimization considerably shortens the time to search for a feasible solution in MRAP with path set constraints. PS optimization is expected to reduce search time and propose the better solution for various problems related to MRAP.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.48-54
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• 2004

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. In practical applications, it is customary to transform the dynamic loads into static loads by dynamic factors, design codes, and etc. But the optimization results with the unreasonably transformed loads cannot give us good solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple loading conditions which are not costly to include in modem structural optimization. In this research, the proposed algorithm is applied to the optimization of flexible multibody dynamic systems. The equivalent static load is derived from the equations of motion of a flexible multibody dynamic system. A few examples that have been solved before are solved to be compared with the results from the proposed algorithm.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.