• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.27 no.1
• /
• pp.1-8
• /
• 2014

Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.11 no.7
• /
• pp.680-688
• /
• 2001

In this paper, we propose a reliable method for searching the optimally performing generalized brain-state-in-a-box (GBSB) neural associative memory using an evolution program (EP) given a set of prototype patterns to be stored as stable equilibrium points. First, we exploit some qualitative guidelines necessary to synthesize the GBSB model. Next, we parameterize the solution space utilizing the limited number of parameters to represent the solution space. Then, we recast the synthesis of GBSB neural associative memories as two constrained optimization problems, which are equivalent to finding a solution to the original synthesis problem. Finally, we employ an evolution program (EP), which enables us to find an optimal set of parameters related to the size of domains of attraction (DOA) for prototype patterns. The validity of this approach is illustrated by a design example and computer simulations.

• ETRI Journal
• /
• v.27 no.4
• /
• pp.341-354
• /
• 2005

The adaptation of video according to the heterogeneous and dynamic resource constraints on networks and devices, as well as on user preferences, is a promising approach for universal access and consumption of video content. For optimal adaptation that satisfies the constraints while maximizing the utility that results from the adapted video, it is necessary to devise a systematic way of selecting an appropriate adaptation operation among multiple feasible choices. This paper presents a general conceptual framework that allows the formulation of various adaptations as constrained optimization problems by modeling the relations among feasible adaptation operations, constraints, and utilities. In particular, we present the feasibility of the framework by applying it to a use case of rate adaptation of MPEG-4 video with an explicit modeling of adaptation employing a combination of frame dropping and discrete cosine transform coefficient dropping, constraint, utility, and their mapping relations. Furthermore, we provide a description tool that describes the adaptation-constraint-utility relations as a functional form referred to as a utility function, which has been accepted as a part of the terminal and network quality of service tool in MPEG-21 Digital Item Adaptation (DIA).

• Journal of Korean Society of Transportation
• /
• v.27 no.6
• /
• pp.147-156
• /
• 2009

We present a methodology for modeling and solving the transit frequency design problem with variable demand. The problem is described as a bi-level model based on a non-cooperative Stackelberg game. The upper-level operator problem is formulated as a non-linear optimization model to minimize net cost, which includes operating cost, travel cost and revenue, with fleet size and frequency constraints. The lower-level user problem is formulated as a capacity-constrained stochastic user equilibrium assignment model with variable demand, considering transfer delay between transit lines. An efficient algorithm is also presented for solving the proposed model. The upper-level model is solved by a gradient projection method, and the lower-level model is solved by an existing iterative balancing method. An application of the proposed model and algorithm is presented using a small test network. The results of this application show that the proposed algorithm converges well to an optimal point. The methodology of this study is expected to contribute to form a theoretical basis for diagnosing the problems of current transit systems and for improving its operational efficiency to increase the demand as well as the level of service.

• Communications of Mathematical Education
• /
• v.37 no.1
• /
• pp.65-84
• /
• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• Journal of Korea Water Resources Association
• /
• v.54 no.7
• /
• pp.475-484
• /
• 2021

The optimal design for water distribution system (WDS) is not only satisfying the minimum required water pressure of the nodes, but also minimizing pipe cost, etc. The number of designs of WDS increases exponentially due to the arrangement of various pipes. Various optimization algorithms were applied to propose an optimized design of WDS. In this study, Modified Hybrid Vision Correction Algorithm (MHVCA) with improved self-adapting parameter was applied to optimal design of WDS. The performance was improved by changing the Hybrid Rate (HR) of the existing Hybrid Vision Correction Algorithm (HVCA) to nonlinear HR. To verify the performance of the proposed MHVCA, it applied to mathematical problems consisting of 2 and 30 decision variables and constrained mathematical problems. In order to review the application results of MHVCA, it was compared with Harmony Search (HS), Improved Harmony Search (IHS), Vision Correction Algorithm (VCA) and HVCA. Finally, MHVCA was applied to the optimal design problem of WDS and the results were compared with other algorithms. MHVCA showed better results than other algorithms in mathematical problems and WDS problem. MHVCA will be able to show good results by applying to various water resource engineering problems as well as problems applied in this study.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.4 no.4
• /
• pp.37-48
• /
• 1984

The yield-line analysis is used for earring out the limit analysis of reinforced concrete slabs which are for example like those of vertical walls of tanks subjected to the loads of hydrostatical type. It is considered both isotropic and orthotropic reinforcement using the coefficient of orthotropy with different edge conditions. The yield-line analysis is carried out by using the vertical work method and four collapse mechanisms including the fan mechanisms which is more realistic than over diagonal mechanisms is considered. It is found that the fan mechanisms are more complicated than ever simple diagonal mechanisms which have used for the orthotropically reinforced concrete slabs subjected to hydrostatic pressures. Especially Horton's study is extended in this study, and they are formulated to the constrained multi-variables nonlinear optimization problems, which are solved by the Rosen-Brock Hillclimb Procedure Program and are more critical.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.32 no.8C
• /
• pp.758-766
• /
• 2007

High peak-to-average power ratio(PAPR) is one of serious problems in the orthogonal frequency division multiplexing(OFDM) systems. This paper proposes a PAPR reduction technique for limited feedback multiple input multiple output(MIMO) OFDM systems. The proposed method is based on the null space of the MIMO channel where a dummy signal is made in the channel's null space and then, subtracted from the original signal to reduce the PAPR. First, we show that a problem occurs when the existing method is directly applied to limited feedback MIMO case. Then, a weight function for the dummy signal is proposed to mitigate the degradation of the receiver performance while still reducing PAPR significantly. The weight function is derived from a constrained nonlinear optimization problem to minimize the mean square error between the received signal and its ideal signal. Simulation results shows that the proposed technique provides about 2.5dB PAPR reduction with 0.2dB bit-error probability loss.

• Journal of Intelligence and Information Systems
• /
• v.13 no.4
• /
• pp.121-135
• /
• 2007

Constraint directed scheduling techniques, representing problem constraints explicitly and constructing schedules by constrained heuristic search, have been successfully applied to real world scheduling problems that require satisfying a wide variety of constraints. However, there has been little basic research on the representation and optimization of the objective value of a schedule in the constraint directed scheduling literature. In particular, the cost objective is very crucial for enterprise decision making to analyze the effects of alternative business plans not only from operational shop floor scheduling but also through strategic resource planning. This paper aims to explicitly represent and optimize the total cost of a schedule including the tardiness and inventory costs while satisfying non-relaxable constraints such as resource capacity and temporal constraints. Within the cost based scheduling framework, a cost propagation algorithm is presented to update cost information throughout temporal constraints within the same job.

• Journal of Astronomy and Space Sciences
• /
• v.22 no.3
• /
• pp.249-262
• /
• 2005

Optimization problems are formulated to calculate optimal impulses for deflecting Earth-Crossing Objects using a Nonlinear Programming. This formulation allows us to analyze the velocity changes in normal direction to the celestial body's orbital plane, which is neglected in many previous studies. The constrained optimization in the three-dimensional space is based on a patched conic method including the Earth's gravitational effects, and yields impulsive ${\Delta}V$ to deflect the target's orbit. The optimal solution is dependent on relative positions and velocities between the Earth and the Earth-crossing objects, and can be represented by optimal magnitude and angle of ${\Delta}V $ as a functions of a impulse time. The perpendicular component of ${\Delta}V $ to the orbit plane can sometimes play un-negligible role as the impulse time approaches the impact time. The optimal ${\Delta}V $ is increased when the original orbit of Earth-crossing object is more similar to the Earth's orbit, and is also exponentially increased as the impulse time reaches to the impact time. The analyses performed in present paper can be used to the deflection missions in the future.