• Journal of Korean Society of Transportation
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• v.23 no.1
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• pp.103-114
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• 2005

The transit fare resulted from the renovation of public transit system in Seoul is basically determined based on the distance-based fare policy (DFP). In DFP, the total fare a passenger has to pay for is calculated by the basic-transfer-premium fare decision rule. The fixed amount of the basic fare is first imposed when a passenger get on a mode and it lasts within the basic travel distance. The transfer fare is additionally imposed when a passenger switches from one mode to another and the fare of the latter mode is higher than the former. The premium fare is also another and the fare of the latter begins to exceed the basic travel distance and increases at the proportion of the premium fare distance. The purpose of this study is to propose an algorithm for finding K number of paths, paths that are sequentially sorted based on total amount of transit fare, under DFP of the idstance-based fare policy. For this purpose, the link mode expansion technique is proposed in order to save notations associated with the travel modes. Thus the existing K shortest path algorithms adaptable for uni-modal network analysis are applicable to the analysis for inter-modal transportation networks. An optimality condition for finding the K shortest fare routes is derived and a corresponding algorithms is developed. The case studies demonstrate that the proposed algorithm may play an important role to provide diverse public transit information considering fare, travel distance, travel time, and number of transfer.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 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 the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.1-8
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• 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 Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.559-567
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• 2012

A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.15 no.3
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• pp.60-67
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• 2016

In cumulative transfer functions, as number of transfer increase, the impact of individual transfer to transfer cost increase linearly or non linearly. This function can effectively explain various passengers's travel behavior who choose their travel routes in integrated transit line networks including bus and railway modes. Using the function, it is possible to simulate general situations such that even though more travel times are expected, less number of transfer routes are preferred. However, because travel cost with cumulative transfer function is known as non additive cost function types in route search algorithms, finding an optimal route in integrated transit networks is confronted by the insolvable enumeration of all routes in many cases. This research proposes a methodology for finding an optimal path considering cumulative transfer function. For this purpose, the reversal phenomenon of optimal path generated in route search process is explained. Also a heuristic methodology for selecting an optimal route among multiple routes predefined by the K path algorithm. The incoming link based entire path deletion method is adopted for finding K ranking path thanks to the merit of security of route optimality condition. Through case studies the proposed methodology is discussed in terms of the applicability of real situations.

• Journal of Korean Society of Steel Construction
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• v.24 no.6
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• pp.671-682
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• 2012

The use of sinusoidal corrugated web girder for the box-type girders and gable steel main frames has recently been increasing very much. The reasons are that the thin web of the girder affords a significant weight reduction compared with rolled beam and welded built-up girder, and that corrugation prevents the buckling failure of the web. Improvements of the automatic fabrication process makes mass production of the corrugated web and unit possible, and applications of this girder have been extended considerably. Thus, the research for the optimum design processer considering the production data is needed practically. For doing this research, we develope the discrete optimum structural design program in consideration of production list data for the research, and the program apply to the single girder under the uniform load and the concentrated load as numerical example. We consider objective function as minimum weight of the girder, and use slenderness ratio, stress of flanges and corrugated web, and the girder deflection as the constraint functions. And also the Genetic Algorithms is adopted to search the global minimum point by using the production list as a discrete design variable. Finally, to verify the optimality of the design, we conduct a comparison of the results of the discrete optimum design with those of the continuous one, and also analyze the characteristics of the optimum cross-section.

• Journal of KIISE:Computer Systems and Theory
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• v.28 no.5
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• pp.213-217
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• 2001

Excessive memory buffer requirement in continuous media playback is a serious impediment of wide spread usage of on-line multimedia service. Skewed access frequency of available video files provides an opportunity of re-using the date blocks which has been loaded by one session for later usage. We present novel algorithm which minimizes the buffer requirement in multiple sessions of multimedia playbacks. In continuous media playback originated from the disk, a certain amount of memory buffer is required to synchronize asynchronous disk. Read operation and synchronous playback operation. As aggregate playback bandwodth increases, larger amount of buffer needs to be allocated for this synchronization purpose. The focus of this work is to study the asymptotic behavior of the synchronization buffer requirement and to develop an algorithm coping with this excessive buffer requirement under bandwidth congestioon. We argue that in a large scale continuous media server, it may not be necessary to read the blocks for each session directly from the disk. The beauty of our work lies in the fact that it dynamically adapts to disk utilization of the server and finds the optimal way of servicinh the individual sessions while minimizing the overall buffer space requirement. Optimality of the proposed algorithm is shown by proof. The effectiveness and performance of the proposed scheme is examined via simulation.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.5
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• pp.515-521
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• 2015

The SymMerge algorithm is an efficient merging algorithm for input sequences u and v of sizes $\left|u \right|=m$ and $\left|v \right|=n$, $m{\leq}n$. We consider complexity analysis for SymMerge algorithm regarding to the required number of comparisons. The focus of the previous complexity analysis was on finding the values of upper bounds, i.e. showing the asymptotical optimality. In this paper, in a different way from the previous complexity analysis, we show that the overall required number of comparisons for two representative special cases "symmetric case" and "maximum spanning case" can be calculated exactly i.e. the least upper bounds regarding to the required number of comparisons are calculated. Symmerge requires exactly $m\;log\frac{n}{m}+4m-logm-3$ comparisons for symmetric case of sizes $m=2^k,\;n=2^l,l{\geq}k$ of input sequences and exactly $\frac{1}{2}m^2+(m+1)logm-\frac{3}{2}m+2$ comparisons for maximum spanning case of sizes $m=2^k,n=2^m-m$ of input sequences. Additionally we show that the complexity of the Symmerge algorithm regarding to the overall required number of comparisons for these special cases can be defined by recurrence relations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.9-16
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• 2014

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.