• Journal of the Korea Society of Computer and Information
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• v.21 no.3
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• pp.1-8
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• 2016

The printed circuit board (PCB) can be used only 2 layers of front and back. Therefore, the wiring line segments are located in 2 layers without crossing each other. In this case, the line segment can be appear in both layers and this line segment is to resolve the crossing problem go through the via. The via minimization problem (VMP) has minimum number of via in layout design problem. The VMP is classified by NP-complete because of the polynomial time algorithm to solve the optimal solution has been unknown yet. This paper suggests polynomial time algorithm that can be solve the optimal solution of VMP. This algorithm transforms n-line segments into vertices, and p-crossing into edges of a graph. Then this graph is partitioned into 3-coloring sets of each vertex in each set independent each other. For 3-coloring sets $C_i$, (i=1,2,3), the $C_1$ is assigned to front F, $C_2$ is back B, and $C_3$ is B-F and connected with via. For the various experimental data, though this algorithm can be require O(np) polynomial time, we obtain the optimal solution for all of data.

• Journal of Korean Society of Transportation
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• v.25 no.6
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• pp.161-170
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• 2007

The purpose of this study is to find the solution that overcomes the existing assumption of symmetric cost functions in multi-class assignment. In the assignment problem, the assumption of a symmetric cost function means that the link cost is determined by each unique mode and is not affected by any other modes. In this study, the authors have applied a diagonalized algorithm and a heuristic model based on column generation to a multi-class assignment model and analyzed the result. Through the study, the authors found that the diagonalized algorithm produces equilibrium solutions by the initial convergence condition. In contrast to the diagonalized algorithm, the column generation algorithm has improved the solution model to overcome the problem of equilibrium solutions in the diagonalized algorithm.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.2
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• pp.185-191
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• 2023

To the exact cover problem that remains NP-complete to which no polynomial time algorithm is made available, this paper proposes a linear time algorithm that yields an optimal solution. The proposed algorithm makes use of the set cover problem's major feature which states that "no identical element shall be included in more than one covering set". To satisfy this criterion, the proposed algorithm initially selects a subset with the minimum cardinality and deletes those that contain the cardinality identical to that of the selected subset. This process is repeatedly performed on remaining subsets until the final solution is obtained. Provided that the solution is unattainable, it selects subsets with the maximum cardinality and repeats the same process. The proposed algorithm has not only obtained the optimal solution with ease but also proved its wide applicability on N-queens problems, hence disproving the NP-completeness of the exact cover problem.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.8 no.4
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• pp.251-258
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• 2018

In mathematics and computer science, an optimization problem is the problem of finding the best solution from feasible ones. In the context of genetic algorithm, the difficulty of an optimization problem can be explained in terms of problem epistasis. In biology, epistasis means that the phenotype of a gene is suppressed by one or more genes, but in an evolutionary algorithm it means the interaction between genes. In this paper, we experimentally show that problem epistasis and the performance of genetic algorithm are closely related. We compared problem epistasis (One-Max, Royal Road, and NK-Landscape) using a framework that quantifies problem epistasis based on Shannon's information theory, and could show that problem becomes more difficult as problem epistasis grows. In the case that a genetic algorithm finds the optimal solution, performance is compared through the number of generations, otherwise through the ratio of the fitness of the optimal solution to that of the best solution.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.501-506
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• 1993

An efficient solution algorithm of the optimal load distribution problem with joint torque constraints is presented. Multiple robot system where each robot is rigidly grasping a common object is considered. The optimality criteria used is the sum of weighted norm of the joint torque vectors. The maximum and minimum bounds of each joint torque in arbitrary form are considered as constraints, and the solution that reduces the internal force to zero is obtained. The optimal load distribution problem is formulated as a quadratic optimization problem in R, where I is the number of robots. The general solution can be obtained using any efficient numerial method for quadratic programming, and for dual robot case, the optimal solution is given in a simple analytical form.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.729-739
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• 2017

The objective of this study was to optimize minimum-energy impulsive spacecraft intercept using genetic algorithms. A mathematical model was established on two-body system based on f and g solution and universal variable to address spacecraft intercept problem for non-coplanar elliptical orbits. This nonlinear problem includes many local optima due to discontinuity and strong nonlinearity. In addition, since it does not provide a closed-form solution, it must be solved using a numerical method. Therefore, the initial guess is that a very sensitive factor is needed to obtain globally optimal values. Genetic algorithms are effective for solving these kinds of optimization problems due to inherent properties of random search algorithms. The main goal of this paper was to find minimum energy solution for orbit transfer problem. The numerical solution using initial values evaluated by the genetic algorithm matched with results of Hohmann transfer. Such optimal solution for unrestricted arbitrary elliptic orbits using universal variables provides flexibility to solve orbit transfer problems.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.2
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• pp.406-414
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• 2002

A new approach, referred to as a successive zooming genetic algorithm (SZGA), is Proposed for identifying a global solution for continuous optimization problems. In order to improve the local fine-tuning capability of GA, we introduced a new method whereby the search space is zoomed around the design point with the best fitness per 100 generation. Furthermore, the reliability of the optimized solution is determined based on the theory of probability. To demonstrate the superiority of the proposed algorithm, a simple genetic algorithm, micro genetic algorithm, and the proposed algorithm were tested as regards for the minimization of a multiminima function as well as simple functions. The results confirmed that the proposed SZGA significantly improved the ability of the algorithm to identify a precise global minimum. As an example of structural optimization, the SZGA was applied to the optimal location of support points for weight minimization in the radial gate of a dam structure. The proposed algorithm identified a more exact optimum value than the standard genetic algorithms.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.4
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• pp.165-170
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• 2023

This paper proposes an algorithm that can obtain a solution with linear time for a set cover problem(SCP) in which there is no polynomial time algorithm as an NP-complete problem so far. Until now, only heuristic greed algorithms are known to select sets that can be covered to the maximum. On the other hand, the proposed algorithm is a competitive algorithm that applies an inclusion-exclusion principle rule to N nodes up to 2nd or 3rd in the maximum number of elements to obtain a set covering all k nodes, and selects the minimum cover set among them. The proposed algorithm compensated for the disadvantage that the greedy algorithm does not obtain the optimal solution. As a result of applying the proposed algorithm to various application cases, an optimal solution was obtained with a polynomial time of O(kn²).

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.12
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• pp.1093-1098
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• 2000

This paper presents an efficient algorithm for including the kinematic calibration data into the motion controller to improve the positioning accuracy of the manipulators. Rather than spending several iterations for finding the inverse solution of the calibrated kinematics, our approach requires only the nominal inverse solution and the calibrated forward kinematics for providing a better position command promptly. Thus, real-time application is guaranteed whenever the manipulators nominal inverse solution can be expressed in a closed form. Experimental results show that the line tracking performances can be remarkably improved by employing our algorithm.