• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.1-13
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• 1998

The purpose of this paper is to formulate the three-dimensional loading problem and to develop an exact algorithm. The three-dimensional loading problem is not only to load as many boxes as possible, but also to ensure load stability. In this Paper, we propose formulation by zero-one integer programming. Further we propose as an algorithm the branch-and-bound enforced by efficient bounding criteria. As an upper bound, we use the solution of the Lagrangean relaxation problem which relaxes constraints of zero-one IP, and as a lower bound, we use a heuristic solution induced by the solution of the Lagrangean relaxation problem. Last, we show computational experiments on convergency of upper and lower bounds.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.203-206
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• 2001

Finding the optimal solution in the river water quality management system is very hard with the non-linearity of the water quality model. Many suggested methods for that using the linear programming, non-linear programming and dynamic programming, are failed to give an optimal solution of sufficient accuracy and satisfaction. We studied a method to find a solution optimizing the river water quality management in the aspect of the efficiency and the cost of the waste water treatment facilities satisfying the water Quality goals. In the suggested method, we use the QUAL2E water quality model and the genetic algorithm. A brief result of the project to optimize the water quality management in the Youngsan river is presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.1
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• pp.153-165
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• 2009

This paper apollos an ant colony system (ACS) for the vehicle routing problem with time window (VRPTW). The VRPTW is a generalization of the VRP where the service of a customer can begin within the time windows defined by the earliest and latest times when the customer will permit the start of service. The ACS has been applied effectively in geographical environment such as TSP or VRP by meta-heuristic that imitate an ant's biologic special duality in route construction, 3 saving based ACS (SB-ACS) is introduced and its solution is improved by local search. Through iterative precesses, the SB-ACS is shown to drive the best solution. The algorithm has been tested on 56 Solomon benchmarking problems and compared to the best-known solutions on literature. Experimental results shows that SB-ACS algorithm could obtain food solution in total travel distance minimization.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.131-135
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• 2008

In this paper, we deal with a hierarchical location-allocation problem in designing the broadband convergence networks (BcN). The objective is to minimize the total cost of switch and cable while satisfying the quality of service (QoS). We formulate the problem as an integer programming model and develop the Tabu Search (TS) heuristic algorithm to find a good feasible solution within a reasonable time limit. Initial solution is obtained by using the tree structure. Three neighborhood generation mechanisms are used by local search heuristic: insertion, switch up, and switch down. In order to demonstrate the effectiveness of the proposed algorithm, we generate lower bounds from nonlinear QoS relaxation problem. We present promising computational results of the proposed solution procedures.

• East Asian mathematical journal
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• v.24 no.2
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• Korean Journal of Computational Design and Engineering
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• v.4 no.3
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• pp.259-268
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• 1999

In order to reduce the cost of product and save the processing time, optimal nesting of two-dimensional part is an important application in number of industries like shipbuilding and garment making. There have been many studies on finding the optimal solution of two-dimensional nesting. The problem of two-dimensional nesting has a non-deterministic characteristic and there have been various attempts to solve the problem by reducing the size of problem rather than solving the problem as a whole. Heuristic method and linearlization are often used to find an optimal solution of the problem. In this paper, theoretical and practical nesting algorithm for rectangular, circular and irregular shape of two-dimensional parts is proposed. Both No-Fit-Polygon and Minkowski-Sum are used for solving the overlapping problem of two parts and the dynamic programming technique is used for reducing the number search spae in order to find an optimal solution. Also, nesting designer's expertise is complied into the proposed algorithm to supplement the heuristic method.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1233-1245
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• 2008

In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Korean Management Science Review
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• v.24 no.1
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• pp.35-43
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• 2007

Minimizing the total number of setup changes of a machine increases the throughput and improves the stability of a production process, and as a result enhances the product qualify. In this context, we consider a new product-mix problem that minimizes the total number of setup changes while producing the required quantities of a product over a given planning horizon. For this problem, we develop a mixed integer programming model. Also, we develop an efficient heuristic algorithm to find a feasible solution of good quality within reasonable time bounds. Computational results show that the developed heuristic algorithm finds a feasible solution as good as the optimal solution in most test problems.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.493-496
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• 2000

We study the problem of designing at minimum cost a two-connected network topology such that the shortest cycle to which each edge belongs does not exceed a given maximum number of hops. This problem is considered as part of network planning and arises in the design of backbone networks. We propose a genetic algorithm approach that uses a solution representation, in which the connectivity and ring constraints can be easily encoded. We also propose a crossover operator that ensures a generated solution is feasible. By doing so, the checking of constraints is avoided and no repair mechanism is required. We carry out experimental evaluations to investigate the solution representation issues and GA operators for the network design problem.