• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.2
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• pp.117-127
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• 2000

In this paper, we propose a new convex combination weight rule for the cross decomposition method which is known to be one of the most reliable and promising strategies for the large scale optimization problems. It is called generalized cross decomposition, a modification of linear mean value cross decomposition for specially structured linear programming problems. This scheme puts more weights on the recent subproblem solutions other than the average. With this strategy, we are having more room for selecting convex combination weights depending on the problem structure and the convergence behavior, and then, we may choose a rule for either faster convergence for getting quick bounds or more accurate solution. Also, we can improve the slow end-tail behavior by using some combined rules. Also, we provide some computational test results that show the superiority of this strategy to the mean value cross decomposition in computational time and the quality of bounds.

• Journal of the Society of Naval Architects of Korea
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• v.61 no.1
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• pp.8-18
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• 2024

The present study concerns reduced order modeling of a marine diesel engine, which can be used for outlier detection in status monitoring and carbon intensity index calculation. Principal Component Analysis (PCA) is introduced for the reduced order modeling, focusing on the feasibility of detecting and treating nonlinear variables. By cross-correlation, it is found that there are seven non-linear data channels among 23 data channels, i.e., fuel mode, exhaust gas temperature after the turbocharger, and cylinder coolant temperatures. The dataset is handled so that the mean is located at the nominal continuous rating. Polynomial presentation of the dataset is also applied to reflect the linearity between the engine speed and other channels. The first principal mode shows strong effects of linearity of the most data channels to show the linearity of the system. The non-linear variables are effectively explained by other modes. second mode concerns the temperature of the cylinder cooling water, which shows small correlation with other variables. The third and fourth modes correlates the fuel mode and turbocharger exhaust gas temperature, which have inferior linearity to other channels. PCA is proven to be applicable to data given in binary type of fuel mode selection, as well as numerical type data.