• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.10
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• pp.426-432
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• 2006

This paper describes the concepts of Static Line Rating (SLR) and Dynamic Line Rating (DLR) and the computational methods to demonstrate them. Calculation of the line capacity needs the heat balance equation which is also used for computing the reduced tension in terms of line aging. SLR is calculated with the data from the worst condition of weather throughout the year. Even now, the utilization ratio is obtained from this SLR data in Korea. DLR is the improved method compared to SLR. A process for DLR reveals not only improved line ratings but also more accurate allowed line ratings based on line aging and real time conditions of weather. In order to reflect overhead transmission line aging in DLR, this paper proposes the method that considers the amount of decreased tension since the lines have been installed. Therefore, the continuous allowed temperature for remaining life time is newly acquired. In order to forecast DLR, this paper uses weather forecast models, and applies the concept of Thermal Overload Risk Probability (TORP). Then, the new concept of Dynamic Utilization Ratio (DUR) is defined, replacing Static Utilization Ratio (SUR). For the case study, the two main transmission lines which are responsible for the north bound power flow in the Seoul metropolitan area are chosen for computing line rating and utilization ratio. And then line rating and utilization ratio are analyzed for each transmission line, so that comparison of the present and estimated utilization ratios becomes available. Finally, this paper proves the validity of predictive DUR as the objective index, with simulations of emergency state caused by system outages, overload and so on.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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• pp.64-71
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• 2015

In this paper, we present a multi-period 0-1 knapsack problem which has the cardinality constraints. Theoretically, the presented problem can be regarded as an extension of the multi-period 0-1 knapsack problem. In the multi-period 0-1 knapsack problem, there are n jobs to be performed during m periods. Each job has the execution time and its completion gives profit. All the n jobs are partitioned into m periods, and the jobs belong to i-th period may be performed not later than in the i-th period, i = 1, ${\cdots}$, m. The total production time for periods from 1 to i is given by $b_i$ for each i = 1, ${\cdots}$, m, and the objective is to maximize the total profit. In the extended problem, we can select a specified number of jobs from each of periods associated with the corresponding cardinality constraints. As the extended problem is NP-hard, the branch and bound method is preferable to solve it, and therefore it is important to have efficient procedures for solving its linear programming relaxed problem. So we intensively explore the LP relaxed problem and suggest a polynomial time algorithm. We first decompose the LP relaxed problem into m subproblems associated with each cardinality constraints. Then we identify some new properties based on the parametric analysis. Finally by exploiting the special structure of the LP relaxed problem, we develop an efficient algorithm for the LP relaxed problem. The developed algorithm has a worst case computational complexity of order max[$O(n^2logn)$, $O(mn^2)$] where m is the number of periods and n is the total number of jobs. We illustrate a numerical example.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.125-132
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• 2023

To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. Conventionally well-known DPLLs should perform O(2^𝑙) in the worst case by performing backtracking if they fail to find a solution in a brute-force search of a branch-and-bound for the number of literals 𝑙. DPLL forms the core of the SAT Solver by substituting true(T) or false(F) for a literal so that a clause containing the least frequency literal is true(T) and removing a clause containing that literal. Contrary to DPLL, the proposed algorithm selects a literal _max𝑙 with the maximum frequency and sets $_{\max}({\mid}l{\mid},{\mid}{\bar{l}}{\mid})=1$. It then deletes 𝑙∈c_i clause in addition to ${\bar{l}}$ from ${\bar{l}}{\in}c_i$ clause. Its test results on various k-SAT problems not only show that it performs less than existing DPLL algorithm, but prove its simplicity in satisfiability verification.