• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.19-38
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• 2007

Graph theory is becoming increasingly significant as it is applied of mathematics, science and technology. It is being actively used in fields as varied as biochemistry(genomics), electrical engineering(communication networks and coding theory), computer science(algorithms and computation) and operations research(scheduling). The powerful results in other areas of pure mathematics. Rhis paper, besides giving a general outlook of these facts, includes new graph theoretical proofs of Fermat's Little Theorem and the Nielson-Schreier Theorem. New applications to DNA sequencing (the SNP assembly problem) and computer network security (worm propagation) using minimum vertex covers in graphs are discussed. We also show how to apply edge coloring and matching in graphs for scheduling (the timetabling problem) and vertex coloring in graphs for map coloring and the assignment of frequencies in GSM mobile phone networks. Finally, we revisit the classical problem of finding re-entrant knight's tours on a chessboard using Hamiltonian circuits in graphs.

• Journal of the Korea Society of Computer and Information
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• v.23 no.8
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• pp.133-142
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• 2018

Subway metro scheduling is one of the most important problems impacting passenger convenience today. To operate efficiently, the Seoul metro uses regular, periodic schedules for all lanes, both north and southbound. However, many past studies suggest that non-periodic scheduling would better optimize costs. Since the Seoul metro is continuously facing a deficit, adopting a non-periodic schedule may be necessary. Two objectives are presented; the first, to minimize the average passengers' waiting time, and the second, to minimize total costs, the sum of the passenger waiting time, and the operational costs. In this paper, we use passenger smart card data and a precise estimation of transfer times. To find the optimal time-table, a genetic algorithm is used to find the best solution for both objectives. Using Python 3.5 for the analysis, for the first objective, we are able to reduce the average waiting time, even when there are fewer trains. For the second objective, we are able to save about 4.5 thousand USD with six fewer trains.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11a
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• pp.389-392
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• 2002

본 논문에서는 대표적인 NP 문제의 하나인 강의시간표 문제를 분산 제약조건 만족 문제로 해결하는 시스템을 제안한다. 제안한 시스템에서는 복잡하고 방대한 강의시간표 문제를 여러 개의 작은 모듈 단위의 에이전트로 분할한 후 개별 문제외 해를 구하고 이들을 결합시켜 가능해(feasible solution)를 찾는다. 한편, 분리된 에이전트에 의해 해결되는 부-문제들이 상호 의존적이면서 중첩된 경우에 해들 사이의 모순을 해결하면서 최종 해를 구한다. 제안한 시스템에서는 다음과 같은 방법으로 문제를 해결한다. 제약조건을 점진적으로 추가하여 탐색공간을 줄여 나간 후, 국소 탐색을 통해 변수에 일관된 도메인 값을 할당한다. nogood에 대하여 점진적인 제약조건 완화로 탐색공간을 확장하여 모든 변수에 도메인 값을 배정한다. 제약조건 완화는 제약조건들을 몇몇 단계로 정의하고, 휴리스틱 순서와 제약조건의 중요도에 따라 되추적 탐색 기법을 이용하여 순차적으로 완화한다. 만일 과잉-제약조건이 발생할 경우 가중치의 합이 최소로 하는 값을 배정한다. 즉 모든 변수에 도메인 값은 모든 제약조건을 만족하든 초기의 부-문제에 가능해가 될 수 있는 제약조건을 만족해야 한다.

• The Journal of the Korea Contents Association
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• v.18 no.12
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• pp.229-237
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• 2018

This paper considers effective timetable modules in order to easily satisfy various user requirements during scheduling timetables in universities. Noticing that the methods for allocating time blocks change according to the timetable modules, we suggest six models of symmetric timetable modules composed of 4 blocks, and show that our models have more benefits without any loss from the viewpoint of customers, if the suppliers consider the decreasing upper bound of ratio utilizing space resources. By adapting a concept of potentially determined blocks and suggesting their management strategies, finally, we accomplish a method for supporting flexibility and controllability when the universities timetables are scheduled.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.4
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• pp.843-859
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• 2024

The university course scheduling problem (UCSP) aims at optimally arranging courses to corresponding rooms, faculties, students, and timeslots with constraints. Previously, the university staff solved this thorny problem by hand, which is very time-consuming and makes it easy to fall into chaos. Even some meta-heuristic algorithms are proposed to solve UCSP automatically, while most only utilize one single algorithm, so the scheduling results still need improvement. Besides, they lack an in-depth analysis of the inner algorithms. Therefore, this paper presents a novel and practical approach based on Tabu search and simulated annealing algorithms for solving USCP. Firstly, the initial solution of the UCSP instance is generated by one construction heuristic algorithm, the first fit algorithm. Secondly, we defined one union move selector to control the moves and provide diverse solutions from initial solutions, consisting of two changing move selectors. Thirdly, Tabu search and simulated annealing (SA) are combined to filter out unacceptable moves in a parallel mode. Then, the acceptable moves are selected by one adaptive decision algorithm, which is used as the next step to construct the final solving path. Benefits from the excellent design of the union move selector, parallel tabu search and SA, and adaptive decision algorithm, the proposed method could effectively solve UCSP since it fully uses Tabu and SA. We designed and tested the proposed algorithm in one real-world (PKNU-UCSP) and ten random UCSP instances. The experimental results confirmed its effectiveness. Besides, the in-depth analysis confirmed each component's effectiveness for solving UCSP.

• Journal of the Korean Society for Railway
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• v.12 no.2
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• pp.267-275
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• 2009

Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.

• Journal of the Korean Society for Railway
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• v.14 no.2
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• pp.167-173
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• 2011

This paper considers the problem of revising train departure time to reduce electric power consumption of mass rapid transit (MRT) railways. The motion of a train running between stations is divided into three phases: traction, coasting, and deceleration phases. The traction phase requires high electric power to operate MRT railways. In the coasting phase, the train moves stably by consuming little or no power. The deceleration phase is a braking mode and produces some electric power called regenerated brake power owing to inertia force for the train generated In the traction and coasting phases. The regenerative energy can be used by other accelerating trains within a specific range from the train and thereby the power consumptions of train can be reduced. We developed a mixed integer programming model to solve the problem. To validate the suggested model, a computational experiment was conducted using real data from Korea Metropolitan Subway.