• 한국컴퓨터정보학회논문지
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• 제20권9호
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• pp.21-29
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• 2015

The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.

• 경영과학
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• 제21권1호
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• pp.39-55
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• 2004

Efficient crew scheduling for cockpit crew is important in airline industry due to operational safety and cost associated with the flight duty time. Because of complexity of regulations imposed to the cockpit crew. it is complicated to generate an efficient schedule. Schedule of cockpit crew can be generated through two steps; selecting of flight patterns. and scheduling of them to the specific time horizon. Heuristic method is developed and applied with massive data in a limited time of computation. A set of flight patterns is selected from all possible flight patterns. which are generated by composing the flight leg based on regulations. by using the set partitioning problem with objective function of oversea stay cost. The selected set of flight patterns found at the first step is allocated to 4 week crew schedule to minimize the variance of total fight time assigned to each crew. The crew schedules obtained are evaluated and compared with the ones currently used in one of major airline company.

• 한국경영과학회지
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• 제19권3호
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• pp.219-233
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• 1994

A fixed k-coloring problem is introduced and dealt with by efficient heuristic algorithms. It is shown that the problem can be transformed into the graph partitioning problem. Initial coloring and improving methods are proposed for problems with and with and without the size restriction. Algorithm Move, LEE and OEE are developed by modifying the Kernighan-Lin's two way uniform partitioning procedure. The use of global information in the selection of the node and the color set made the proposed algorithms superior to the existing method. The computational result also shows that the superiority does not sacrifice the time demand of the proposed algorithms.

• 한국철도학회논문집
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• 제7권4호
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• pp.326-331
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• 2004

A routing is the path that an actual trainset follows as it moves from one train to another train in a timetable. The number of routings is equivalent to the number of trainsets required to cover the timetable. The primary factors of rolling stock requirement plan include evaluating the minimum number of routings. This can be formulated as a set partitioning problem and solved using enumeration method or column generation method. In this paper we presents an enumeration algorithm which is useful to implement the enumeration method for the rolling stock requirement plan.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2004년도 춘계학술대회 논문집
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• pp.401-405
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• 2004

Column subtraction, originally proposed by Harche and Thompson(]994), is an exact method for solving large set covering, packing and partitioning problems. Since the constraint set of ship scheduling problem(SSP) have a special structure, most instances of SSP can be solved by LP relaxation. This paper aims at applying the column subtraction method to solve SSP which can not be solved by LP relaxation. For remained instances of unsolvable ones, we subtract columns from the finale simplex table to get another integer solution in an iterative manner. Computational results having up to 10,000 0-1 variables show better performance of the column subtraction method solving the remained instances of SSP than complex branch-and-bound algorithm by LINDO.

• 한국항해항만학회지
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• 제28권2호
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• pp.129-133
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• 2004

Column subtraction, originally proposed by Harche and Thompson(1994), is an exact method for solving large set covering, packing and partitioning problems. Since the constraint set of ship scheduling problem(SSP) have a special structure, most instances of SSP can be solved by LP relaxation This paper aim, at applying the column subtraction method to solve SSP which am not be solved by LP relaxation For remained instances of unsolvable ones, we subtract columns from the finale simplex table to get another integer solution in an iterative manner. Computational results having up to 10,000 0-1 variables show better performance of the column subtraction method solving the remained instances of SSP than complex branch and-bound algorithm by LINDO.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2005년도 추계학술대회 및 정기총회
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• pp.57-78
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• 2005

차량경로문제의 Set-Partitioning 모형에 적용된 열생성 프로세스에서 차량경로를 생성하는 하위문제는 순회외판원 문제와 같은 combinatorial 구조를 가지므로 연산상의 어려움이 크다. 본 논문은 각 차량경로를 분할하여 하위문제에서 분할된 부분경로를 생성하는 경로분할모형을 소개한다. 열생성이 용이해지는 반면 주문제가 복잡해지는 단점이 있으나 이 모형은 set-partitioning 모형으로 다루기 힘든 크기의 VRP에 접근하도록 한다. 경로분할모형은 최대 199곳의 수요지를 갖는 Symmetric VRP의 실험문제에서 평균93.5%, 수요지수 최대 70곳의 Asymmetric VRP의 실험문제에서 평균 97.6%의 하한값을 도출해 특히 Asymmetric VRP의 경우에서 잘 알려진 다른 하한값 기법들보다 우수함을 보였다. 개발된 Branch-and-Price 프로세스로는 도출된 하한값을 사용하여 수요지 최대 48곳의Asymmetric VRP의 최적해를 구할 수 있었다. 경로분할모형은 성능이 비교되는 다른 모형과 달리 다른 크기의 차량을 다룰 수 있는 장점이 있고, Asymmetric VRP 문제에서는 현재 가장 우수한 하한값을 제시한다. 이러한 점에서 본 모형은 향후 연구가치가 있다고 판단된다.

• 대한산업공학회지
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• 제33권2호
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• pp.265-272
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• 2007

The purpose of Vehicle Routing Problem (VRP) is to design the least costly (distance, time) routes for a fleet of identically capacitated vehicles to serve geographically scattered customers. There may be some restrictions such as the maximal capacity for each vehicle, maximal distance for each vehicle, time window to visit the specific customers, and so forth. This paper is concerned with VRP to minimize the sum of elapsed time from departure, where the elapsed time is defined as the time taken in a moving vehicle from the depot to each customer. It is important to control the time taken from departure in the delivery of perishable products or foods, whose freshness may deteriorate during the delivery time. An integer linear programming formulation is suggested and a heuristic for practical use is constructed. The heuristic is based on the set partitioning problem whose performances are compared with those of ILOG dispatcher. It is shown that the suggested heuristic gave good solutions within a short computation time by computational experiments.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2005년도 한국컴퓨터종합학술대회 논문집 Vol.32 No.1 (A)
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• pp.892-894
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• 2005

Graph partitioning provides an important tool for data clustering, but is an NP-hard combinatorial optimization problem. Spectral clustering where the clustering is performed by the eigen-decomposition of an affinity matrix [1,2]. This is a popular way of solving the graph partitioning problem. On the other hand, semidefinite relaxation, is an alternative way of relaxing combinatorial optimization. issuing to a convex optimization[4]. In this paper we present a semidefinite programming (SDP) approach to graph equi-partitioning for clustering and then we use eigen-decomposition to obtain an optimal partition set. Therefore, the method is referred to as semidefinite spectral clustering (SSC). Numerical experiments with several artificial and real data sets, demonstrate the useful behavior of our SSC. compared to existing spectral clustering methods.

• 정보처리학회논문지A
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• 제11A권5호
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• pp.303-312
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• 2004

본 논문에서는 재구성 가능한 시스템에서 Y-chart 설계공간 탐색 기법을 응용하여 하드웨어 소프트웨어 분할문제를 해결하기 위한 방법론을 제시하고 이 방법에 기초하여 성능분석 도구를 개발하였다. 이 방법론은 어플리케이션모델의 각 Task들로부터 범용프로세서나 FPGA와 같은 하드웨어 요소들로의 사상의 경우들을 생성하고 각각의 사상의 경우에 대한 시뮬레이션을 수행하여 시스템의 성능을 평가한다. 시뮬레이션 결과로 산출된 처리율에 기초하여 가장 좋은 성능을 산출하여 사상의 경우를 선택할 수 있다. 본문에서는 또한 시뮬레이션 속도를 향상시키기 위하여 작업량과 병렬성과의 관계에 기초하여 사상집합의 크기를 줄이는 휴리스틱 알고리즘을 제안한다. 제안된 사상집합 축소 휴리스틱을 적용한 시뮬레이션 결과 사상집합의 크기를 80%가량 줄일 수 있었다.