• 대한수학회논문집
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• 제18권4호
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• pp.745-754
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• 2003

Maximum clique problem is to find a maximum clique(largest in size) in an undirected graph G. We present a method that computes either a maximum clique or an upper bound for the size of a maximum clique in G. We show that this method performs well on certain class of graphs and discuss the application of this method in a branch and bound algorithm for solving maximum clique problem, whose efficiency is depended on the computation of good upper bounds.

• 정보처리학회논문지:소프트웨어 및 데이터공학
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• 제2권10호
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• pp.697-704
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• 2013

인간의 한쪽 염색체상에 나타나는 SNP의 서열인 일배체형을 식별해내면 효과적인 유전질병 연관검사를 할 수 있다. 주어진 SNP 단편들로부터 계산적인 방법으로 한 쌍의 일배체형을 조합하기 위해 제시된 모델 중 하나인 최소오류수정 모델은 단편에 손실이 없는 경우조차 NP-hard임이 증명되었다. 기존의 분기한정 알고리즘은 많은 계산시간을 요구함에 따라 실제 응용에 사용하기 어려웠다. 그러나 최근에 개선된 분기한정 알고리즘이 제시되었고, 꿀벌(Apis mellifera)의 유전자형 데이터를 대상으로 성능을 분석해봄으로써 개선된 알고리즘이 기존 분기한정 알고리즘보다 효율적임을 보였다. 본 논문에서는 인간의 유전자형 데이터를 대상으로 개선된 분기한정 알고리즘을 적용해 일배체형 조합문제를 수행한다. 실험을 통한 성능분석 결과, 개선된 분기한정 알고리즘이 인간 유전체에 대해서도 성공적으로 적용됨을 확인함으로써 다양한 생명체의 일배체형 조합문제에 적용 가능함을 보인다.

• 한국정보과학회논문지:시스템및이론
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• 제30권9호
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• pp.477-486
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• 2003

조합 경매에서는 구매자들이 원하는 상품들을 조합해서 입찰할 수 있다. 그러나 판매자의 이익을 최대로 하는 구매자들, 즉 조합 경매의 승자를 결정하는 문제는 NP-complete이다. 적절한 시간 내에 승자를 찾기 위해서 분기 한정법(branch-and-bound)을 사용할 때, 구매자들의 비드(bid)들 중에서 어떤 비드를 선택해서 분기할 것인가를 결정해야 한다. 이 때, 비드를 선택하는 휴리스틱이 분기 한정법의 성능을 결정하는 중요한 역할을 한다. 본 논문에서는 조합경매의 승자를 결정하기 위해서 분기 한정법과 Linear Programming(LP)를 사용하는 알고리즘을 설계하고, 분기할 비드를 선택하기 위하여 분기할 비드와 충돌하는 비드들을 동시에 고려하는 비드 선택 휴리스틱을 제안한다. 그리고 최대 한계치를 재 사용하는 경우를 찾아내서 알고리즘의 수행시간을 줄였다. 알고리즘의 수행 성능을 평가하기 위해서 다섯 가지의 데이타 분포에 대한 실험 결과를 이전 논문들과 비교했다. 제시한 휴리스틱을 사용한 알고리즘은 두 가지 데이타 분포에서는 더 빠른 성능을 보였고 나머지 세 분포에서는 비슷한 성능을 보였다.

• 산업경영시스템학회지
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• 제38권4호
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• pp.132-141
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• 2015

We focus on the fire scheduling problem (FSP), the problem of determining the sequence of targets to be fired at, for the objective of minimizing makespan to achieve tactical goals. In this paper, we assume that there are m available weapons to fire at n targets (> m) and the weapons are already allocated to targets. One weapon or multiple weapons can fire at one target and these fire operations should start simultaneously while the finish time of them may be different. We develop several dominance properties and a lower bound for the problem, and suggest a branch and bound algorithm implementing them. Also, In addition, heuristic algorithms that can be used for obtaining an initial upper bound in the B&B algorithm and for obtaining good solutions in a short time were developed. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of a medium size in a reasonable amount of computation time. The proposed lower bound, the dominance properties, and the heuristics for upper bound are tested in B&B respectively, and the result showed that lower bound is effective to fathoming nodes and the dominance properties and heuristics also worked well. Also, it is showed that the CPU time required by this algorithm increases rapidly as the problem size increases. Therefore, the suggested B&B algorithm would be limited to solve large size problems. However, the employed heuristic algorithms can be effectively used in the B&B algorithm and can give good solutions for large problems within a few seconds.

• 산업경영시스템학회지
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• 제32권1호
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• pp.79-84
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• 2009

In this paper, a best-first branch and bound algorithm based upon the bottom-up approach for the unweighted unconstrained two-dimensional cutting problem is proposed to find the optimal solution to the problem. The algorithm uses simple and effective methods to prevent constructing duplicated patterns and reduces the searching space by dividing the branched node set. It also uses a efficient bounding strategy to fathom the set of patterns. Computational results are compared with veil-known exact algorithms and demonstrate the efficiency of the proposed algorithm.

• Journal of Information Technology Applications and Management
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• 제22권2호
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• pp.1-17
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• 2015

In this research, we develop and suggest branch and bound algorithms for a two-machine permutation flowshop scheduling problem with the objective of minimizing makespan. In this scheduling problem, after each job is operated on the machine 1 (first machine), the job has to start its second operation on machine 2 (second machine) within its corresponding limited waiting time. In addition, each job has its corresponding ready time at the machine 1. For this scheduling problem, we develop various dominance properties and three lower bounding schemes, which are used for the suggested branch and bound algorithm. In the results of computational tests, the branch and bound algorithms with dominance properties and lower bounding schemes, which are suggested in this paper, can give optimal solution within shorter CPU times than the branch and bound algorithms without those. Therefore, we can say that the suggested dominance properties and lower bounding schemes are efficient.

• 한국경영과학회지
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• 제22권3호
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• pp.59-80
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• 1997

Designing highly survivable interoffice telecommunication networks is considered. The problem is formulated as a minimum-cost network design problem with three node connectivity constraints. These valid and facet-defining inequalities for the convex hull of the solution are presented. A branch and cut algorithm is proposed based on the inequalities to obtain the optimal solution. With the lower bound by the cutting plane algorithm, a delete-ink heuristic is proposed to otain a good upper bound in the branch and bound procedure. The effeciveness of the branch and cut algorithm is demonstrated with computational results for a variety of problem sets : different lower bounds, two types of link costs and large number of links. The cutting plane procedure based on the three inequalities provides excellent lower bounds to the optimal solutions.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.420-424
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• 2003

Stacking sequence optimization needs discrete programming techniques because ply angles are limited to a fixed set of angles such as $0^{\circ},\;{\pm}45^{\circ},\;90^{\circ}$. Two typical methods are genetic algorithm and branch and bound method. The goal of this paper is to compare the methods in the light of their efficiency and performance in handling the constraints and finding the global optimum. For numerical examples, maximization of buckling load is used as objective and optimization results from each method are compared.

• 대한산업공학회지
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• 제33권2호
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• pp.213-220
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• 2007

This paper considers a two-stage hybrid flow shop scheduling problem for the objective of minimizing the number of tardy jobs. Each job is processed through the two production stages in stages, each of which has multiple identical parallel machines. The problem is to determine the allocation and sequence of jobs at each stage. A branch and bound algorithm that gives the optimal solutions is suggested that incorporates the methods to obtain the lower and upper bounds. Dominance properties are also suggested to reduce the search space. To show the performance of the algorithm, computational experiments are done on randomly generated problems, and the results are reported.

• Industrial Engineering and Management Systems
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• 제3권2호
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• pp.100-115
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• 2004

The network representation and branch and bound algorithm with efficient lower and upper bounding procedures are developed to determine a global optimal production schedule on a machine that minimizes sequence-dependent setup cost and earliness/tardiness penalties. Lower bounds are obtained based on heuristic and Lagrangian relaxation. Priority dispatching rule with local improvement procedure is used to derive an initial upper bound. Two dominance criteria are incorporated in a branch and bound procedure to reduce the search space and enhance computational efficiency. The computational results indicate that the proposed procedure could optimally solve the problem with up to 40 jobs in a reasonable time using a personal computer.