• Communications of the Korean Mathematical Society
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• v.18 no.4
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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.

• KIPS Transactions on Software and Data Engineering
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• v.2 no.10
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• pp.697-704
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• 2013

The identification of haplotypes, which encode SNPs in a single chromosome, makes it possible to perform haplotype-based association tests with diseases. Minimum Error Correction model, one of models to computationally assemble a pair of haplotypes for a given organism from Single Nucleotide Polymorphism fragments, has been known to be NP-hard even for gapless cases. In the previous work, an improved branch and bound algorithm was suggested and showed that it is more efficient than naive branch and bound algorithm by performing experiments for Apis mellifera (honeybee) data set. In this paper, to show the extensibility of the algorithm to other organisms we apply the improved branch and bound algorithm to the human data set and confirm the efficiency of the algorithm.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.9
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• pp.477-486
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• 2003

In combinatorial auctions buyers nay bid for arbitrary combinations of goods. But determining the winners of combinatorial auctions who maximize the profit of a seller is known to be NP-complete. A branch-and-bound method can be one of practical algorithm for winner determination. However, bid selection heuristics play a very important role in the efficiency of a branch-and-bound method. In this paper, we designed and implemented an algorithm which used a branch-and-bound method and Linear Programming for winner determination in combinatorial auctions. We propose new bid selection heuristics which consider a branching bid and conflicting bids simultaneously to select a branching bid in the algorithm. In addition, upper bounds are reused to reduce the running time in specific cases. We evaluated the performance of the algorithm by experiments with five data distributions and compared our method with others. The algorithm using heuristics showed a superior efficiency in two data distributions and a similar efficiency in three distributions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.1
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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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• v.22 no.2
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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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.

• Proceedings of the KSME Conference
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• 2003.04a
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.2
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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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• v.3 no.2
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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.