• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.5
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• pp.1069-1084
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• 2011

This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited. Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.26 no.4
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• pp.42-49
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• 2003

The branch and bound techniques based on cut tree and eigenvector have been Introduced in the literature [1, 2, 3, 6, 9, 12]. These techniques are used as a basis to allocate departments to floors and then to fit departments with unchangeable dimensions into floors. Grouping algorithms to allocate departments to each floor are developed and branch and bound forms the basis of optimizing using the criteria of rectilinear distance. The proposed branch and bound technique, in theory, will provide the optimal solution on two dimensional layout. If the runs are time and/or node limited, the proposed method is a strong heuristic The technique is made further practical by the fact that the solution is constrained such that the rectangular shape dimensions length and width are fixed and a perfect fit is generated if a fit is possible. Computational results obtained by cut tree-based algorithm and eigenvector-based algorithm are shown when the number of floors are two or three and there is an elevator.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.26 no.4
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• pp.63-71
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• 2003

This paper analyses a deterministic scheduling problem concerned with manufacturing multiple types of components at a pre-assembly stage composed of parallel fabrication machines. Each component part is machined on a fabrication machine specified in advance. The manufactured components are subsequently assembled into products. The completion time of a job(product) is measured by the latest completion time of its all components at the pre-assembly stage. The problem has the objective measure of minimizing the total weighted completion time of a finite number of jobs. Two lower bounds are derived and tested in a branch-and-bound scheme. Also, three constructive heuristic algorithms are developed based on the machine aggregation and greedy strategies. Some empirical evaluation of the performance of the proposed branch-and-bound and heuristic algorithms are also performed.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.4
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• pp.661-671
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• 1998

It is important to minimize the number of disk accesses which is necessary to transfer data in disk into main memory when processing transactions in physical database design. A vertical file partitioning method is used to reduce the number of disk accesses by partitioning relations vertically and accessing only necessay fragments. In this paper, SOFM(Self-Organizing Feature Maps) network is used to solve vertical partitioning problems. This paper shows that SOFM network is efficient in solving vertical partitioning problem by comparing approximate solution of SOFM network with optimal solution of N-ary branch and bound method. And this paper presents a heuristic algorithm for allocating duplicate attributes to vertically partitioned fragments. As branch and bound method requires particularly much computing time to solve large-sized problems, it is shown that SOFM network is able to overcome this limitation of branch and bound method and solve large-sized problems efficiently in a short time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.29 no.4
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• pp.34-42
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• 2006

This paper considers an assembly-type flowshop scheduling problem in which each job is assembled with two types of components. One type of the components is outsourced with positive lead time but the other type is fabricated in-house at the first stage. The two types of the components should be prepared at the first stage before starting the assembly operation for each job at the second stage. The objective is to schedule the jobs so that the makespan is minimized. Some solution properties and lower bounds are derived and incorporated into a branch and bound algorithm. Also, an efficient heuristic is developed. The performances of the proposed branch and bound algorithm and heuristic are evaluated through computational experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.28A no.12
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• pp.73-87
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• 1991

This paper presents a new approach to the scheduling problem in the high level synthesis. In this approach, iterative rescheduling processes starting with ASAP(As Soon As Possible) scheduling result are performed in a branch-and-bound manner so to arrive at the scheduling result of the lowest hardware cost under the given timing constraint. At each iteration step, only the selected nodes are considered for rescheduling, and the lower bound cost estimation is performed to avoid the unnecessary attempts to search for an optimal result. This branch-and-bound method turns out to be effective in pruning the search space, and thus reducing run time considerably in many cases.

• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.3
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• pp.1-12
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• 2017

In this paper, we generalize lifted inequalities to a 0-1 mixed-integer bilinear covering set with linear terms. This work is motivated by the observation that Generalized Bilinear Inequality (GBI) occurs in the Branch and Bound process. We find some conditions and prove the subadditivity of lifting functions for lifting to be sequence-independent. Using the theoretical results, we develop facet-defining inequalities for a GBI-defined set through three steps of lifting.