• Journal of Korean Institute of Industrial Engineers
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• v.18 no.2
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• pp.141-147
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• 1992

This article evaluates the efficiency of three branch-and-bound heuristics for a job scheduling problem that minimizes the sum of absolute deviations of completion times from a common due date. To improve the performance of the branch-and-bound procedure, Algorithm SA is presented for the initial feasible schedule and three heuristics : breadth-first, depth-first and best-first search are investigated depending on the candidate selection procedure. For the three heuristics the CPU time, memory space, and the number of nodes generated are computed and tested with nine small examples (6 ${\leq}$ n ${\leq}$ 4). Medium sized random problems (10 ${\leq}$ n ${\leq}$ 30) are also generated and examined. The computational results are compared and discussed for the three heuristics.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.1-8
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• 2002

A Branch-and-Cut algorithm is a branch-and-bound algorithm in which rutting planes are generated throughout the branch-and-bound tree. It is now one of the most widespread and successful methods for solving mixed integer programming problems. In this paper we presents efficient implementation techniques of branch-and-cut algorithm for miked integer programming problems.

• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.1 no.2
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• pp.73-81
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• 1975

In an earlier paper ('Scheduling Jobs on a Number of Identical Machines' by Elmaghraby and Park, March 1974, AIIE Transactions) a branch-and-bound algorithm was developed for the sequencing problem when all jobs are available to process at time zero and are independet (i.e., there are not a priori precedence relationships among jobs.). However, the amount of computation required by the algorithm was not considered to be short if more than 50 jobs were processed. As an effort to improve the algorithm, the present paper modifies the implicit enumeration procedure in the algorithm so that moderately large problems can be treated with what appears to be a short computational time. Mainly this paper is concerned with improving the lower bound in the implicit enumeration procedure. The computational experiences with this new branch-and-bound algorithm are given.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.653-654
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• 2006

• KIEE International Transactions on Power Engineering
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• v.2A no.3
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• pp.121-128
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• 2002

This study proposes a new method for transmission system expansion planning using fuzzy integer programming. It presents stepwise cost characteristics analysis which is a practical condition of an actual system. A branch and bound method which includes the network flow method and the maximum flow - minimum cut set theorem has been used in order to carry out the stepwise cost characteristics analysis. Uncertainties of the permissibility of the construction cost and the lenient reserve rate and load forecasting of expansion planning have been included and also processed using the fuzzy set theory in this study. In order to carry out the latter analysis, the solving procedure is illustrated in detail by the branch and bound method which includes the network flow method and maximum flow-minimum cut set theorem. Finally, case studies on the 21- bus test system show that the algorithm proposed is efficiently applicable to the practical expansion planning of transmission systems in the future.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.12
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• pp.2525-2532
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• 2009

In this paper, a fast sphere decoder is proposed for the joint detection of phase-shift keying (PSK) signals in uncoded Vertical Bell Laboratories Layered Space Time (V-BLAST) systems. The proposed decoder, PSD, consists of preprocessing stage and search stage. The search stage of PSD relies on the depth-first branch-and-bound (BB) algorithm with "best-first" orders stored in lookup tables. Simulation results show that the PSD is able to provide the system with the maximum likelihood (ML) performance at low complexity.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.47 no.2
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• pp.48-56
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• 2024

We examine a single machine scheduling problem with step-improving jobs in which job processing times decrease step-wisely over time according to their starting times. The objective is to minimize total completion time which is defined as the sum of completion times of jobs. The total completion time is frequently considered as an objective because it is highly related to the total time spent by jobs in the system as well as work-in-progress. Many applications of this problem can be observed in the real world such as data gathering networks, system upgrades or technological shock, and production lines operated with part-time workers in each shift. Our goal is to develop a scheduling algorithm that can provide an optimal solution. For this, we present an efficient branch and bound algorithm with an assignment-based node design and tight lower bounds that can prune branch and bound nodes at early stages and accordingly reduce the computation time. In numerical experiments well designed to consider various scenarios, it is shown that the proposed algorithm outperforms the existing method and can solve practical problems within reasonable computation time.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.725-732
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• 2021

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

• 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.