• Title/Summary/Keyword: branch-and-bound

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Two-sided assembly line balancing using a branch-and-bound method (분지한계법을 이용한 양면조립라인 밸런싱)

  • Kim, Yeo-Keun;Lee, Tae-Ok;Shin, Tae-Ho
    • Journal of Korean Institute of Industrial Engineers
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    • v.24 no.3
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    • pp.417-429
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    • 1998
  • This paper considers two-sided (left and right side) assembly lines which are often used, especially in assembling large-sized products such as trucks and buses. A large number of exact algorithms and heuristics have been proposed to balance one-sided lines. However, little attention has been paid to balancing two-sided assembly lines. We present an efficient algorithm based on a branch and bound for balancing two-sided assembly lines. The algorithm involves a procedure for generating an enumeration tree. To efficiently search for the near optimal solutions to the problem, assignment rules are used in the method. New and existing bound strategies and dominance rules are else employed. The proposed algorithm can find a near optimal solution by enumerating feasible solutions partially. Extensive computational experiments are carried out to make the performance comparison between the proposed algorithm and existing ones. The computational results show that our algorithm is promising and robust in solution quality.

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A Scheduling Problem to Minimize Total Tardiness in the Two-stage Assembly-type Flowshop (총 납기지연시간 최소화를 위한 두 단계 조립시스템에서의 일정계획에 관한 연구)

  • Ha, Gui-Ryong;Lee, Ik-Sun;Yoon, Sang-Hum
    • Journal of the Korean Operations Research and Management Science Society
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    • v.33 no.3
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    • pp.1-16
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    • 2008
  • This paper considers a scheduling problem to minimize the total tardiness in the two-stage assembly-type flowshop. The system is composed of multiple fabrication machines in the first stage and a final-assembly machine in the second stage. Each job consists of multiple tasks, each task is performed on the fabrication machine specified in advance. After all the tasks of a job are finished, the assembly task can be started on the final-assembly machine. The completion time of a job is the time that the assembly task for the job is completed. The objective of this paper is to find the optimal schedule minimizing the total tardiness of a group of jobs. In the problem analysis, we first derive three solution properties to determine the sequence between two consecutive jobs. Moreover, two lower objective bounds are derived and tested along with the derived properties within a branch-and-bound scheme. Two efficient heuristic algorithms are also developed. The overall performances of the proposed properties, branch-and-bound and heuristic algorithms are evaluated through numerical experiments.

Time Series Pattern Recognition based on Branch and Bound Dynamic Time Warping (분기 한정적인 동적 타임 워핑 기반의 시계열 패턴인식)

  • Jang, Seok-Woo;Park, Young-Jae;Kim, Gye-Young
    • Journal of KIISE:Software and Applications
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    • v.37 no.7
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    • pp.584-589
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    • 2010
  • The dynamic time warping algorithm generally used in time series pattern recognition spends most of the time in generating the correlation table, and it establishes the global path constraint to reduce the corresponding time complexity. However, the constraint restrains just in terms of the time axis, not considering the contents of input patterns. In this paper, we therefore propose an efficient branch and bound dynamic time warping algorithm which sets the global constraints by adaptively reflecting the patterns. The experimental results show that the proposed method outperforms conventional methods in terms of the speed and accuracy.

Design of High-Speed 2-D State-Space Digital Filters Based on a Improved Branch-and-Bound Algorithm (개량된 분기한정법에 의한 고속연산 2차원 상태공간 디지털필터의 설계)

  • Lee Young-Ho
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.10 no.7
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    • pp.1188-1195
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    • 2006
  • This paper presents an efficient design method of 2-D state-space digital filter based on an improved branch-and -bound algorithm. The resultant 2-D state-space digital filters whose coefficients are represented as the sum of two power-of-two terms, are attractive for high-speed operation and simple implementation. The feasibility of the proposed method is demonstrated by several experiments. The results show that the approximation error and group delay characteristic of the resultant filters are similar to those of the digital filters which designed in the continuous coefficient space.

Scheduling of Three-Operation Jobs in a Two-Machine Flow Shop with mean flow time measure

  • Ha, Hee-Jin;Sung, Chang-Sup
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.11a
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    • pp.138-141
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    • 2006
  • This paper considers a two-machine flow-shop scheduling problem for minimizing mean flow time. Each job has three non-preemptive operations, where the first and third operations must be Processed on the first and second machines, respectively, but the second operation can be processed on either machine. A lower bound based on SPT rule is derived, which is then used to develop a branch-and-bound algorithm. Also, an efficient simple heuristic algorithm is developed to generate a near-optimal schedule. Numerical experiments are performed to evaluate the performances of the proposed branch-and-bound and the heuristic algorithm

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An Efficient Algorithm for the Generalized Continuous Multiple Choice linear Knapsack Problem (일반연속 다중선택 선형배낭문제의 효율적인 해법연구)

  • Won, Joong-Yeon
    • Journal of Korean Institute of Industrial Engineers
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    • v.23 no.4
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    • pp.661-667
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    • 1997
  • We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.

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A Wavelength Path Accommodation Method in Wavelength Routed WDM Network (파장 라우팅 WDM망에서의 파장 경로 설정 방식)

  • 김병재;박진식;신기수
    • Proceedings of the Korean Information Science Society Conference
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    • 1998.10a
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    • pp.636-638
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    • 1998
  • WDM망을 구성하는데 있어서 광학적 파장은 가장 중요한 자원의 하나이다. 그러나 주어진 통신 요구를 모두 수용하면서 동시에 최소한의 파장만을 사용하는 WDM망의 설계 문제는 이미 NP-complete 계열의 문제인 것으로 밝혀졌으며 많은 휴리스틱 알고리즘들이 제안되었다. 본 논문에서는 임의의 물리적 망 위상(topology)과 완전 연결(full connection)형태의 통신 요구가 주어질 경우, 요구되는 파장 경로(Wavelength Path, lightpath)를 확립하기 위한 방법으로써 각 노드 사이의 최단 거리 경로를 기반으로 하여 탐색 공간을 만들고 구성된 탐색 공간 내에서 Branch-and-bound 탐색방식을 수행하는 파장 경로 설정 알고리즘을 제안한다. Branch-and-bound탐색방식은 초기에 좋은 bound조건을 가질 경우 주어진 시간 안에 보다 넓은 탐색 공간을 검색할 수 있으므로 최초의 탐색에서 가능한 좋은 성능의 파장 경로 설정을 발견할 수 있어야한다. 시뮬레이션 실험을 통하여 최초의 탐색에서 발견한 파장 경로 설정과 구성된 탐색 공간내의 최적해를 얻고, cut-set를이용하여 요구 파장 개수의 하위 한계값을 계산한후, 이를 상호 비교하여 제안된 알고리즘의 성능을 평가한다.

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다단계-병렬 흐름 생산시스템하에서의 제품별 로트 투입순서 결정

  • 김중순;강석호
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1993.10a
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    • pp.10-10
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    • 1993
  • 본 연구에서는 다품종(multiple products) 다단계(multi-stage) 흐름 생산시스템에서의 제품별 로트 투입순서결정무제를 다루었다. 다단계 흐름 생산시스템의 투입순서 결정문제에 대한 기존연구는 각 단계의 기계대수가 1대인 경우에 관한 것이 대부분이지만, 본 연구에서는 각 단계의 기계대수가 복수이고 각 제품의 생산량이 로트로 주어지며, 또한 각 단계마다의 이송이 로트로 이루어지는 것이 아니라 1단위로 이루어지는 생산시스템을 대상으로 하였다. 그리고 각 제품의 생산준비기간은 투입순서와 관계 없이 일정하며 앞 단계에서 제품이 도착하지 않더라도 생산준비는 먼저 수행될 수 있다고 가정하였다. 제품별 로트 투입순서 결정문제에서 사용된 성능평가기준(performance measure)은 총작업소요시간(makespan)이며 순열투입순서(permutation schedule)만을 대상으로 하였다. 결정기법으로는 투입순서 결정문제에서 효율적인 것으로 알려져 있는 분지한계법(Branch & Bound)이 사용되었으며 분지한계법에서 이용되는 부분투입순서(partial sequence)에 대한 하한값(lower bound)을 제시하였다. 제시된 기법을 사용하면 현실적인 크기의 제품별 로트 투입순서 결정문제를 적당한 시간내에 충분히 해결할 수 있을 것으로 보인다. 제시된 해법으로 해결된 수치예제가 주어져 있다.

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Design and Performance Analysis of a Parallel Optimal Branch-and-Bound Algorithm for MIN-based Multiprocessors (MIN-based 다중 처리 시스템을 위한 효율적인 병렬 Branch-and-Bound 알고리즘 설계 및 성능 분석)

  • Yang, Myung-Kook
    • Journal of IKEEE
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    • v.1 no.1 s.1
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    • pp.31-46
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    • 1997
  • In this paper, a parallel Optimal Best-First search Branch-and-Bound(B&B) algorithm(pobs) is designed and evaluated for MIN-based multiprocessor systems. The proposed algorithm decomposes a problem into G subproblems, where each subproblem is processed on a group of P processors. Each processor group uses tile sub-Global Best-First search technique to find a local solution. The local solutions are broadcasted through the network to compute the global solution. This broadcast provides not only the comparison of G local solutions but also the load balancing among the processor groups. A performance analysis is then conducted to estimate the speed-up of the proposed parallel B&B algorithm. The analytical model is developed based on the probabilistic properties of the B&B algorithm. It considers both the computation time and communication overheads to evaluate the realistic performance of the algorithm under the parallel processing environment. In order to validate the proposed evaluation model, the simulation of the parallel B&B algorithm on a MIN-based system is carried out at the same time. The results from both analysis and simulation match closely. It is also shown that the proposed Optimal Best-First search B&B algorithm performs better than other reported schemes with its various advantageous features such as: less subproblem evaluations, prefer load balancing, and limited scope of remote communication.

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A Branch and Bound Algorithm for the Hierarchical Transportation Network Design Problem in Directed Networks (유방향 네트워크에서 계층수송망 설계 문제에 대한 분지한계법)

  • Shim, Hyun-Taik;Park, Son-Dal
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.2
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    • pp.86-102
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    • 1991
  • The purpose of this paper is to present a branch and bound algorithm for the hierarchical transportation network design problem in 2-level directed networks. This problem is to find the least cost of hierarchical transportation networks which consist of a primary path and a secondary path. The primary path is a simple path from a prespecified orgin node to a prespecified terminal node. All nodes must be either a transsipment node on the primary path or connected to that path via secondary arcs. This problem is formulated to a 0-1 inter programming problem with assignment and illegal subtour elimination equations as constaints. We show that the subproblem relaxing subtour elimination constraints is transformed to a linear programming problem by means of the totally unimodularity. Optimal solutions of this subproblem are polynoially obtained by the assignment algorithm and complementary slackness conditions. Therefore, the optimal value of this subproblme is used as a lower bound. When an optimal solution of the subproblem has an illegal subtour, a better disjoint rule is adopted as the branching strategy for reducing the number of branched problems. The computational comparison between the least bound rule and the depth first rule for the search strategy is given.

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