• Title, Summary, Keyword: Column generation

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Routing and Wavelength Assignment in Survivable WDM Networks without Wavelength Conversion

  • Lee, Tae-Han;Park, Sung-Soo;Lee, Kyung-Sik
    • Management Science and Financial Engineering
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    • v.11 no.2
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    • pp.85-103
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    • 2005
  • In this paper, we consider the routing and wavelength assignment problem in survivable WDM transport network without wavelength conversion. We assume the single-link failure and a path protection scheme in optical layer. When a physical network and a set of working paths are given, the problem is to select a link-disjoint protection path for each working path and assign a wavelength for each working and protection path. We give an integer programming formulation of the problem and propose an algorithm to solve it. Though the formulation has exponentially many variables, we solve the linear programming relaxation of it by using column generation technique. We devise a branch-and price algorithm to solve the column generation problem. After solving the linear programming relaxation, we apply a variable fixing procedure combined with the column generation to get an integral solution. We test the proposed algorithm on some randomly generated data and test results show that the algorithm gives very good solutions.

An Explicit Column Generation Algorithm for the Profit Based Unit Commitment Problem in Electric Power Industry (전력산업에서의 Profit-Based Unit Commitment Problem 최적화를 위한 명시적 열생성 알고리즘)

  • Lee, Kyung-Sik;Song, Sang-Hwa
    • IE interfaces
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    • v.20 no.2
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    • pp.186-194
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    • 2007
  • Recent deregulation of Korean electricity industry has made each power generation company pay more attention to maximizing its own profit instead of minimizing the overall system operation cost while guaranteeing system security. Electricity power generation problem is typically defined as the problem of determining both the on and off status and the power generation level of each generator under the given fuel constraints, which has been known as Profit-Based Unit Commitment (PBUC) problem. To solve the PBUC problem, the previous research mostly focused on devising Lagrangian Relaxation (LR) based heuristic algorithms due to the complexity of the problem and the nonlinearity of constraints and objectives. However, these heuristic approaches have been reported as less practical in real world applications since the computational run time is usually quite high and it may take a while to implement the devised heuristic algorithms as software applications. Especially when considering long-term planning problem which spans at least one year, the complexity becomes higher. Therefore, this paper proposes an explicit column generation algorithm using power generation patterns and the proposed algorithm is successfully applied to a Korean power generation company. The proposed scheme has a robust structure so that it is expected to extend general PBUC problems.

Reuse of HPLC Guard Column by Ultrasonic Cleaning

  • Lee, Byung-Dae
    • Journal of the Korean Applied Science and Technology
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    • v.33 no.3
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    • pp.459-465
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    • 2016
  • This study investigated reusability of costly guard column by ultrasonic. It also investigated various effects that affect to guard column generation by ultrasonic. When investigated 30 KHz of frequency, area of ascorbic acid is 73.0% compared to unused guard column. As a result of investigation of effect of pH, guard column by ultrasonic is effective at alkali area. As a result of investigation of solvent effect, when ethanol is used, generation rate is 81.9% as of peak area compared to the case of analysis in un used column. From the result, it indicates that regenerated guard by ultrasonic is reusable.

The Study on the solution of the assignment model based on asymmetric cost function (비대칭 비용함수 기반의 통행배정모형의 해석에 관한 연구)

  • Park, Jun-Hwan;Sin, Seong-Il;Im, Yong-Taek
    • Proceedings of the KOR-KST Conference
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    • pp.89-97
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    • 2007
  • 본 연구에서는 통행배정 모형이 갖는 여러 가지 가정 중 대칭적 통행비용 함수를 갖는 가정을 극복할 수 있는 방법에 대해 살펴보았다. 통행배정 문제에 있어서 대칭적 비용함수 가정이라는 것은 링크의 통행비용은 다른 링크의 교통량에 전혀 영향을 받지 않는 않으면서, 동시에 해당 링크를 통과하는 단하나의 수단에 의해서만 결정된다는 의미이다. 본 연구에서는 이러한 가정을 극복할 수 있는 비대칭 통행배정모형의 특성을 살펴보고, 그 해석 모형에 대해 고찰하였다. 이 때 대표적 비대칭 통행배정 문제인 다수단 통행배정 모형을 중심으로 문제를 정의하여 검토하였다. 대각화(Diagonalized) 알고리즘과 Column Generation에 기반한 heuristic 모형을 다수단 통행배정 모형에 적용하여 그 결과를 분석하였다. 그 과정을 통해 대각화 알고리즘은 초기해의 수단과 수렴기준 수단에 따라 서로다른 해를 갖는 복수의 평형해(Equilibria)특성을 가지고 있었다. 그에 비해 Column Generation에 기반한 heuristic 모형은 Euclidean Norm을 이용한 부분최적화를 통해 복수의 평형해(Equilibria)에 관한 문제점을 개선할 수 있었다.

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Study on the Solution of the Assignment Model Based on an Asymmetric Cost Function (비대칭 비용함수 기반의 통행배정모형 해석에 관한 연구)

  • Park, Jun-Hwan;Sin, Seong-Il;Im, Yong-Taek
    • Journal of Korean Society of Transportation
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    • v.25 no.6
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    • pp.161-170
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    • 2007
  • The purpose of this study is to find the solution that overcomes the existing assumption of symmetric cost functions in multi-class assignment. In the assignment problem, the assumption of a symmetric cost function means that the link cost is determined by each unique mode and is not affected by any other modes. In this study, the authors have applied a diagonalized algorithm and a heuristic model based on column generation to a multi-class assignment model and analyzed the result. Through the study, the authors found that the diagonalized algorithm produces equilibrium solutions by the initial convergence condition. In contrast to the diagonalized algorithm, the column generation algorithm has improved the solution model to overcome the problem of equilibrium solutions in the diagonalized algorithm.

An Integer Programming Approach to the Problem of Daily Crew Scheduling (일간승무계획문제의 정수계획해법)

  • 변종익;이경식;박성수
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.613-616
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    • 2000
  • This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

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Column Generation Approach to the Constraint Based Explicit Routing Problem in MPLS Based IP Networks (MPLS 기반 IP 방에서 열생성 기법을 이용한 경로 설정 해법)

  • Kim Deokseong;Park Sungsoo
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.410-417
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    • 2002
  • We consider the constraint based explicit routing problem in MPLS based IP Network. In this problem, we are given a set of traffic demands and a network with different link capacities. The problem is to assign the demand commodities to the paths in the network while minimizing the maximum link load ratio. We formulate this problem as an integer programming problem and propose an efficient column generation technique. To strengthen the formulation, we consider some valid inequalities. We also incorporate the column generation technique with variable fixing scheme Computational results show that the algorithm gives high quality solutions in a short execution time.

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An Optimal Algorithm for Aircraft Scheduling Problem by Column Generation (열(列) 생성(生成) 기법(技法)에 의한 항공기(航空機) 운항계획(運航計劃) 문제(問題)의 최적해법(最適解法))

  • Ki, Jae-Seug;Kang, Maing-Kyu
    • Journal of Korean Institute of Industrial Engineers
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    • v.19 no.4
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    • pp.13-22
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    • 1993
  • The aircraft scheduling, which is used to determine flight frequency, departure times and aircraft type assignments, is main problem of airline's planning. This paper proposes a new algorithm for aircraft scheduling that is to maximize airline profits. This paper proposes a column generation algorithm to get an optimal solution of the continous relaxation not using all the feasible variables, but using only a limited number of variables that is generated whenever it is necessary. Using this algorithm, proposes an optimal algorithm to get an optimal integer solution of aircraft scheduling problem efficiently. The effectiveness of the column generation algorithm and the optimal algorithm is illustrated by the computational results obtained from a series of real airline problems.

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A Route-Splitting Approach to the Vehicle Routing Problem

  • Kang Sungmin;Thomas L. Joseph
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.389-392
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    • 2004
  • The column generation process for the set-partitioning model of the vehicle routing problem requires repeated solutions of column generation subproblems which has a combinatorial structure similar to that of the traveling salesman problem. This limits the size of the problem that can be addressed. We introduce a new modeling approach, termed route-splitting, which splits each vehicle route into segments, and results in more tractable subproblems. A lower bounding scheme that yields an updated bound at each iteration of the column generation process is developed. Implementation issues, including a technique of controlling columns in the master problem, are explored. Lower bounds are computed on standard benchmark problems with up to 199 customers.

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Studies of electron emitters for a miniaturized electron column design (초소형 전자 칼럼 설계를 위한 전자 방출원 연구)

  • Kim, Young-Chul;Kim, Dae-Wook;Ahn, Seung-Joon;Kim, Ho-Seob;Jang, Won-Kweon
    • Korean Journal of Optics and Photonics
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    • v.13 no.4
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    • pp.314-318
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    • 2002
  • We examine the adjustment of the semiconvergent angle and current for the miniaturized micro column working at low voltage but producing maximized current. Our study shows that the minimum electron beam sizes are 10 ㎚ for the cold field emitter (CFE) and 20 ㎚ for the thermal field emitter (TFE) at a given condition.