• Title, Summary, Keyword: Linear programming (LP)

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A Survey: SDP, its Duality, Complexity and Applications (SDP의 개관: 쌍대성, 계산복잡성 및 응용)

  • 류춘호;명영수;홍성필
    • Journal of the Korean Operations Research and Management Science Society
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    • v.26 no.2
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    • pp.13-46
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    • 2001
  • SDP (Semidefinite Programming), as a sort of “cone-LP”, optimizes a linear function over the intersection of an affine space and a cone that has the origin as its apex. SDP, however, has been developed in the process of searching for better solution methods for NP-hard combinatorial optimization problems. We surveyed the basic theories necessary to understand SDP researches. First, We examined SDP duality, comparing it to LP duality, which is essential for the interior point method, Second, we showed that SDP can be optimized from an interior solution in polynomial time with a desired error limit. finally, we summarized several research papers that showed SDP can improve solution methods for some combinatorial optimization problems, and explained why SDP has become one of the most important research topics in optimization. We tried to integrate SDP theories. relatively diverse and complicated. to survey research papers with our own perspective, and thus to help researcher to pursue their SDP researches in depth.

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Daily Unit Commitment Scheduling of Power System with Energy Storage System (전력저장장치를 고려한 일간 최적 기동정지계획 수립연구)

  • Song, Ha-Na;Jang, Se-Hwan;Kim, Hyeong-Jung;Roh, Jae-Hyung;Park, Jong-Bae
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.4
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    • pp.717-725
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    • 2011
  • In the power system with an electric storage system that can increase utilization rate of the source of such new renewable energy, this paper introduces the approach on the daily unit commitment scheduling that determines simultaneously optimum operational condition and output of thermal generators and electric storage device. The unit commitment is one of the most important issues in economic operation and security of short-term operational plan of the power system. It is to determine on/off status of generator to minimize operational cost during the given period. The committed generator should satisfy various operational limitation such as estimated demand by system, spinning reserve condition within minimum operational cost. In order to determine on/off or charge/discharge/idle condition and output level of units and electric storage system, the MILP(Mixed Integer Linear Programming) is suggested. The proposed approach is the mixed method between LP(Linear Programming) and IP(integer programming) which seeks the value of real number and integer that maximize or minimize function objective within given condition. The daily unit commitment problem with the electric storage system is applied to MILP algorithm through linearization and formulation process. The proposed approach is applied to the test system.

Linear programming技法에 있어서 Basic Matrix의 Bartels-Golub Decomposition 및 그 응용

  • 문영현
    • 전기의세계
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    • v.32 no.11
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    • pp.664-669
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    • 1983
  • 대규모 system을 취급하는 공학분야에 있어서 Matrix의 demension이 커짐에 따라 전산부담을 줄이기 위한 소요기억용량 절감 및 계산시간의 단축이 주된 관심사 중의 하나가 되어 왔다. LP(Linear Programming)기법 역시 대규모 선형 system에 적용될 경우 Basic Matrix 에 대한 dimensionality 문제를 포함하고 있으며 이에 대한 효과적인 해결방법으로 Bartels-Golub Decomposition 방법이 연구되어 있다. 이 방법은 Chan과 Yip등이 LSGA(Load Shedding and Generator Rescheduling) 문제에의 적용을 시도한 바 있으며, 일반적인 선형최적화 문제뿐만 아니라, dimensionality가 큰 Matrix의 Inverse 계산을 요하는 문제에 널리 적용될 수 있으므로 그 개요를 소개하고자 한다.

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Optimal Design of Robust Quantitative Feedback Controllers Using Linear Programming and Genetic Algorithms

  • Bokharaie, Vaheed S.;Khaki-Sedigh, Ali
    • 제어로봇시스템학회:학술대회논문집
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    • pp.428-432
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    • 2003
  • Quantitative Feedback Theory (QFT) is one of most effective methods of robust controller design and can be considered as a suitable method for systems with parametric uncertainties. Particularly it allows us to obtain controllers less conservative than other methods like $H_{\infty}$ and ${\mu}$-synthesis. In QFT method, we transform all the uncertainties and desired specifications to some boundaries in Nichols chart and then we have to find the nominal loop transfer function such that satisfies the boundaries and has the minimum high frequency gain. The major drawback of the QFT method is that there is no effective and useful method for finding this nominal loop transfer function. The usual approach to this problem involves loop-shaping in the Nichols chart by manipulating the poles and zeros of the nominal loop transfer function. This process now aided by recently developed computer aided design tools proceeds by trial and error and its success often depends heavily on the experience of the loop-shaper. Thus for the novice and First time QFT user, there is a genuine need for an automatic loop-shaping tool to generate a first-cut solution. In this paper, we approach the automatic QFT loop-shaping problem by using an algorithm involving Linear Programming (LP) techniques and Genetic Algorithm (GA).

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A Minimum Crosstalk Wire Spacing Method by Linear Programming (선형프로그래밍에 의한 최소 혼신 배선간 간격조정방법)

  • 전재한;임종석
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.40 no.11
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    • pp.62-72
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    • 2003
  • This paper deals with a crosstalk minimization method by wire spacing. The suggested method uses linear programming method and consider crosstalk of both horizontal segments and vertical segments. In this paper, we suggest a method which can predict the coupling length between vertical segments in the final routing result using longest path algorithm. By the suggested method, we can make LP problem without integer variable. Therefore, it is much faster to solve the problem. In the case of crosstalk optimization, the suggested method optimized peak crosstalk 11.2%, and 3% total crosstalk more than wire perturbation method. The execution time of the suggested method is as fast as it takes 11 seconds when Deutsch is optimized.

An Application of Linear Programming to Multiple-Use Forest Management Planning (다목적(多目的) 산림경영계획(山林經營計劃)을 위한 선형계획법(線型計劃法)의 응용(應用))

  • Park, Eun Sik;Chung, Joo Sang
    • Journal of Korean Society of Forest Science
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    • v.88 no.2
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    • pp.273-281
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    • 1999
  • In this study, linear programming (LP) was applied to solving for optimal harvesting schedules of multiple-use forest management in Mt. Kari area managed by Chunchun National Forest Station. Associated with the geographic characteristics, the study area was classified into 4 large management units or watersheds and simultaneously applied were the site-specific levels of management constraints : nondeclining yield, initial cut for existing stands, % cut area, the volume of soil erosion, timber production and carbon storage, ending inventory condition and % area species selection for regeneration. The problem was formulated using both Model I and Model II techniques. In this paper, the formulations are presented and the results of the optimal solutions are discussed for comparison purposes.

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Credit Score Modelling in A Two-Phase Mathematical Programming (두 단계 수리계획 접근법에 의한 신용평점 모델)

  • Sung Chang Sup;Lee Sung Wook
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.1044-1051
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    • 2002
  • This paper proposes a two-phase mathematical programming approach by considering classification gap to solve the proposed credit scoring problem so as to complement any theoretical shortcomings. Specifically, by using the linear programming (LP) approach, phase 1 is to make the associated decisions such as issuing grant of credit or denial of credit to applicants. or to seek any additional information before making the final decision. Phase 2 is to find a cut-off value, which minimizes any misclassification penalty (cost) to be incurred due to granting credit to 'bad' loan applicant or denying credit to 'good' loan applicant by using the mixed-integer programming (MIP) approach. This approach is expected to and appropriate classification scores and a cut-off value with respect to deviation and misclassification cost, respectively. Statistical discriminant analysis methods have been commonly considered to deal with classification problems for credit scoring. In recent years, much theoretical research has focused on the application of mathematical programming techniques to the discriminant problems. It has been reported that mathematical programming techniques could outperform statistical discriminant techniques in some applications, while mathematical programming techniques may suffer from some theoretical shortcomings. The performance of the proposed two-phase approach is evaluated in this paper with line data and loan applicants data, by comparing with three other approaches including Fisher's linear discriminant function, logistic regression and some other existing mathematical programming approaches, which are considered as the performance benchmarks. The evaluation results show that the proposed two-phase mathematical programming approach outperforms the aforementioned statistical approaches. In some cases, two-phase mathematical programming approach marginally outperforms both the statistical approaches and the other existing mathematical programming approaches.

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A Scheme of Preventing Product Shortage for Die Casting Scheduling (다이캐스팅 스케줄링의 결품 방지 기법)

  • Park, Yong-Kuk;Yang, Jung-Min
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.12 no.4
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    • pp.1565-1574
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    • 2011
  • Scheduling of die casting is a procedure of determining quantities of cast products so as to optimize a predetermined performance criterion. This paper presents a novel scheme of preventing product shortage raised by defective castings when die casting scheduling is applied to real casting operations. The previously developed linear programming (LP) model for die casting scheduling maximizes the average efficiency of melting furnaces in regard of the usage of molten alloy. However, the LP model is not able to cope with the problem of defective products occurring in the casting process. The proposed scheme is that whenever defective products are found in a shift, the foundryman produces additional cast products using the residue of molten alloy left at the end of the next shift. Neither the calculated amount of molten alloy nor the scheduling result of the LP model does not have to be altered for this method. The simulation result demonstrates the superiority and applicability of the newly proposed scheme.

Load-Balanced One-hop Overlay Multipath Routing with Path Diversity

  • Liao, Jianxin;Tian, Shengwen;Wang, Jingyu;Li, Tonghong;Qi, Qi
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.8 no.2
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    • pp.443-461
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    • 2014
  • Overlay routing has emerged as a promising approach to improve reliability and efficiency of the Internet. For one-hop overlay source routing, when a given primary path suffers from the link failure or performance degradation, the source can reroute the traffic to the destination via a strategically placed relay node. However, the over-heavy traffic passing through the same relay node may cause frequent package loss and delay jitter, which can degrade the throughput and utilization of the network. To overcome this problem, we propose a Load-Balanced One-hop Overlay Multipath Routing algorithm (LB-OOMR), in which the traffic is first split at the source edge nodes and then transmitted along multiple one-hop overlay paths. In order to determine an optimal split ratio for the traffic, we formulate the problem as a linear programming (LP) formulation, whose goal is to minimize the worse-case network congestion ratio. Since it is difficult to solve this LP problem in practical time, a heuristic algorithm is introduced to select the relay nodes for constructing the disjoint one-hop overlay paths, which greatly reduces the computational complexity of the LP algorithm. Simulations based on a real ISP network and a synthetic Internet topology show that our proposed algorithm can reduce the network congestion ratio dramatically, and achieve high-quality overlay routing service.

Scheduling of Die Casting Processes Considering Power Usage (전력 사용을 고려한 다이캐스팅 공정의 스케줄링)

  • Yang, Jung-Min;Park, Yong-Kuk
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.8
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    • pp.3358-3365
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    • 2012
  • This paper presents a scheduling scheme for die casting processes considering power usage. The scheduling problem of a shift-based die casting process is represented by a linear programming (LP) model that maximizes the average efficiency of melting furnaces in regard of the usage of molten alloy, where the product quantities of each shift are used as primary variables. In this research, we propose a novel LP model that considers power usage of foundries. The developed LP model can derive product plans in which the expended power of a casting shift does not exceed a prescribed limit, while optimizing the efficiency of alloy usage. The simulation result of a case study demonstrates the superiority and applicability of the proposed scheme. This paper serves as a basic research on the role of foundries as an intelligent costumer in smart grid environment where the limit of power usage should be fulfilled.