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

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On the Use of Adaptive Weights for the F-Norm Support Vector Machine

  • Bang, Sung-Wan;Jhun, Myoung-Shic
    • The Korean Journal of Applied Statistics
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    • v.25 no.5
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    • pp.829-835
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    • 2012
  • When the input features are generated by factors in a classification problem, it is more meaningful to identify important factors, rather than individual features. The $F_{\infty}$-norm support vector machine(SVM) has been developed to perform automatic factor selection in classification. However, the $F_{\infty}$-norm SVM may suffer from estimation inefficiency and model selection inconsistency because it applies the same amount of shrinkage to each factor without assessing its relative importance. To overcome such a limitation, we propose the adaptive $F_{\infty}$-norm ($AF_{\infty}$-norm) SVM, which penalizes the empirical hinge loss by the sum of the adaptively weighted factor-wise $L_{\infty}$-norm penalty. The $AF_{\infty}$-norm SVM computes the weights by the 2-norm SVM estimator and can be formulated as a linear programming(LP) problem which is similar to the one of the $F_{\infty}$-norm SVM. The simulation studies show that the proposed $AF_{\infty}$-norm SVM improves upon the $F_{\infty}$-norm SVM in terms of classification accuracy and factor selection performance.

Optimization of Multi-reservoir Operation with a Hedging Rule: Case Study of the Han River Basin (Hedging Rule을 이용한 댐 연계 운영 최적화: 한강수계 사례연구)

  • Ryu, Gwan-Hyeong;Chung, Gun-Hui;Lee, Jung-Ho;Kim, Joong-Hoon
    • Journal of Korea Water Resources Association
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    • v.42 no.8
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    • pp.643-657
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    • 2009
  • The major reason to construct large dams is to store surplus water during rainy seasons and utilize it for water supply in dry seasons. Reservoir storage has to meet a pre-defined target to satisfy water demands and cope with a dry season when the availability of water resources are limited temporally as well as spatially. In this study, a Hedging rule that reduces total reservoir outflow as drought starts is applied to alleviate severe water shortages. Five stages for reducing outflow based on the current reservoir storage are proposed as the Hedging rule. The objective function is to minimize the total discrepancies between the target and actual reservoir storage, water supply and demand, and required minimum river discharge and actual river flow. Mixed Integer Linear Programming (MILP) is used to develop a multi-reservoir operation system with the Hedging rule. The developed system is applied for the Han River basin that includes four multi-purpose dams and one water supplying reservoir. One of the fours dams is primarily for power generation. Ten-day-based runoff from subbasins and water demand in 2003 and water supply plan to water users from the reservoirs are used from "Long Term Comprehensive Plan for Water Resources in Korea" and "Practical Handbook of Dam Operation in Korea", respectively. The model was optimized by GAMS/CPLEX which is LP/MIP solver using a branch-and-cut algorithm. As results, 99.99% of municipal demand, 99.91% of agricultural demand and 100.00% of minimum river discharge were satisfied and, at the same time, dam storage compared to the storage efficiency increased 10.04% which is a real operation data in 2003.

Lifetime Maximizing Routing Algorithm for Multi-hop Wireless Networks (다중-홉 무선 네트워크 환경에서 수명 최대화를 위한 라우팅 알고리즘)

  • Lee, Keon-Taek;Han, Seung-Jae;Park, Sun-Ju
    • Journal of KIISE:Information Networking
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    • v.35 no.4
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    • pp.292-300
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    • 2008
  • In multi-hop wireless networks like Wireless Mesh Networks (WMN) and Wireless Sensor Networks (WSN), nodes often rely on batteries as their power source. In such cases, energy efficient routing is critical. Many schemes have been proposed to find the most energy efficient path, but most of them do not achieve optimality on network lifetime. Once found, the energy efficient path is constantly used such that the energy of the nodes on the path is depleted quickly. As an alternative, the approaches that dynamically change the path at run time have also been proposed. These approaches, however, involve high overhead of establishing multiple paths. In this paper, we first find an optimal multi-path routing using LP. Then we apply an approximation algorithm to derive a near-optimal solution for single-path routing. We compare the performance of the proposed scheme with several other existing algorithms through simulation.

A Study on the Forest Yield Regulation by Systems Analysis (시스템분석(分析)에 의(依)한 삼림수확조절(森林收穫調節)에 관(關)한 연구(硏究))

  • Cho, Eung-hyouk
    • Korean Journal of Agricultural Science
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    • v.4 no.2
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    • pp.344-390
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    • 1977
  • The purpose of this paper was to schedule optimum cutting strategy which could maximize the total yield under certain restrictions on periodic timber removals and harvest areas from an industrial forest, based on a linear programming technique. Sensitivity of the regulation model to variations in restrictions has also been analyzed to get information on the changes of total yield in the planning period. The regulation procedure has been made on the experimental forest of the Agricultural College of Seoul National University. The forest is composed of 219 cutting units, and characterized by younger age group which is very common in Korea. The planning period is devided into 10 cutting periods of five years each, and cutting is permissible only on the stands of age groups 5-9. It is also assumed in the study that the subsequent forests are established immediately after cutting existing forests, non-stocked forest lands are planted in first cutting period, and established forests are fully stocked until next harvest. All feasible cutting regimes have been defined to each unit depending on their age groups. Total yield (Vi, k) of each regime expected in the planning period has been projected using stand yield tables and forest inventory data, and the regime which gives highest Vi, k has been selected as a optimum cutting regime. After calculating periodic yields and cutting areas, and total yield from the optimum regimes selected without any restrictions, the upper and lower limits of periodic yields(Vj-max, Vj-min) and those of periodic cutting areas (Aj-max, Aj-min) have been decided. The optimum regimes under such restrictions have been selected by linear programming. The results of the study may be summarized as follows:- 1. The fluctuations of periodic harvest yields and areas under cutting regimes selected without restrictions were very great, because of irregular composition of age classes and growing stocks of existing stands. About 68.8 percent of total yield is expected in period 10, while none of yield in periods 6 and 7. 2. After inspection of the above solution, restricted optimum cutting regimes were obtained under the restrictions of Amin=150 ha, Amax=400ha, $Vmin=5,000m^3$ and $Vmax=50,000m^3$, using LP regulation model. As a result, about $50,000m^3$ of stable harvest yield per period and a relatively balanced age group distribution is expected from period 5. In this case, the loss in total yield was about 29 percent of that of unrestricted regimes. 3. Thinning schedule could be easily treated by the model presented in the study, and the thinnings made it possible to select optimum regimes which might be effective for smoothing the wood flows, not to speak of increasing total yield in the planning period. 4. It was known that the stronger the restrictions becomes in the optimum solution the earlier the period comes in which balanced harvest yields and age group distribution can be formed. There was also a tendency in this particular case that the periodic yields were strongly affected by constraints, and the fluctuations of harvest areas depended upon the amount of periodic yields. 5. Because the total yield was decreased at the increasing rate with imposing stronger restrictions, the Joss would be very great where strict sustained yield and normal age group distribution are required in the earlier periods. 6. Total yield under the same restrictions in a period was increased by lowering the felling age and extending the range of cutting age groups. Therefore, it seemed to be advantageous for producing maximum timber yield to adopt wider range of cutting age groups with the lower limit at which the smallest utilization size of timber could be produced. 7. The LP regulation model presented in the study seemed to be useful in the Korean situation from the following point of view: (1) The model can provide forest managers with the solution of where, when, and how much to cut in order to best fulfill the owners objective. (2) Planning is visualized as a continuous process where new strateges are automatically evolved as changes in the forest environment are recognized. (3) The cost (measured as decrease in total yield) of imposing restrictions can be easily evaluated. (4) Thinning schedule can be treated without difficulty. (5) The model can be applied to irregular forests. (6) Traditional regulation methods can be rainforced by the model.

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