• Title/Summary/Keyword: 혼합 정수계획법

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Discrete Optimization of Unsymmetric Composite Laminates Using Linear Aproximation Method (선형 근사화방법을 이용한 비대칭 복합 적층평판의 이산최적화)

  • 이상근;구봉근;한상훈
    • Computational Structural Engineering
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    • v.10 no.2
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    • pp.255-263
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    • 1997
  • The optimum design of most structural systems used in practice requires considering design variables as discrete quantities. The present paper shows that the linear approximation method is very effective as a tool for the discrete optimum designs of unsymmetric composite laminates. The formulated design problem is subjected to a multiple in-plane loading condition due to shear and axial forces, bending and twisting moments, which is controlled by maximum strain criterion for each of the plys of a composite laminate. As an initial approach, the process of continuous variable optimization by FDM is required only once in operating discrete optimization. The nonlinear discrete optimization problem that has the discrete and continuous variables is transformed into the mixed integer programming problem by SLDP. In numerical examples, the discrete optimum solutions for the unsymmetric composite laminates consisted of six plys according to rotated stacking sequence were found, and then compared the results with the nonlinear branch and bound method to verify the efficiency of present method.

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A Study on the Allocation and Engagement Scheduling of Air Defense Missiles by Using Mixed Integer Programming (혼합정수계획법을 이용한 요격미사일의 할당 및 교전 일정계획에 관한 연구)

  • Lee, Dae Ryeock;Yang, Jaehwan
    • Korean Management Science Review
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    • v.32 no.4
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    • pp.109-133
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    • 2015
  • This paper considers the allocation and engagement scheduling of air defense missiles by using MIP (mixed integer programming). Specifically, it focuses on developing a realistic MIP model for a real battle situation where multiple enemy missiles are headed toward valuable defended assets and there exist multiple air defense missiles to counteract the threats. In addition to the conventional objective such as the minimization of surviving target value, the maximization of total intercept altitude is introduced as a new objective. The intercept altitude of incoming missiles is important in order to minimize damages from debris of the intercepted missiles and moreover it can be critical if the enemy warhead contains an atomic or chemical bomb. The concept of so called the time window is used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. Lastly, the model is extended to simulate the situation where the guidance radar, which guides a defense missile to its target, has the maximum guidance capacity. The initial mathematical model developed contains several non-linear constraints and a non-linear objective function. Hence, the linearization of those terms is performed before it is solved by a commercially available software. Then to thoroughly examine the MIP model, the model is empirically evaluated with several test problems. Specifically, the models with different objective functions are compared and several battle scenarios are generated to evaluate performance of the models including the extended one. The results indicate that the new model consistently presents better and more realistic results than the compared models.

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.

A-team Based Approach for Reactive Power/Voltage Control Considering Steady State Security Assessment (정태 안전성 평가를 고려한 무효전력 전압제어를 위한 A-team기반 접근법)

  • Kim, Doo-Hyun
    • Journal of the Korean Society of Safety
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    • v.11 no.2
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    • pp.150-159
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    • 1996
  • In this paper, an A-team(Asynchronous Team ) based approach for Reactive power and volage control considering static security assessment in a power system with infrastructural deficiencies is proposed. Reactive power and voltage control problem is the one of optimally establishing voltage level given several constraints such as reactive generation, voltage magnitude, line flow, and other switchable reactive power sources. It can be formulated as a mixed-integer linear programming(MILP) problem without deteriorating of solution accuracy to a certain extent. The security assessment is to estimate the relative robustness of the system in Its present state through the evaluation of data provided by security monitoring. Deterministic approach based on AC load flow calculations is adopted to assess the system security, especially voltage security. A security metric, as a standard of measurement for power system security, producting a set of discrete values rather than binary values, is employed. In order to analyze the above two problems, reactive power/voltage control problem and static security assessment problem, in an integrated fashion for real-time operations, a new organizational structure, called an A-team, is adopted. An A-team is an organization for agents which ale all autonomeus, work in parallel and communicate asynchronously, which is well-suited to the development of computer-based, multi-agent systems for operations. This A-team based approach, although it is still in the beginning stage, also has potential for handling other difficult power system problems.

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Radio Parameter Optimization for Indoor WiBro Radio Access Station (소형 실내 와이브로 기지국을 위한 무선 파라미터 최적화)

  • Han, Kwang-Hun;Na, Min-Soo;Choi, Young-Kyu;Kim, Dong-Myoung;Choi, Sung-Hyun;Han, Ki-Young;Yoon, Soon-Young
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.7A
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    • pp.776-785
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    • 2008
  • Compared with the existing cellular base station whose radio parameters are configured manually, the small base station named as self-configurable base station configures its radio parameters automatically by the central controller. When installing the self-configurable base station, it should be considered primarily that the seamless coverage for the target area is secured while the signal interference to the existing cellular service area must to be minimized. In order to achieve this, it is very important to select the correct radio parameters, e.g., transmission power and working frequency. In this work, we formulate and solve the optimization problem by using mixed integer programming to optimize the air parameter for the self-configurable base stations.

Optimization of Integrated District Heating System (IDHS) Based on the Forecasting Model for System Marginal Prices (SMP) (계통한계가격 예측모델에 근거한 통합 지역난방 시스템의 최적화)

  • Lee, Ki-Jun;Kim, Lae-Hyun;Yeo, Yeong-Koo
    • Korean Chemical Engineering Research
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    • v.50 no.3
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    • pp.479-491
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    • 2012
  • In this paper we performed evaluation of the economics of a district heating system (DHS) consisting of energy suppliers and consumers, heat generation and storage facilities and power transmission lines in the capital region, as well as identification of optimal operating conditions. The optimization problem is formulated as a mixed integer linear programming (MILP) problem where the objective is to minimize the overall operating cost of DHS while satisfying heat demand during 1 week and operating limits on DHS facilities. This paper also propose a new forecasting model of the system marginal price (SMP) using past data on power supply and demand as well as past cost data. In the optimization, both the forecasted SMP and actual SMP are used and the results are analyzed. The salient feature of the proposed approach is that it exhibits excellent predicting performance to give improved energy efficiency in the integrated DHS.

Adequacy assessment of the water supply adjustment standard for Hapcheon Dam operation in drought periods and proposal of an alternative (가뭄 기간을 대상으로 한 합천댐 용수공급 조정 기준의 가뭄대응 적절성 평가 및 대안 제시)

  • Kim, Kwanghoon;Lee, Sangho;Jin, Youngkyu
    • Proceedings of the Korea Water Resources Association Conference
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    • 2017.05a
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    • pp.491-491
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    • 2017
  • K-water에서는 가뭄으로 인한 피해를 완화시키기 위해 '댐 용수공급 조정 기준'을 만들어 전국 다목적 댐들을 대상으로 시범적으로 적용하고 있다. 그런데 가뭄 기간(2008~2009)에 대하여 합천댐의 용수공급 조정기준을 이용해 저수지를 모의운영한 결과, 이 기준은 가뭄에 효과적으로 대응하지 못할 수도 있다고 판단되었고, 그에 따라 대안 기준을 제시하고자 한다. 용수공급 조정기준은 가뭄 대응 단계를 4단계(관심, 주의, 경계, 심각)로 나누고 있으며, 순단위로 각 단계별 감량공급 실행 저수량과 감량 공급량을 제시하고 있다. 이기준을 이용한 합천댐의 모의 운영 결과, 가뭄기간동안 용수공급에 실패한 경우가 발생하였다. 이는 K-water의 합천댐 용수공급 조정 기준이 가뭄 대응에 적합하지 못할 수도 있다는 것을 의미한다. 본 연구에서 제시하고자 하는 대안은 이산화 용수 감량공급 기법에서 도출된 용수 감량공급 현 저수량 기준곡선이다. 과거 심각한 가뭄이 발생한 1994년과 1995년을 대상으로 하여 기준곡선을 도출하였으며, 각 단계별 감량공급 실행 저수량은 혼합정수계획법을 이용해 결정하였다. 또한, 이 기준곡선을 이용하여 동일한 가뭄 기간 (2008~2009)에 대해 저수지 모의운영을 실시하였다. 그 결과 K-water의 합천댐 용수공급 조정 기준을 적용한 모의운영 결과에서는 용수공급 실패가 발생한데 비해 대안으로 제시하는 기준곡선을 적용한 모의운영 결과에서는 용수공급을 실패한 경우가 없었다. 이는 대안으로 제시한 기준곡선이 K-water의 기준곡선에 비해 가뭄 대응에 보다 적합한 것을 의미한다. 그 이유로는 대안으로 제시한 기준곡선의 감량공급 실행 저수량이 댐 용수공급 조정 기준의 값들보다 커 미리 감량공급이 이루어지기 때문이다.

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A Study on the Deployment Plan of Fighter Aircraft Considering the Threat of Enemy Missiles (적 미사일 위협 고려한 전투기 전력 배치방안 연구)

  • Park, Inkyun;Ha, Yonghoon
    • Journal of the Korea Society for Simulation
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    • v.29 no.4
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    • pp.47-54
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    • 2020
  • North Korea has recently developed and deployed missiles with various ranges as asymmetrical forces. Among them, short-range ballistic missiles with improved accuracy are expected to aim at achieving tactical goals by hitting important military facilities in Korea with a small number of missiles. Damage to the air force airfields, one of North Korea's main targets of missiles attack, could limit the operation of air force fighters essential to gaining air superiority. Based on the attack by the short range ballistic missiles, the damage probability of military airfields was simulated. And as the one of the concepts of passive defense, the way to reduce the loss of combat power was studied through the changes of the air force squadrons deployment. As a result, the effective deployment plan could be obtained to reduce the amount of power loss compared to the current deployment.

An Improvement of Backhaul Transport with the Mathematical Model of Inter-Terminal Transportation Using Buffer Space (완충지역을 활용한 타부두 환적 컨테이너 운송 모형의 복화율 개선 효과 분석)

  • Park, Hyoung-Jun;Shin, Jae-Young
    • Journal of Navigation and Port Research
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    • v.46 no.3
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    • pp.236-242
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    • 2022
  • Busan Port is operated separately by a number of terminal operators, resulting in a large number of ITT (Inter-Terminal Transportation) volumes. The occurrence of ITT volume causes various problems such as additional transportation cost, empty truck trips, truck delays and terminal congestion, weakening Busan Port's competitiveness. Among them, the empty truck trip problem is a representative factor, that exacerbates the cost problem of the ITT operation at Busan Port. But the ITT backhaul rate at Busan Port remains low. To strengthen the transhipment competitiveness of Busan Port, it is necessary to increase the ITT backhaul rate. In this paper, to improve ITT backhaul rate, we present a mathematical model for maximizing backhaul transport using buffer space. And we analyzed the improving effects of backhaul transport using buffer space through experiments based on actual operating data.

Evaluating Reverse Logistics Networks with Centralized Centers : Hybrid Genetic Algorithm Approach (집중형센터를 가진 역물류네트워크 평가 : 혼합형 유전알고리즘 접근법)

  • Yun, YoungSu
    • Journal of Intelligence and Information Systems
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    • v.19 no.4
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    • pp.55-79
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    • 2013
  • In this paper, we propose a hybrid genetic algorithm (HGA) approach to effectively solve the reverse logistics network with centralized centers (RLNCC). For the proposed HGA approach, genetic algorithm (GA) is used as a main algorithm. For implementing GA, a new bit-string representation scheme using 0 and 1 values is suggested, which can easily make initial population of GA. As genetic operators, the elitist strategy in enlarged sampling space developed by Gen and Chang (1997), a new two-point crossover operator, and a new random mutation operator are used for selection, crossover and mutation, respectively. For hybrid concept of GA, an iterative hill climbing method (IHCM) developed by Michalewicz (1994) is inserted into HGA search loop. The IHCM is one of local search techniques and precisely explores the space converged by GA search. The RLNCC is composed of collection centers, remanufacturing centers, redistribution centers, and secondary markets in reverse logistics networks. Of the centers and secondary markets, only one collection center, remanufacturing center, redistribution center, and secondary market should be opened in reverse logistics networks. Some assumptions are considered for effectively implementing the RLNCC The RLNCC is represented by a mixed integer programming (MIP) model using indexes, parameters and decision variables. The objective function of the MIP model is to minimize the total cost which is consisted of transportation cost, fixed cost, and handling cost. The transportation cost is obtained by transporting the returned products between each centers and secondary markets. The fixed cost is calculated by opening or closing decision at each center and secondary markets. That is, if there are three collection centers (the opening costs of collection center 1 2, and 3 are 10.5, 12.1, 8.9, respectively), and the collection center 1 is opened and the remainders are all closed, then the fixed cost is 10.5. The handling cost means the cost of treating the products returned from customers at each center and secondary markets which are opened at each RLNCC stage. The RLNCC is solved by the proposed HGA approach. In numerical experiment, the proposed HGA and a conventional competing approach is compared with each other using various measures of performance. For the conventional competing approach, the GA approach by Yun (2013) is used. The GA approach has not any local search technique such as the IHCM proposed the HGA approach. As measures of performance, CPU time, optimal solution, and optimal setting are used. Two types of the RLNCC with different numbers of customers, collection centers, remanufacturing centers, redistribution centers and secondary markets are presented for comparing the performances of the HGA and GA approaches. The MIP models using the two types of the RLNCC are programmed by Visual Basic Version 6.0, and the computer implementing environment is the IBM compatible PC with 3.06Ghz CPU speed and 1GB RAM on Windows XP. The parameters used in the HGA and GA approaches are that the total number of generations is 10,000, population size 20, crossover rate 0.5, mutation rate 0.1, and the search range for the IHCM is 2.0. Total 20 iterations are made for eliminating the randomness of the searches of the HGA and GA approaches. With performance comparisons, network representations by opening/closing decision, and convergence processes using two types of the RLNCCs, the experimental result shows that the HGA has significantly better performance in terms of the optimal solution than the GA, though the GA is slightly quicker than the HGA in terms of the CPU time. Finally, it has been proved that the proposed HGA approach is more efficient than conventional GA approach in two types of the RLNCC since the former has a GA search process as well as a local search process for additional search scheme, while the latter has a GA search process alone. For a future study, much more large-sized RLNCCs will be tested for robustness of our approach.