• Title/Summary/Keyword: Mathematical Optimization

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Reverse-Simulation Method for Single Run Simulation Optimization (단일 실행 시뮬레이션 최적화를 위한 Reverse-Simulation 기법)

  • 이영해
    • Journal of the Korea Society for Simulation
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    • v.5 no.2
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    • pp.85-93
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    • 1996
  • Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. This objective is similar to that of optimization problems and thus, mathematical programming techniques may be applied to simulation. However, the application of mathematical programming techniques, e.g., the gradient methods, to simulation is compounded by the random nature of simulation responses and by the complexity of the statistical issues involved. In this paper, therefore, we explain the Reverse-Simulation method to optimize a simulation model in a single simulation run. First, we point the problem of the previous Reverse-Simulation method. Secondly, we propose the new algorithm to solve the previous method and show the efficiency of the proposed algorithm.

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A study on mathematical modeling by neural networks (신경회로망을 이용한 수학적 모델에 관한 연구)

  • 이영진;이권순
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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    • pp.624-627
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    • 1992
  • Mathematical modeling is majorly divided into three parts: the derivation of models, the fitting of models to data, and the simulation of data from models. This paper focuses on the parameter optimization which is necessary for the fitting of models to data. The method of simulated annealing(SA) is a technique that has recently attracted significant attention as suitable for optimization problem of very large scale. If the temperature is too high, then some of the structure created by the heuristic will be destroyed and unnecessary extra work will be done. If it is too low then solution is lost, similar to the case of a quenching cooling schedule in the SA phase. In this study, therfore, we propose a technique of determination of the starting temperature and cooling schedule for SA phase.

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SYNERGISTIC INTERACTION OF ENVIRONMENTAL TEMPERATURE AND MICROWAVES: PREDICTION AND OPTIMIZATION

  • Petin, Vladislav G.;Kim, Jin-Kyu;Kolganova, Olga I.;Zhavoronkov, Leonid P.
    • Journal of Radiation Protection and Research
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    • v.36 no.1
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    • pp.1-7
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    • 2011
  • A simple mathematical model of simultaneous combined action of environmental agents has been proposed to describe the synergistic interaction of microwave and high ambient temperature treatment on animal heating. The model suggests that the synergism is caused by the additional effective damage arising from an interaction of sublesions induced by each agent. These sublesions are considered to be ineffective if each agent is taken individually. The additional damage results in a higher body temperature increment when compared with that expected for an independent action of each agent. The model was adjusted to describe the synergistic interaction, to determine its greatest value and the condition under which it can be achieved. The prediction of the model was shown to be consistent with experimental data on rabbit heating. The model appears to be appropriate and the conclusions are valid.

HOMOGENEOUS MULTILINEAR FUNCTIONS ON HYPERGRAPH CLIQUES

  • Lu, Xiaojun;Tang, Qingsong;Zhang, Xiangde;Zhao, Cheng
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.1037-1067
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    • 2017
  • Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

Robust Capacity Planning in Network Coding under Demand Uncertainty

  • Ghasvari, Hossien;Raayatpanah, Mohammad Ali
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.9 no.8
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    • pp.2840-2853
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    • 2015
  • A major challenge in network service providers is to provide adequate resources in service level agreements based on forecasts of future demands. In this paper, we address the problem of capacity provisioning in a network subject to demand uncertainty such that a network coded multicast is applied as the data delivery mechanism with limited budget to purchase extra capacity. We address some particular type of uncertainty sets that obtain a tractable constrained capacity provisioning problem. For this reason, we first formulate a mathematical model for the problem under uncertain demand. Then, a robust optimization model is proposed for the problem to optimize the worst-case system performance. The robustness and effectiveness of the developed model are demonstrated by numerical results. The robust solution achieves more than 10% reduction and is better than the deterministic solution in the worst case.

A LARGE-UPDATE INTERIOR POINT ALGORITHM FOR $P_*(\kappa)$ LCP BASED ON A NEW KERNEL FUNCTION

  • Cho, You-Young;Cho, Gyeong-Mi
    • East Asian mathematical journal
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    • v.26 no.1
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    • pp.9-23
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    • 2010
  • In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

AN ACTIVE SET SQP-FILTER METHOD FOR SOLVING NONLINEAR PROGRAMMING

  • Su, Ke;Yuan, Yingna;An, Hui
    • East Asian mathematical journal
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    • v.28 no.3
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    • pp.293-303
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    • 2012
  • Sequential quadratic programming (SQP) has been one of the most important methods for solving nonlinear constrained optimization problems. Recently, filter method, proposed by Fletcher and Leyffer, has been extensively applied for its promising numerical results. In this paper, we present and study an active set SQP-filter algorithm for inequality constrained optimization. The active set technique reduces the size of quadratic programming (QP) subproblem. While by the filter method, there is no penalty parameter estimate. Moreover, Maratos effect can be overcome by filter technique. Global convergence property of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

Solving Mixed Strategy Equilibria of Multi-Player Games with a Transmission Congestion (다자게임 전력시장에서 송전선 혼잡시의 복합전략 내쉬균형 계산)

  • Lee, Kwang-Ho
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.55 no.11
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    • pp.492-497
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    • 2006
  • Nash Equilibrium (NE) is essential to investigate a participant's bidding strategy in a competitive electricity market. The transmission line constraints make it difficult to compute the NE due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The competition among multi-participants is modeled by a two-level hierarchical optimization problem. A mathematical programming approach is widely used in finding this equilibrium. However, there are difficulties to solving a mixed strategy NE. This paper presents two propositions to add heuristics to the mathematical programming method. The propositions are based on empirical studies on mixed strategies in numerous sample systems. Based on the propositions a new formulation is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the prepositions and the newly-formulated equations.

EXPERIMENT AND SIMULATION OF A WIND-DRIVEN REVERSE OSMOSIS DESALINATION SYSTEM

  • Park, Sang-Jin;Clark C.K. Liu
    • Water Engineering Research
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    • v.4 no.1
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    • pp.1-17
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    • 2003
  • A mathematical model was developed to simulate the performance of a prototype wind-powered reverse osmosis desalination system. The model consists of two sub-models operated in a series. The first sub-model is the wind-energy conversion sub-model, which has wind energy and feed water as its input and pressurized feed water as its output. The second sub-model is a reverse osmosis (RO) process sub-model, with pressurized feed water as its input and the flow and salinity of the product water or permeate as its output. Model coefficients were determined based on field experiments of a prototype wind powered RO desalination system of the University of Hawaii, from June to December 2001. The mathematical model developed by this study predicts the performance of wind-powered RO desalination systems under different design conditions. The system optimization is achieved using a linear programming approach. Based on the results of system optimization, a design guide is prepared, which can be used by both manufacturer and end-user of the wind-driven reverse osmosis system.

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Optimization of compression ratio in closed-loop CO2 liquefaction process

  • Park, Taekyoon;Kwak, Hyungyeol;Kim, Yeonsoo;Lee, Jong Min
    • Korean Journal of Chemical Engineering
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    • v.35 no.11
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    • pp.2150-2156
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    • 2018
  • We suggest a systematic method for obtaining the optimal compression ratio in the multi-stage closed-loop compression process of carbon dioxide. Instead of adopting the compression ratio of 3 to 4 by convention, we propose a novel approach based on mathematical analysis and simulation. The mathematical analysis prescribes that the geometric mean is a better initial value than the existing empirical value in identifying the optimal compression ratio. In addition, the optimization problem considers the initial installation cost as well as the energy required for the operation. We find that it is best to use the fifth stage in the general closed-loop type carbon dioxide multi-stage compression process.