• 제목/요약/키워드: Linear Optimization

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DUALITY FOR LINEAR CHANCE-CONSTRAINED OPTIMIZATION PROBLEMS

  • Bot, Radu Ioan;Lorenz, Nicole;Wanka, Gert
    • 대한수학회지
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    • 제47권1호
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    • pp.17-28
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    • 2010
  • In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

위상최적설계를 이용한 리니어 모터의 설계 (Linear Motor Design by using Topology Optimization)

  • 이헌;강제남;왕세명;홍언표;박경배
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2003년도 하계학술대회 논문집 B
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    • pp.843-845
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    • 2003
  • In this paper, the design of the outer core which is one part of the linear motor is investigated by using the topology optimization and FEM. The object functions are to reduce the outer core area of the linear motor with the maximum magnetic energy in airgap. For topology optimization, the finite element model is made through the result of ANSYS, and the sensitivity calculation is done using ANSTOP(developed general software for topology optimization of electromagnetics). In ANSTOP, the optimization routine is implemented using SLP in DOT and the ANSYS is used as a function solver.

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헬리콥터 주로터 블레이드 동적밸런싱 시험을 위한 조절변수 최적화 연구 (A Study on Adjustment Optimization for Dynamic Balancing Test of Helicopter Main Rotor Blade)

  • 송근웅;최종수
    • 한국소음진동공학회논문집
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    • 제26권6_spc호
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    • pp.736-743
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    • 2016
  • This study describes optimization methods for adjustment of helicopter main rotor tracking and balancing (RTB). RTB is a essential process for helicopter operation and maintenance. Linear and non-linear models were developed with past RTB test results for estimation of RTB adjustment. Then global and sequential optimization methods were applied to the each of models. Utilization of the individual optimization method with each model is hard to fulfill the RTB requirements because of different characteristics of each blade. Therefore an ensemble model was used to integrate every estimated adjustment result, and an adaptive method was also applied to adjustment values of the linear model to update for next estimations. The goal of this developed RTB adjustment optimization program is to achieve the requirements within 2 run. Additional tests for comparison of weight factor of the ensemble model are however necessary.

한계상태를 고려한 구조물의 최적화에 관한 연구 (A Study on Optimization of Structure with Limit State Constraints)

  • 김기대
    • 한국산업융합학회 논문집
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    • 제7권2호
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    • pp.181-186
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    • 2004
  • This study presents a optimization of structure, in which constraints contain the conditions of stress and serviceability, while the sequential linear programming method (SLP) is used as a rational approach. The optimum design results contained on the limit state constraints are compared with those obtained by the only stress and ministry of construction enacted standard plans. A simple slab bridge is analysed numerically for illustration of the structural optimization. It may be asserted that serviceability constraints is very important to a structure design.

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등가정하중을 사용한 선형 동적반응 위상최적설계 기초연구 (Preliminary Study on Linear Dynamic Response Topology Optimization Using Equivalent Static Loads)

  • 장환학;이현아;박경진
    • 대한기계학회논문집A
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    • 제33권12호
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    • pp.1401-1409
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    • 2009
  • All the forces in the real world act dynamically on structures. Design and analysis should be performed based on the dynamic loads for the safety of structures. Dynamic (transient or vibrational) responses have many peaks in the time domain. Topology optimization, which gives an excellent conceptual design, mainly has been performed with static loads. In topology optimization, the number of design variables is quite large and considering the peaks is fairly costly. Topology optimization in the frequency domain has been performed to consider the dynamic effects; however, it is not sufficient to fully include the dynamic characteristics. In this research, linear dynamic response topology optimization is performed in the time domain. First, the necessity of topology optimization to directly consider the dynamic loads is verified by identifying the relationship between the natural frequency of a structure and the excitation frequency. When the natural frequency of a structure is low, the dynamic characteristics (inertia effect) should be considered. The equivalent static loads (ESLs) method is proposed for linear dynamic response topology optimization. ESLs are made to generate the same response field as that from dynamic loads at each time step of dynamic response analysis. The method was originally developed for size and shape optimizations. The original method is expanded to topology optimization under dynamic loads. At each time step of dynamic analysis, ESLs are calculated and ESLs are used as the external loads in static response topology optimization. The results of topology optimization are used to update the design variables (density of finite elements) and the updated design variables are used in dynamic analysis in a cyclic manner until the convergence criteria are satisfied. The updating rules and convergence criteria in the ESLs method are newly proposed for linear dynamic response topology optimization. The proposed updating rules are the artificial material method and the element elimination method. The artificial material method updates the material property for dynamic analysis at the next cycle using the results of topology optimization. The element elimination method is proposed to remove the element which has low density when static topology optimization is finished. These proposed methods are applied to some examples. The results are discussed in comparison with conventional linear static response topology optimization.

Topology Optimization of Linear Motor for Rope-less Elevator by Using Density Method and ON/OFF Method

  • Okamoto Yoshifumi;Takahashi Norio
    • KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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    • 제5B권3호
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    • pp.233-237
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    • 2005
  • The reduction of the ripple of driving force is especially required for the practical utilization of linear synchronous motor for rope-less elevator. In this paper, the magnetic region of the linear motor is optimized by using topology optimization techniques (density method and ON/OFF method) in order to reduce the ripple of driving force. The optimal results of both methods are compared, and useful information for the optimal design of linear motor is obtained.

Design Optimization of Linear Synchronous Motors for Overall Improvement of Thrust, Efficiency, Power Factor and Material Consumption

  • Vaez-Zadeh, Sadegh;Hosseini, Monir Sadat
    • Journal of Power Electronics
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    • 제11권1호
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    • pp.105-111
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    • 2011
  • By having accurate knowledge of the magnetic field distribution and the thrust calculation in linear synchronous motors, assessing the performance and optimization of the motor design are possible. In this paper, after carrying out a performance analysis of a single-sided wound secondary linear synchronous motor by varying the motor design parameters in a layer model and a d-q model, machine single- and multi-objective design optimizations are carried out to improve the thrust density of the motor based on the motor weight and the motor efficiency multiplied by its power factor by defining various objective functions including a flexible objective function. A genetic algorithm is employed to search for the optimal design. The results confirm that an overall improvement in the thrust mean, efficiency multiplied by the power factor, and thrust to the motor weight ratio are obtained. Several design conclusions are drawn from the motor analysis and the design optimization. Finally, a finite element analysis is employed to evaluate the effectiveness of the employed machine models and the proposed optimization method.

등가하중을 이용한 원자로 핵연료봉 지지격자 스프링의 비선형 응답 구조 최적설계 (Nonlinear Response Structural Optimization of a Nuclear Fuel Rod Spacer Grid Spring Using the Equivalent Load)

  • 김도원;이현아;송기남;김용일;박경진
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2007년도 춘계학술대회A
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    • pp.694-699
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    • 2007
  • The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring,nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). In NROEL, the external loads are teansformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response no EL. The objective function is defined by minimizing the maximum stress in the spring while is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.

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An Algorithm for Optimizing over the Efficient Set of a Bicriterion Linear Programming

  • Lee, Dong-Yeup
    • 한국경영과학회지
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    • 제20권1호
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    • pp.147-158
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    • 1995
  • In this paper a face optimization algorithm is developed for solving the problem (P) of optimizing a linear function over the set of efficient solution of a bicriterion linear program. We show that problem (P) can arise in a variety of practical situations. Since the efficient set is in general a nonoconvex set, problem (P) can be classified as a global optimization problem. The algorithm for solving problem (P) is guaranteed to find an exact optimal or almost exact optimal solution for the problem in a finite number of iterations. The algorithm can be easily implemented using only linear programming method.

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FLEXIBLE OPTIMIZATION MODEL FOR LINEAR SCHEDULING PROBLEMS

  • Shu-Shun Liu;Chang-Jung Wang
    • 국제학술발표논문집
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    • The 1th International Conference on Construction Engineering and Project Management
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    • pp.802-807
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    • 2005
  • For linear projects, it has long been known that resource utilization is important in improving work efficiency. However, most existing scheduling techniques cannot satisfy the need for solving such issues. This paper presents an optimization model for solving linear scheduling problems involving resource assignment tasks. The proposed model adopts constraint programming (CP) as the searching algorithm for model formulation, and the proposed model is designed to optimize project total cost. Additionally, the concept of outsourcing resources is introduced here to improve project performance.

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