• East Asian mathematical journal
• /
• v.31 no.3
• /
• pp.371-377
• /
• 2015

We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

• CDE review
• /
• v.3 no.2
• /
• pp.89-92
• /
• 1997

이 글에서 소개하는 topology optimization은 structural optimization의 한 분야로서 최근 10여년 동안 급격하게 발전되어 온 분야이다. Structural optimization은 오랜 역사(일반적으로 최초의 structural optimization은 17세기 Galileo에 의하여 되어졌다고 받아들임)를 가지고 발달되어 왔음에도 불구하고 아직도 최적화 방법론과 응용 관점에서 빠르게 발전되고 있다. 이 분야는 사회적인 요구(한정된 자원과 에너지, 안전도, 환경문제)와 컴퓨터 관련 학문(고성능 컴퓨터, computational geometry, finite element method)의 발달에 힘입어 최근 30년간 많은 진전이 있었다.

• East Asian mathematical journal
• /
• v.37 no.5
• /
• pp.543-551
• /
• 2021

Recently, semidefinite optimization problems have been intensively studied since many optimization problem can be changed into the problems and the the problems are very computationable. In this paper, we consider a semidefinite linear vector optimization problem (VP) and we establish the optimality theorems for (VP), which holds without any constraint qualification.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2008.03a
• /
• pp.130-135
• /
• 2008

An aerodynamic optimization design process of multistage axial turbine is presented in this article: first, applying quasi-three dimensional(Q3D) design methods to conduct preliminary design and then adopting modern optimization design methods to implement multistage local optimization. Quasi-three dimensional(Q3D) design methods, which mainly refer to S2 flow surface direct problem calculation, adopt the S2 flow surface direct problem calculation program of Harbin Institute of Technology. Multistage local optimization adopts the software of Numeca/Design3D, which jointly adopts genetic algorithm and artificial neural network. The major principle of the methodology is that the successive design evaluation is performed by using an artificial neural network instead of a flow solver and the genetic algorithms may be used in an efficient way. Flow computation applies three-dimensional viscosity Navier Stokes(N-S) equation solver. Such optimization process has three features: (i) local optimization based on aerodynamic performance of every cascade; (ii) several times of optimizations being performed to every cascade; and (iii) alternate use of coarse grid and fine grid. Such process was applied to optimize a three-stage axial turbine. During the optimization, blade shape and meridional channel were respectively optimized. Through optimization, the total efficiency increased 1.3% and total power increased 2.4% while total flow rate only slightly changed. Therefore, the total performance was improved and the design objective was achieved. The preliminary design makes use of quasi-three dimensional(Q3D) design methods to achieve most reasonable parameter distribution so as to preliminarily enhance total performance. Then total performance will be further improved by adopting multistage local optimization design. Thus the design objective will be successfully achieved without huge expenditure of manpower and calculation time. Therefore, such optimization design process may be efficiently applied to the aerodynamic design optimization of multistage axial turbine.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.31 no.11
• /
• pp.1059-1068
• /
• 2007

Nonlinear response structural optimization is performed using equivalent loads (NROEL). Nonlinear response optimization is extremely cost because many nonlinear analyses are required. In NROEL, the external loads are transformed 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 field of linear analysis as that of nonlinear analysis. The primitive from of theory has been published. In this research, the theory is investigated with large scale example problems. Four examples are solved by using NROEL. Conventional optimization with sensitivity analysis using the finite difference method (FDM) is also applied to the same examples. Moreover, response surface optimization method is applied to the last two examples. The results of the optimizations are compared. In nonlinear response optimization of large scale problems, hundreds (or even thousands) of nonlinear analyses are expected to satisfy the convergence criteria. However, in nonlinear response optimization using equivalent loads, only tens of nonlinear analyses are required. The results are discussed and the usefulness of NROEL is presented.

• Journal of computational fluids engineering
• /
• v.11 no.2 s.33
• /
• pp.19-24
• /
• 2006

A research to evaluate the efficiency of design optimization was carried out for aerodynamic design optimization problem in distributed computing environment. The aerodynamic analyses which take most of computational work during design optimization were divided into several jobs and allocated to associated PC clients through network. This is not a parallel process based on domain decomposition in a single analysis rather than a simultaneous distributed-analyses using network-distributed computers. GBOM(gradient-based optimization method), SAO(Sequential Approximate Optimization) and RSM(Response Surface Method) were implemented to perform design optimization of transonic airfoils and evaluate their efficiencies. dimensional minimization followed by direction search involved in the GBOM was found an obstacle against improving efficiency of the design process in the present distributed computing system. The SAO was found fairly suitable for the distributed computing environment even it has a handicap of local search. The RSM is apparently the most efficient algorithm in the present distributed computing environment, but additional trial and error works needed to enhance the reliability of the approximation model deteriorate its efficiency from the practical point of view.

• Journal of Mechanical Science and Technology
• /
• v.15 no.8
• /
• pp.1143-1155
• /
• 2001

In order to reduce the expensive CPU time for design sensitivity analysis in dynamic response optimization, this study introduces the design sensitivities approximated within estimated confidence radius in dynamic response optimization with ALM method. The confidence radius is estimated by the linear approximation with Hessian of quasi-Newton formula and qualifies the approximate gradient to be validly used during optimization process. In this study, if the design changes between consecutive iterations are within the estimated confidence radius, then the approximate gradients are accepted. Otherwise, the exact gradients are used such as analytical or finite differenced gradients. This hybrid design sensitivity analysis method is embedded in an in-house ALM based dynamic response optimizer, which solves three typical dynamic response optimization problems and one practical design problem for a tracked vehicle suspension system. The optimization results are compared with those of the conventional method that uses only exact gradients throughout optimization process. These comparisons show that the hybrid method is more efficient than the conventional method. Especially, in the tracked vehicle suspension system design, the proposed method yields 14 percent reduction of the total CPU time and the number of analyses than the conventional method, while giving similar optimum values.

• Journal of computational fluids engineering
• /
• v.21 no.3
• /
• pp.39-47
• /
• 2016

We conducted a multi-stage optimization to secure the desired performance of a centrifugal fan for home appliance in an early stage of product development. In optimization, the static pressure at the outlet of the fan is chosen as an objective function that is to be maximized, providing the required flow rate at the operating point of the fan. The optimization procedure begins with parameters for an initial baseline fan design. The baseline design is optimized by using a commercial optimization package. Accordingly, the corresponding blade models with a set of geometrical parameters are generated. Flow through a fan is simulated by solving the Reynolds-averaged Navier-Stokes equations. A multi-stage optimization scheme is employed to determine the family of optimum values for the parameters, leading to the pressure increase at the outlet of the fan. To validate the numerically obtained optimal design parameters, we fabricated the three types of fans using rapid prototyping and assessed the performance using a fan tester. Experimental results show that the design parameters at each stage satisfy the goal of optimization. The multi-stage optimization process turned out to be a useful tool in the development of a centrifugal fan.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.2
• /
• pp.268-283
• /
• 2016

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet new market demands while keeping the development time and cost to a minimum. Many researchers have studied the derivative design process, but these research efforts consider baseline and derivative designs together, while using the whole set of design variables. Therefore, an efficient process that can reduce cost and time for aircraft derivative design is needed. In this research, a more efficient design process is proposed which obtains global changes from local changes in aircraft design in order to develop aircraft derivatives efficiently. Sensitivity analysis was introduced to remove unnecessary design variables that have a low impact on the objective function. This prevented wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, uncertainty from the fidelity of analysis tools was considered in design optimization to increase the probability of optimization results. The Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were proposed to handle the uncertainty in aircraft conceptual design optimization. In this paper, Collaborative Optimization (CO) based framework with RBDO and PBDO was implemented to consider uncertainty. The proposed method was applied for civil jet aircraft derivative design that increases cruise range and the number of passengers. The proposed process provided deterministic design optimization, RBDO, and PBDO results for given requirements.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.7 no.1
• /
• pp.142-156
• /
• 2015

A new method for ship Inner Shell optimization, which is called Parametric Inner Shell Optimization Method (PISOM), is presented in this paper in order to improve both hull performance and design efficiency of transport ship. The foundation of PISOM is the parametric Inner Shell Plate (ISP) model, which is a fully-associative model driven by dimensions. A method to create parametric ISP model is proposed, including geometric primitives, geometric constraints, geometric constraint solving etc. The standard optimization procedure of ship ISP optimization based on parametric ISP model is put forward, and an efficient optimization approach for typical transport ship is developed based on this procedure. This approach takes the section area of ISP and the other dominant parameters as variables, while all the design requirements such as propeller immersion, fore bottom wave slap, bridge visibility, longitudinal strength etc, are made constraints. The optimization objective is maximum volume of cargo oil tanker/cargo hold, and the genetic algorithm is used to solve this optimization model. This method is applied to the optimization of a product oil tanker and a bulk carrier, and it is proved to be effective, highly efficient, and engineering practical.