Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems

비선형계획법에서 목적함수의 상한함수를 이용한 강건최적설계

  • Received : 2013.12.12
  • Accepted : 2014.03.03
  • Published : 2014.05.01
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Abstract

In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.

강건최적설계 분야에서 목적함수의 강건성은 목적함수의 변화가 둔감한 해를 강조한다. 일반적으로 목적함수의 강건성은 설계변수나 파라미터에 대한 목적함수의 변동을 줄임으로써 달성할 수 있다. 하지만, 기존의 방법들에서는 변동에 둔감한 목적을 달성하기 위해 목적함수의 값이 희생되는 경우가 있다. 또한, 설계변수의 수가 증가할수록 비선형계획법을 이용한 강건최적설계의 수치적 계산비용은 증가한다. 본 연구에서는 상한함수를 사용한 새로운 강건성지수와 비선형계획법에서의 강건최적설계 방법을 제안한다. 또한, 제안한 방법의 효율성을 향상시키기 위하여 선형화된 함수의 상한 값을 이용한 방법도 소개한다. 이를 다양한 수학예제에 적용하고 기존의 강건성지수와 수치적 성능 비교를 통해 제안한 방법의 유용성을 검증한다. 제안한 강건성지수는 목적함수의 성능에 손실이 발생하지 않으며 효율성을 크게 향상시킬 수 있다.

Keywords

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