• 대한기계학회논문집A
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• 제35권8호
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• pp.921-931
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• 2011

본 연구는 B-스플라인 하이퍼볼륨을 사용하여 주어진 비정렬 데이터를 근사화하는 데이터 근사기법에 관한 것이다. 개발 구현을 위한 B-스플라인 하이퍼볼륨의 자료 구조가 기술되며 해당 메모리 크기의 측정을 통해 간결한 표현 모델임을 보인다. 제안하는 근사 기법은 두 가지 알고리즘으로 구성된다. 하나는 B-스플라인 하이퍼볼륨의 절점 벡터 결정에 관한 것이고, 다른 하나는 조정점 결정에 관한 것으로 최소자승 최소화 문제의 해를 구함으로써 얻게 된다. 여기서 구한 해는 데이터 복잡성에 의존하지 않는다. 본 연구 방식은 다양한 형태의 데이터 분포를 가지고 근사 정밀도, 메모리 사용량, 계산 시간 등의 근사화 성능(수준)을 평가한다. 더불어 기존 방법과의 비교를 통해 유용성을 보이며, 비구속 최적화 예제를 통하여 다양한 응용 분야로의 가능성을 보여준다.

• 한국CDE학회논문집
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• 제17권4호
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• 한국CDE학회논문집
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• 제15권1호
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• pp.24-32
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• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.