| Summary: | 博士 === 國立臺灣科技大學 === 工業管理系 === 90 === Geometric algorithms can be used to solve research problems modeled by geometric means. In this research, geometric characterization is used for solving geometric problems appeared in areas such as circularity assessment, the categorization of defects, multidimensional clusters, multidimensional rotation, facility layout and scaffold layout problems.
The first class of problems is solved with the shape classification. For the circularity measurement in three dimensions, the characterization of oblique of cylinder is considered, and a compensation procedure is therefore developed for solving the circularity measurement problems where the cylinder is oblique. After the compensation procedure, the compensated measured point can be used for measuring circularity. Thus, the probability of rejecting in-tolerance product will decrease. For the problem of categorization of defective aluminum foils, the properties of convex polygon are used to determine the defective belongs to what kind of the defectives.
The second class of problems is solved in the higher dimensional space. For a cluster of points close to a line problem, a scan-line approach is developed to find a cluster of points close to a line when data points are displayed in the parallel coordinate system. For the N-dimensional rotation problem, orthonormal matrix is used to translate the rotation problem into a dealing with N(N+1)/2 variables problem. Finally, the Simulated Annealing (SA) is used to find a satisfactory N-dimension rotation.
The third class of problems is solved with the aid of geometric patterns. For the facility problem, the combination of Multidimensional Scaling (MDS), Bay structure and SA is used to construct a satisfactory layout. First, MDS is used to compute the relative position of facilities in two-dimensions, and bay structure is used to derive the layout. Finally, SA is used to search the rotation degree of MDS and construct different bay structure in order to derive a satisfactory layout. For the scaffold layout problem, the profile of building is analyzed under some assumptions, and a sequence analytic approach is developed to derive the scaffold layout.
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