An Optimal Path Design Taking Advantage of Hierarchical Structure of Problem

概要

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Optimal path design is a problem that is considered to have wide range of applications. In this study, we deal with a path design problem of a pattern that consists of a number of small pattern elements; a pattern consisting of characters or symbols is a typical example. In such a case, we can naturally introduce a kind of hierarchical structure to the problem. We develop an approach to this type of path design problem that takes advantage of the hierarchical structure. In order to avoid the degradation of the optimality of the solution due to the separation of the problem by means of the introduction of hierarchical layers, we utilize an abstraction of the paths of the small pattern elements that make up the entire pattern. A local optimization approach in order to reduce the computational cost is also proposed. Path design problems of patterns consisting of alphabet character patterns are dealt with as examples; the applicability and the performance of the proposed optimal path design approach are discussed.