Generating optimal layouts or placements of technical components is a computationally intensive task. The induced optimization problems encounter very large search spaces, which are to be explored in a systematic or randomized fashion. Whereas many publications discuss modeling aspects and solution algorithms, little gets published on the actual encoding scheme used to represent different layouts, despite of the influence of efficient encoding schemes on the overall project success. In this article, we present a very compact encoding scheme and efficient encoding algorithms that describe layouts and placements by the relative positioning of components to each other. Horizontal and vertical arrangements as well as rotations of components and sub-components can be modeled and encoded as compact integer vectors. The manipulation of these vectors reduces to counting with integers, which provides a very efficient foundation for any state-based search algorithm and which can be easily tailored and configured to the needs of a specific application. Our encoding fits layout requirements where the relative arrangement of components takes center stage and specific physical layouts can be computed in a post-processing step. In particular, our techniques are applicable to manufacturing problems where processing orders of the components are predefined by the manufacturing processes.

+ Sprache: eng + Reihe: Technical Report, 1/2017