A Modeling and Encoding Method for Relative Layout Generation and Optimization in Manufacturing

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.