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

Pouly, Marc; Koehler, Jana

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    <subfield code="a">A Modeling and Encoding Method for Relative Layout Generation and Optimization in Manufacturing</subfield>
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    <subfield code="a">&lt;p&gt;Generating optimal layouts or placements of technical components is a computationally intensive&lt;br&gt;
task. The induced optimization problems encounter very large search spaces, which are to be&lt;br&gt;
explored in a systematic or randomized fashion. Whereas many publications discuss modeling&lt;br&gt;
aspects and solution algorithms, little gets published on the actual encoding scheme used to&lt;br&gt;
represent different layouts, despite of the influence of efficient encoding schemes on the overall&lt;br&gt;
project success.&lt;/p&gt;

&lt;p&gt;In this article, we present a very compact encoding scheme and efficient encoding algorithms that&lt;br&gt;
describe layouts and placements by the relative positioning of components to each other. Horizontal&lt;br&gt;
and vertical arrangements as well as rotations of components and sub-components can be modeled&lt;br&gt;
and encoded as compact integer vectors. The manipulation of these vectors reduces to counting with&lt;br&gt;
integers, which provides a very efficient foundation for any state-based search algorithm and which&lt;br&gt;
can be easily tailored and configured to the needs of a specific application.&lt;/p&gt;

&lt;p&gt;Our encoding fits layout requirements where the relative arrangement of components takes center&lt;br&gt;
stage and specific physical layouts can be computed in a post-processing step. In particular, our&lt;br&gt;
techniques are applicable to manufacturing problems where processing orders of the components&lt;br&gt;
are predefined by the manufacturing processes.&lt;/p&gt;</subfield>
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