Packing Optimization of Free-Form Objects in Engineering Design

Packing for engineering design involves the development and use of methods to determine the arrangement of a set of subsystems or components within some enclosure to achieve a set of objectives without violating spatial or performance constraints. Packing problems, also known as layout optimization problems are challenging because they are highly multimodal, are characterized by models that lack closed-form representations, and require expensive computational procedures. The time needed to resolve intersection calculations increases exponentially with the number of objects to be packed while the space available for the placement of these components becomes less and less available. This paper presents a multiyear research effort targeting the development of computational tools for packing optimization problems which are encountered at different stages of engineering design with special interest in automotive design. Due to increasingly realistic engineering applications, the problems feature a rising level of complexity and therefore require optimization models and approaches with growing sophistication. To be relevant to automotive design, the packing problems account for the free shape of objects and consider either their compact packing within an envelope or their noncompact packing in the presence of multiple criteria used to evaluate system performance. The packing problems are represented by single or multiobjective optimization problems (MOPs) while the solution approaches rely on evolutionary algorithms due to the level of complexity that precludes development of effective exact methods.