An extended pattern search algorithm is presented for the placement of shapeable components within a product layout. The algorithm is applied to an automobile transmission layout taking into account the shapeability of the components. Overlap between components is allowed and penalized during the optimization process. Shapeable octrees are used to evaluate the amount of overlap between pairs of components. The algorithm minimizes the connection cost in addition to optimizing the position and size of the components. A shapeable component has a defined geometry, but its size may vary within limits. The size of clutches in a transmission is determined by the torque capacity requirement, thermal requirement, and gain requirement. Under a given load, the size of a clutch satisfying a set of functional requirements is related to its location in the transmission assembly, making it necessary to design the clutches on the fly while laying out the components.

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