Geometrical complexity considered in the present study is characterized by a large degree of freedom in placement of constituents in a composite system. The constituent sizes are not negligibly small compared to the system's expanse, so approximations of their configurations and placement patterns by some simple equivalents are not feasible. Numerical analysis is a means to estimate heat transfer performance of the system, but a strategy is required to navigate through a vast number of possible constituent patterns to find ones that produce higher heat transfer performance. In the proposed methodology the constituent pattern is captured as a two-dimensional mosaic image of solid cells embedded in a substrate. On an image assumed as a starter, the singular-value decomposition (SVD) analysis is performed to find its (SVD) building block elements. By shuffling the building block elements variants of the starter image are created. Heat transfer analysis is performed on sample systems that are picked up from the ensemble of variants. Using the Taguchi method and through a genetic algorithm-type reasoning, those element arrangements that do not significantly affect the heat transfer performance are weeded out. The methodology is demonstrated on the cases of heat conduction through composite slabs. (C) 2003 Elsevier Science Ltd. All rights reserved.