Design optimisation using convex programming: Towards waste-efficient building designs

A non-modular building layout is amongst the leading sources of offcut waste, resulting from a substantial amount of onsite cutting and fitting of bricks, blocks, plasterboard, and tiles. The field of design for dimensional coordination is concerned with finding an optimal configuration for non-overlapping spaces in the layout to reduce materials waste. In this article, we propose a convex optimisation-based algorithm for finding alternative floor layouts to enforce the design for dimensional coordination. At the crux of the proposed algorithm lies two mathematical models. The first is the convex relaxation model that establishes the topology of spaces within the layout through relative positioning constraints. We employed acyclic graphs to generate a minimal set of relative positioning constraints to model the problem. The second model optimises the geometry of spaces based on the modular size. The algorithm exploits aspect ratio constraints to restrict the generation of alternate layouts with huge variations. The algorithm is implemented in the BIMWaste tool for automating the design exploration process. BIMWaste is capable of investigating the degree to which designers consider dimensional coordination. We tested the algorithm over 10 completed building projects to report its suitability and accuracy. The algorithm generates competitive floor layouts for the same client intent that are likely to be tidier and more modular. More importantly, those floor layouts have improved waste performance (i.e., 8.75% less waste) due to a reduced tendency for material cutting and fitting. This study, for the first time, used convex programming for the design optimisation with a focus to reduce construction waste.