Augmented decomposition method: Form-finding for structural equilibrium with design objectives based on alternating direction method of multipliers

Abstract Form-finding, the process of determining an equilibrated geometric configuration based on boundary and design conditions, is a key technique in design, yet no comprehensive tool has fully met the demands of practice. This paper introduces a robust and adaptable form-finding method, using a decomposition framework based on the Alternating Direction Method of Multipliers. It breaks large optimization problems into smaller, manageable subproblems, coordinating their solutions to achieve global results. The method balances Dual Decomposition and Augmented Lagrangian techniques while enforcing geometric constraints and equilibrium conditions, ensuring structural stability. Integrated into the parametric CAD environment Grasshopper, this approach enhances accessibility for designers. The paper outlines the algorithm’s mechanics and demonstrates its application through design examples. It provides performance evaluations, highlighting its capabilities and limitations. The method’s ability to combine geometric constraints with equilibrium in a flexible and yet simple to implement optimization framework represents a significant advancement in form-finding.