Global optimal actuator placement for adaptive structures: New formulation and benchmarking

Civil structures are often overdesigned to meet safety and functionality criteria under rare, strong events. Adaptive structures, however, can modify their response through sensing and actuation to satisfy design criteria more efficiently with better material utilization, which results in lower resource consumption and associated environmental impacts. Adaptation is performed through actuators integrated into the structural layout. Several methods exist for optimal actuator placement to control displacements and internal force flow. In discrete systems like trusses and frames, actuator placement is typically a binary assignment. Most existing methods use bilevel and heuristic formulations, leading to suboptimal solutions without proving global optimality. This paper introduces a Mixed Integer Programming (MIP) method that produces global optimum solutions by optimizing both actuator placement and commands. Two objective functions are used: minimizing the number of actuators and minimizing control energy. The optimization considers structural and serviceability limits and control feasibility. An extensive benchmark compares the new formulation’s global optima with solutions from greedy, stochastic, and heuristic methods. Results show that the new method consistently produces higher-quality solutions than all other methods benchmarked in this study.