Frame structures are widely used in modern architecture. Building such structures requires traversing through several partially built states. The assembly sequence must be planned thoroughly, otherwise these partial states can be subject to substantial deformation due to self-weight, jeopardizing the assembly process.

As the number of pieces in the structure grows, finding an assembly sequence that minimizes intermediate deformations becomes computationally prohibitive. The authors design a new approach in which intermediary states, called landmarks, are computed in such a way that they present minimum deformation and are temporally coherent, meaning that moving from one landmark to the next does not require removing pieces. Then, each assembly sequence from one landmark to the next can be solved optimally thanks to its reduced size. These two discrete sequence planning problems are formulated as mixed integer nonlinear programs (MINLP) using topology optimization.

The Branch-and-Bound algorithm of Artelys Knitro has been used to solve the MINLP problems. The results obtained show that optimization pays out as the generated sequences induce an improvement of up to 67% on the intermediate deformations when compared to classic greedy approaches. The cutting-edge performances achieved were boosted by the quality of Artelys Knitro’s integrated heuristics in finding good primal integer solutions.

Check out the video to discover the method in motion!