Towards Quantum Accelerated Large-scale Topology Optimization

Abstract

We present a new method that efficiently solves TO problems and provides a practical pathway to leverage quantum computing to exploit potential quantum advantages. This work targets on large-scale, multi-material TO challenges for three-dimensional (3D) continuum structures, beyond what have been addressed in prior studies. Central to this new method is the modified Dantzig-Wolfe (MDW) decomposition, which effectively mitigates the escalating computational cost associated with using classical Mixed-Integer Linear Programming (MILP) solvers to solve the master problems involved in TO, by decomposing the MILP into local and global sub-problems. Evaluated on 3D bridge designs, our classical implementation achieves comparable solution quality to state-of-the-art TO methods while reducing computation time by orders of magnitude. It also maintains low runtimes even in extreme cases where classical MILP solvers fail to converge, such as designs involving over 50 million variables. The computationally intensive local sub-problems, which are essentially Binary Integer Programming (BIP) problems, can potentially be accelerated by quantum computing via their equivalent Quadratic Unconstrained Binary Optimization (QUBO) formulations. Enabled by the MDW decomposition, the resulting QUBO formulation requires only sparse qubit connectivity and incurs a QUBO construction cost that scales linearly with problem size, potentially accelerating BIP sub-problem solutions by an additional order of magnitude. All observed and estimated speedups become increasingly significant with larger problem sizes and when moving from single-material to multi-material designs. This suggests that this new method, along with quantum computing, will play an increasingly valuable role in addressing the scale and complexity of real-world TO applications.