Towards Quantum Accelerated Large-scale Topology Optimization

TL;DR

This work tackles the computational bottleneck of large-scale 3D continuum topology optimization with multiple materials by introducing the Modified Dantzig-Wolfe (MDW) decomposition within the DVTO-MT framework. MDW partitions the MILP master problem into many small, independent local binary sub-problems and a smaller global LP, dramatically reducing per-iteration cost and enabling parallel computation. The local sub-problems are formulated as QUBOs, opening the door to quantum acceleration via quantum annealing or gate-based quantum computing, with QAOA validation showing high fidelity for the tested cases. Results on large 3D bridge designs demonstrate substantial speedups over traditional MILP-based approaches, and the quantum pathway is shown to become more impactful as problem size grows, especially in multi-material designs, highlighting strong practical potential for quantum-accelerated TO in real-world applications.

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.

Figures (4)

• Figure 1: Domain setup and boundary conditions for 3D bridge design.
• Figure 2: Single-material design: The optimal topologies yield by our method with three discretization resolutions.
• Figure 3: Single-material design: The optimal topologies produced by the SIMP method with three discretization resolutions. For each topology, the left half presents the outcome after 200 iteration steps, and the right half after 400 iteration steps. The color intensity reflects the values of the design variable $\rho$ following a post-processing filter with the threshold of 0.5, where darker shades indicate values closer to 1 and lighter shades represent values closer to 0.5.
• Figure 4: Multi-material design: The optimal topologies and material selections obtained from our method at three discretization resolutions. Materials are rendered as follows: Magnesium (dark blue), Aluminum (light blue), Titanium (orange), and Stainless Steel (red).