A novel design update framework for topology optimization with quantum annealing: Application to truss and continuum structures

TL;DR

This paper introduces a new topology optimization framework that integrates quantum annealing for design updates, demonstrating improved efficiency and comparable optimality for truss and continuum structures.

Contribution

It presents a novel quantum annealing-based design updater for topology optimization, formulated as a QUBO model, applicable to both truss and continuum structures.

Findings

Quantum annealing reduces optimization time compared to simulated annealing.

The framework achieves topologies similar to benchmark solutions.

Applicable to 2D and 3D continuum structures.

Abstract

This paper presents a novel design update strategy for topology optimization, as an iterative optimization. The key contribution lies in incorporating a design updater concept with quantum annealing, applicable to both truss and continuum structures. To align with density-based approaches in topology optimization, these updaters are formulated through a multiplicative relationship to represent the design material and serve as design variables. Specifically, structural analysis is conducted on a classical computer using the finite element method, while quantum annealing is utilized for topology updates. The primary objective of the framework is to minimize compliance under a volume constraint. An encoding formulation for the design variables is derived, and the penalty method along with a slack variable is employed to transform the inequality volume constraint. Subsequently, the optimization problem for determining the updater is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. To demonstrate its performance, the developed design framework is tested on different computing platforms to perform design optimization for truss structures, as well as 2D and 3D continuum structures. Numerical results indicate that the proposed framework successfully finds optimal topologies similar to benchmark results. Furthermore, the results show the advantage of reduced time in finding an optimal design using quantum annealing compared to simulated annealing.