An Efficient Quantum Approximate Optimization Algorithm with Fixed Linear Ramp Schedule for Truss Structure Optimization

TL;DR

A novel structural optimization framework based on quantum variational circuits, in which the multiplier acting on the cross-sectional area of each rod in a truss structure as an updater is used as a design variable, highlighting the feasibility and applicability potential of quantum computing in advancing engineering design and optimization.

Abstract

This study proposes a novel structural optimization framework based on quantum variational circuits, in which the multiplier acting on the cross-sectional area of each rod in a truss structure as an updater is used as a design variable. Specifically, we employ a classical processor for structural analysis with the finite element method, and the Quantum Approximate Optimization Algorithm (QAOA) is subsequently performed to update the cross-sectional area so that the compliance is minimized. The advantages of this framework can be seen in three key aspects. First, by defining design variables as multipliers, rather than simply reducing the design variable to a binary candidate of inclusion or exclusion (corresponding to qubit states, ``0" and ``1"), it provides greater flexibility in adjusting the cross-sectional area of the rod at each iteration of the optimization process. Second, the multipliers acting on rods are encoded with on-off encoding, eliminating additional constraints in the convergence judgement. As a result, the objective function is in a simple format, enabling efficient optimization using QAOA.Third, a fixed linear ramp schedule (FLRS) for variational parameter setting bypasses the classical optimization process, thereby improving the operational efficiency of the framework. In the two structural cases investigated in this study, the proposed approach highlights the feasibility and applicability potential of quantum computing in advancing engineering design and optimization. Numerical experiments have demonstrated the effectiveness of this framework, providing a firm foundation for future research on quantum-assisted optimization methods in engineering fields.

Figures (10)

• Figure 1: Architecture of QAOA circuit.
• Figure 2: 2D truss structures.
• Figure 3: Iterative updating scheme.
• Figure 4: Flowchart for the proposed framework.
• Figure 5: Variational parameter setting for FLRS.