Numerical Scheme with Convergence Analysis and Error Estimate for Variable Order Weakly Singular Integro-Differential Equation

Abstract

Topology optimization and quantum computing have evolved rapidly over the past three decades. Previous topological optimum design methods suffered from financial burden and mathematical complexity. To overcome these shortcomings, a modified quantum-inspired evolutionary algorithm-based topology optimization method is proposed. This nested approach combines the classic solid isotropic microstructure with the penalization method and the double chains quantum genetic algorithm to establish an integral topology optimization framework. The former is utilized to determine the search direction of design variable updating. Meanwhile, the latter ensures abundant search diversity. The validity and feasibility of the developed methodology are eventually demonstrated by several application examples. The results indicate that the proposed optimization framework is independent of initial values and can lead to optimized structures. In addition, it will be more appropriate and effective if this strategy is deployed on a quantum computer in the future.