Optimal design of frame structures with mixed categorical and continuous design variables using the Gumbel–Softmax method

2024-02-24

Structural And Multidisciplinary Optimization

AI Summary

Gradient-based optimization fails in frame structural optimization due to mixed discrete cross-section types and continuous dimensional parameters. Method: This paper introduces Gumbel–Softmax reparameterization—first applied in structural optimization—to establish an end-to-end differentiable framework for hybrid variable modeling. It integrates gradient-driven joint topology/size optimization, automatic differentiation of finite element analysis, and probabilistic hybrid-variable representation, circumventing accuracy loss and computational overhead inherent in conventional enumeration or relaxation strategies. Contribution/Results: Across multiple benchmark examples, the proposed method achieves a 5.3× speedup over genetic algorithms and mixed-integer programming, improves optimal solution accuracy by 12.7%, and strictly satisfies structural safety requirements and design code constraints.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Problem

• Optimization
• Gradient-based Optimizers
• Categorical Variables

Innovation

• Gumbel-Softmax
• Gradient-based Optimization
• Structural Design