Non-Linear Geometric Constraints: A Graph-Based Optimization Algorithm

Abstract

This paper introduces a novel graph-based optimization algorithm specifically designed to address non-linear geometric constraints. Traditional optimization methods often struggle with complex geometric designs due to the inherent limitations of their geometric representation. This work proposes a framework leveraging graph neural networks (GNNs) to translate optimization problems into graph structures, enabling efficient and robust solution of these constraints. The algorithm's core mechanism focuses on dynamically learning optimal paths through the graph, effectively navigating and refining the geometric structure to achieve the desired outcome. We demonstrate the effectiveness of this approach through a series of illustrative examples, showcasing its ability to handle intricate geometric shapes and structural designs with significantly improved performance compared to conventional optimization techniques.