Constraint Solving at Scale: Optimizing Performance in Complex Parametric Assemblies

Abstract

This study examines various geometric constraint solvers for parametric Computer-Aided Design (CAD) assembly systems, focusing on scalability, performance, and robustness in parametric environments where assembly design is highly interdependent. The current systems of CAD are highly dependent on constraint solvers to sustain the geometric and dimensional relations among parts. These solvers are efficient with small or moderately complex models, but tend to suffer a performance drop when applied to large models that contain hundreds or thousands of interdependent features. The paper is an analysis of constraint solver methods, both commercial and open-source, and compares their performance in progressively complex models. The paper discusses the scaling issues posed by tightly coupled features, in which the interrelationship between features can lead to nonlinear and even incompatible constraints, and thus may result in an unstable solver or slow convergence. This research methodology involves benchmarking a variety of solver algorithms such as Gauss-Seidel, Newton-Raphson and graph-based solvers. This will be done against a variety of simulated parametric assemblies of different complexity levels. Relevant key performance indicators, including solve time, consistency in convergence, numerical stability, and the reaction of users, are quantified. A well-structured implementation plan is devised that takes into account multi-threaded computation, partitioning of constraints, and dynamic solutions of dependencies. We use typical representative CAD datasets and synthetic models in our experimental setup to ensure the applicability of our results to a variety of industrial applications, such as the aerospace, automotive, and precision manufacturing domains, among others. Findings illustrate that the conceptual hybrid solver architecture will reduce the average solve time by up to 45 per cent compared to typical commercial solutions for assemblies with more than 500 constraints. In addition, it features constraint clustering and the use of parallel computation to promote stability in cyclic dependencies and ill-conditioned constraint networks. This method proves to be reliable, both through computational simulation and subsumption in a mid-scale CAD system, demonstrating a faster response time when editing models and regeneration. This work has three contributions: (1) a fully explored performance evaluation of existing constraint solver strategies on an industrial scale; (2) the architecture of a tuned system exploiting multi-core processing and a graph-based decomposition method; and (3) a repeatable benchmarking system to compare constraint solvers. The results have applications not only to CAD software designers but also to practitioners in fields that demand rapid, stable, and scalable efficiency in handling the constraint resolution process for complex assemblies