A GPU-Based Parallel Bound-and-Classify Method for Continuous Constraint Satisfaction Problems

Abstract

Abstract Continuous constraint satisfaction is prevalent in many science and engineering fields. When solving continuous constraint satisfaction problems, it is more advantageous for practitioners to derive all feasible regions (i.e., the solution space) rather than a limited number of solution points, since these feasible regions facilitate innovative design concept generation and design tradeoff evaluation. Several CPU-based branch-and-prune methods and geometric approximation methods have been proposed in prior research to derive feasible regions for continuous constraint satisfaction problems. However, these methods have not been extensively adopted in practice, mainly because of their high computational expense. To overcome the computational bottleneck of extant CPU-based methods, this paper introduces a GPU-based parallel bound-and-classify method to derive feasible regions for continuous constraint satisfaction problems in a reasonable computational time. Using interval arithmetic, coupled with the computational power of GPU, this method iteratively partitions the design space into many subregions and classifies these subregions as feasible, infeasible, and indeterminate regions. To visualize these classified regions in the design space, a planar visualization approach that projects all classified regions into one figure is also proposed in this paper. The GPU-based parallel bound-and-classify method and the planar visualization approach are validated through a case study of welded beam design. The case study shows that the method and the approach can solve the welded beam design problem and visualize the result effectively and efficiently. A four-step procedure for implementing the GPU-based parallel bound-and-classify method and the planar visualization approach in practice is also outlined.