GPU-Accelerated Relaxed Decision Diagrams for Branch-and-Bound Optimization

Abstract

Branch-and-bound methods for combinatorial optimization rely critically on the efficient computation of strong bounds during search. Decision diagram–based optimization provides such bounds via restricted and relaxed multi-valued decision diagrams (MDDs), but compiling relaxed diagrams can become a computational bottleneck for existing solvers. We present a GPU-accelerated implementation of decision diagram–based branch-and-bound using a decoupled architecture. It separates the compilation of relaxed and restricted diagrams and coordinates them through two queues of search states. This design enables heterogeneous parallelization: restricted diagrams are compiled concurrently on CPU threads while relaxed diagrams are constructed in parallel on a GPU. The GPU implementation exploits the layered structure of decision diagrams by expanding states in parallel and performing successor generation, dominance filtering, and state merging on the GPU. Computational experiments on knapsack, maximum independent set, and Golomb ruler benchmarks demonstrate substantial performance improvements over CPU-based decision diagram solvers, including speedups of up to an order of magnitude on hard instances and the ability to solve Golomb ruler instances up to size 16.