Bandit-based Variable Fixing for Binary Optimization on GPU Parallel Computing

Abstract

This paper explores whether reinforcement learning is capable of enhancing metaheuristics for the quadratic unconstrained binary optimization (QUBO), which have recently attracted attention as a solver for a wide range of combinatorial optimization problems. In particular, we introduce a novel approach called the bandit-based variable fixing (BVF). The key idea behind BVF is to regard an execution of an arbitrary metaheuristic with a variable fixed as a play of a slot machine. Thus, BVF explores variables to fix with the maximum expected reward, and executes a metaheuristic at the same time. The bandit-based approach is then extended to fix multiple variables. To accelerate solving multi-armed bandit problem, we implement a parallel algorithm for BVF on a GPU. Our results suggest that our proposed BVF enhances original metaheuristics.