A Permutational Boltzmann Machine with Parallel Tempering for Solving Combinatorial Optimization Problems

Boltzmann Machines are recurrent neural networks that have been used extensively in combinatorial optimization due to their simplicity and ease of parallelization. This paper introduces the Permutational Boltzmann Machine, a neural network capable of solving permutation optimization problems. We implement this network in combination with a Parallel Tempering algorithm with varying degrees of parallelism ranging from a single-thread variant to a multi-threaded system using a 64-core CPU with SIMD instructions. We benchmark the performance of this new system on Quadratic Assignment Problems, using some of the most difficult known instances, and show that our parallel system performs in excess of 100\(\times \) faster than any known dedicated solver, including those implemented on CPU clusters, GPUs, and FPGAs.