Supplementing Recurrent Neural Networks with Annealing to Solve Optimization Problems

Combinatorial optimization problems can be solved by heuristic algorithms such as simulated annealing (SA) which aims to find the global minima solution within a large search space through thermal fluctuations. The algorithm generates new solutions through Markov-chain Monte Carlo techniques. The latter can result in severe limitations, such as slow convergence and a tendency to stay within the same local search space at small temperatures. To overcome these shortcomings, we use the variational classical annealing (VCA) framework that combines autoregressive recurrent neural networks (RNNs) with traditional annealing to sample solutions independent of each other. In this paper, we demonstrate the potential of using VCA as an approach to solving real-world optimization problems. We explore VCA's performance in comparison with SA at solving three popular optimization problems: the maximum cut problem (Max-Cut), the nurse scheduling problem (NSP), and the traveling salesman problem (TSP). For all three problems, we find that VCA outperforms SA on average in the asymptotic limit. Interestingly, we reach large system sizes up to $256$ cities for the TSP. We conclude that in the best-case scenario, VCA can serve as a great alternative when SA fails to find the optimal solution.