Topology-Aware Simulated Annealing

Simulated annealing is one of the most known and successful algorithms for global optimization. It is widely used in discrete optimization and has also been successfully used for continuous optimization. In this paper, we propose a variation of simulated annealing that takes into consideration the state space topology by making the probability of uphill moves dependent on state degrees. The performance of the proposed strategy is evaluated experimentally. The influence of the topology of the state space and the landscape of the objective function on performance is explored. The results show that the proposed method outperforms classical simulated annealing in state spaces with a purely random network structure. Another interesting result is found in state spaces with a scale-free structure. It is observed that, whereas classical simulated annealing outperforms the proposed method in landscape with shallow minima, the latter gives better results for landscapes with dense and deep local minima, a type of landscapes known to be particularly challenging for simulated annealing.