Positive role of glassy dynamics in finite-time optimization by threshold algorithms
The optimization mechanism of threshold algorithms is investigated in the solving process of a random Euclidean traveling salesman problem. A series of computer experiments previously designed for simulated annealing is conducted with algorithms such as generalized simulated annealing. The results show that if the threshold function decays fast enough, a previous positive view of slow relaxation dynamics in finite-time optimization by simulated annealing is still applicable regardless of the algorithm. These dynamics work effectively as an optimizer at around an intermediate temperature, which can be identified by using the Deborah number.
optimization threshold algorithms traveling salesman problem relaxation glass