Effectiveness of Slow Relaxation Dynamics in Finite-Time Optimization by Simulated Annealing

The origin of the specific temperature beneficial to finite‐time optimization by simulated annealing is discussed on the analogy of the dynamics of complex physical systems. Rate‐cycling experiments are introduced and performed on practical time scales on the random Euclidean traveling salesman problems. In the present systems, the effective relaxation dynamics and the resulting good optimization performance are not only dependent on but also sensitive to the search around an intermediate temperature. This influential temperature is understood to be determined from the temperature dependence of the Deborah number used to identify glass transition.