Evaluation of the physical annealing strategy for simulated annealing: a function-based analysis in the landscape paradigm.

The effectiveness of the actual annealing strategy in finite-time optimization by simulated annealing (SA) is analyzed by focusing on the search function of the relaxation dynamics observed in the multimodal landscape of the cost function. The rate-cycling experiment, which was introduced in the previous study [M. Hasegawa, Phys. Rev. E 83, 036708 (2011)] to examine the role of the relaxation dynamics in optimization, and the temperature-cycling experiment, which was developed for a laboratory experiment on relaxation-related phenomena, are conducted on two types of random traveling salesman problems (TSPs). In each experiment, the SA search starting from a quenched solution is performed systematically under a nonmonotonic temperature control used in the actual heat treatment of metals and glasses. The results show that, as in the previous monotonic cooling from a random solution, the optimizing ability is enhanced by allocating a lot of time to the search performed near an effective intermediate temperature irrespective of the annealing technique. In this productive phase, the relaxation dynamics successfully function as an optimizer and the relevant characteristics analogous to the stabilization phenomenon and the acceleration of relaxation, which are observed in glass-forming materials, play favorable roles in the present optimization. This nonmonotonic approach also has the advantage of a wider operation range of the effective relaxation dynamics, and in conclusion, the actual annealing strategy is useful and more workable than the conventional slow-cooling strategy, at least for the present TSPs. Further discussion is given of an illuminating aspect of computational physics analysis in the optimization algorithm research.