Optimal annealing schedules for a modified Tsallis statistics

In this paper, for a number of example systems, optimal schedules for simulated annealing with a modified Tsallis statistics for various parameters q are analyzed. It turns out that in general depending on the objective function (minimizing the mean energy or maximizing the ground state probability), different schedules have to be chosen. Furthermore, the optimal objective function value, reached with the optimal schedule, shows a monotonic dependency on q, where better values are reached for smaller q. Thus, in stochastic optimization the limit case q --> -infinity corresponding to threshold accepting should be chosen in order to get the best possible optimization results with as little effort as possible. (C) 2002 Elsevier Science (USA).