Construction of Multi-trajectory Dynamic Tunneling Algorithm
貴広 村野, Tokumitsu Fujita, Takao Watanabe, Keiichiro Yasuda · IEEJ Transactions on Electronics Information and Systems · 1998
The dynamic tunneling algorithm (DTA) is an effective method for global optimization problem. It is based on the idea that the global minimum is included in the local minima. And it is consisted of two dynamical systems: the optimization system by which a local minimum from an initial point is found, and the tunneling system by which a new point in a lower valley is searched for. In theory, the global minimum should be found by computing the trajectory of each system by turns. However, according to our numerical experiments, the tunneling system in DTA has numerical instability. In consequence, it is next to impossible to tune its parameters appropriately, and it is few cases that the global minimum is found.In this paper, a multi-trajectory DTA is proposed. In this algorithm, an interaction among each trajectory of the tunneling system is introduced. As a result, it becomes possible to search for the global minimum efficiently, and in addition, as the number of trajectories is increased, the global minimum is found more frequently. Several numerical experiments show the ability of the proposed algorithm.