Abstract
Most of the actual optimization problems are large-scale, nonlinear and multi-peaked (nonconvex). Furthermore, with the widespread use of high-speed and large capacity computers as the background, it is felt necessary in resent years to derive a global solution for nonlinear and multi-peaked optimization problems. It is one of the most important topics in optimization. This paper proposes a new dynamic tunneling algorithm with multi trajectories (Multi-Trajectory Dynamic Tunneling Algorithm) that is composed of two systems, an optimization system and a tunneling system. These systems are used sequentially to approach a global optimal solution of an objective function. The numerical stability of the conventional dynamic tunneling algorithm is theoretically investigated and interaction between each trajectory of the tunneling system is introduced in order to improve search efficiency. The proposed algorithm is applied to 2-variable and 10-variable typical multi-peaked nonlinear optimization problems.
