Abstract
In global optimization, there exist many problems which have multiple global solutions. In this paper, Multi-Trajectory Random Search Method with Territory Competition is proposed for such problems.
In the conventional Random Search, the global optimal solution is searched by only one trajectory. In the proposed method, the multiple global solutions are searched by multiple trajectories.
In order to find multiple global solutions, the concept of territory competition among multiple trajectories is introduced. Finding every global solution is guaranteed under some mild conditions and its proof is given.
The proposed method is applied to find the solutions of simultaneous nonlilear equations. The method is shown to be very powerful and can find every solution at one trial for example problem. The method is compared with the other methods and its superior points are shown.
The proposed method is very effective, and its application to many problems is promising.
