Global optimization method using chaos in dissipative system

Most of the actual optimization problems are nonlinear and have many peaks (nonconvex). With the widespread use of the high-speed and large-capacity computers as the background, it has recently been felt highly necessary to derive the global optimal solution for the optimization problem which is nonlinear and has multiple peaks. It is one of the most important topics of research in the field of optimization. The major global optimization method developed until now can be divided into the trajectory method, the function transformation method, and the simulated annealing method. This paper proposes a new approach which is totally different from the forementioned conventional methods, i.e., the global optimization method for the unconstrained nonlinear optimization problem where chaos is introduced. the proposed method is based on the dissipative system where the inertia term and the nonlinear damping term are added to the conventional gradient method. By appropriately adjusting the characteristics of the nonlinear damping term, the generation of chaos can itself be controlled. Then, by overriding the barrier of the energy function between the local minima, the process converges to the global optimal solution. Finally, the proposed method is applied to the typical multipeaked nonlinear optimization problem with two and ten variables and it is shown that the global optimal solution can be derived by adequately adjusting the parameter of the nonlinear damping term.