Application of Chaos Induced Near-Resonance Dynamics to Locate the Global Optimum of Functions

The problem of locating the global optimum of functions is studied in a dynamic setting. The dynamics of simple multistable systems under the influence of chaotic forcing is investigated. When the magnitude of the forcing signal decays slowly, it is shown that the system attains an equilibrium state, which corresponds to the global optimum of the corresponding multimodal potential function. The role of bifurcations in facilitating the approach to the global optimum is discussed.