Chaotic annealing for optimization

We study the effect of chaotic transient for a global minima search in optimization. For a given energy or cost function, a chaotic evolution system in which chaos provides a scheme for searching the minima of the energy function in the state space can be constructed generally. By controlling a bifurcation parameter from the chaotic dynamics regime to the fixed-point regime gradually the system may eventually reach the global optimum state or its good approximation with very high probability. A double potential well and a traveling salesman problem are used to numerically illustrate the validity of chaotic transient search.