A discrete search technique for global optimization

We have developed a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an objective function in search of global minima. We demonstrate the effectiveness of this algorithm by applying it to a model geometry optimization problem. Significant improvements in optimization efficiency are demonstrated, in that our algorithm returns lower minima than conventional line minimization in 79% of the optimization runs we made. The method is orders of magnitude less computationally intensive than simulated annealing, while returning good minima for functions possessing many local minima. The method is simple to program, and requires only two-point gradient calculations for its implementation.