Continuous Global Optimization Algorithm using Lattice-based Sampling and Topographical Multilevel Single Linkage

We propose an algorithm for solving global optimization problems with objective functions of n-real variables and bounded constraints. This method basically uses sample lattice points and uses topographical information on objective function and a multilevel single linkage technique for avoiding repeated convergence to the same local minima. We show that the algorithm can calculate neighboring points in a much shorter time than that in the case of using the TGO method. Moreover, in order to avoid exponentially increasing sample size with increased number of divisions of each coordinate, we propose a subspace sampling. We show by numerical experiments in simple test functions that the algorithm effectively finds the global minima in a short computational time and in a few function evaluations.