TOPOGRAPHICAL GLOBAL OPTIMIZATION USING PRE-SAMPLED POINTS

A method for global minimization of a function f(x), x is-an-element-of A subset-of R(n) by using presampled global points in A is presented. The global points are obtained by uniform sampling, discarding points too near an already accepted point to obtain a very uniform covering. The accepted points and their nearest-neighbours matrix are stored on a file. When optimizing a given function these pre-sampled points and the matrix are read from file. Then the function value of each point is computed and its k nearest neighbours that have larger function values are marked. The points for which all its neighbours are marked are extracted as promising starting points for local minimizations. Results from a parallel implementation are presented. The working of a sequential version in Fortran is illustrated.