Some local and global search balancing methods in parallel global optimization algorithms

Abstract

The paper continues the study of the informational-statistics approach for minimizing multiextremal functions with nonconvex constraints called the index method of global optimization. The procedure of solving multidimensional problems is reduced to solving equivalent one-dimensional ones. This reduction is based on using the Peano curves reflecting the unit segment of the real axis to a hypercube uniquely. The technique of constructing a set of Peano curves is used (rotated evolvements). It can be efficiently applied to solving a problem on a cluster with tens and hundreds processors. The main attention is paid to the use of a mixed local-global computational scheme to speed up the convergence of the parallel algorithm as well as to the application of a local descent after each improvement of a global optimum estimate (record local refinement) followed by the global search continuation.