Informatica

Spatial Global Optimization branch and bound (B&B) methods aim at enclosing global minimum points in a guaranteed way with a certain accuracy. We extend simplicial B&B (sBB) concepts to polytopal B&B (pBB), with polytope subsets. The main challenges are: polytope division and extension of monotonicity tests theoretically and algorithmically. We compare the performance of interval B&B with linear constraints (iBBLC), sBB and pBB algorithms, to determine the most efficient B&B algorithm for different types of instances.

In this paper public available C and C++ packages for interval arithmetic are investigated and experimentally compared. The results of comparison give suggestions which packages and when are preferable.

The optimization problems occurring in nonlinear regression normally cannot be proven unimodal. In the present paper applicability of global optimization algorithms to this problem is investigated with the focus on interval arithmetic based algorithms.

New ways to estimate ranges of values of functions from standard and inner interval arithmetic have been proposed. Using the proposed ways ranges of values of mathematical test functions for global optimization and of objective functions for practical global optimization problems have been estimated and compared. Results of the experiments show that it is promising to use proposed balanced interval arithmetic in interval global optimization.

The results of experimental testing of balanced random interval arithmetic with typical mathematical test functions and practical problem are presented and discussed. The possibility of evaluation ranges of functions using balanced random interval arithmetic is investigated. The influence of the predefined probabilities of standard and inner interval operations to the ranges of functions is experimentally investigated.