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.

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.

A random walk dan be used to model various types of discrete random processes. It may be of interest at some point to find the peak of this function. A direct method of doing so involves evaluating the function at every point and recording the highest value. However, it may be desirable to find the peak without having, to evaluate the function at every point. A search technique was developed to find the peak of a random walk with a minimal number of function evaluations using probabilistic means to guess at where the peak will most likely occur given the parameters of a specific function. A computer program was written to implement the search strategy and a series-of random walk functions of varying lengths were generated to test its performance. Data was compiled and the results show that the search is capable of finding the peak with a significant reduction in the number of function evaluations needed for a point by point search, especially for functions of greater walk length.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.