STUDYING THE EFFECTIVENESS OF A NEW ALGORITHM WITH A DEFINING FUNCTION FOR FINDING THE GLOBAL MINIMUM OF A SMOOTH FUNCTION
Ключевые слова:
multidimensional optimization, global optimization algorithm, Sobolev’s cubature formulas, De Jong function, Rosenbrock function, Rastrigin function.Аннотация
This article presents a new algorithm with a defining function to find the global minimum of multiextreme
functions of two variables. The stages of the new algorithm are described in detail.
Computational experiments were performed on three different test assignments. We have found the global
minima of the test functions. A convex function was given as the first example. In the second example, a non-convex
function that has a global minimum inside a parabolic strongly elongated surface has been analyzed. In the third
example, a function with a large number of local minima has been analyzed. These functions are different in
complexity, but our algorithm determines the global minimum of different functions in the same amount of time.
A determining function is formed depending on the function considered so that the algorithm to function. If a
function is two variables, then the defining function will contain a double integral. Such integrals were calculated
using Sobolev's cubature formulas with a regular boundary layer. Computer programs were used to calculate
cubature formulas. The calculation algorithm has been implemented using Microsoft Visual Studio in C++.
As a result of the computational experiment, the values and coordinates of the global minima of the test
functions have been found. A comparative analysis of the reference values and those found was made using the new
algorithm.
