The global optimization method with selective averaging of the discrete decision variables

Rouban, Anatoly I.; Михалев, А. С.

doi:10.17223/19988605/50/6

Cited by 1 publication

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We use test functions based on hyperbolic and exponential abilities [15,16], which, in our opinion, are more representative for solving optimization problems compared to the well-known test functions (power, trigonometric and others) considered in our previous works [17,18]. In addition, in this article, unlike previous ones, independent functions with three functions with at least several structures are used.…”

Section: Computational Experimentsmentioning

confidence: 99%

Application of the Auxiliary Function Method to the Search for the Global Minimum of Functions of Many Variables

Salavatovna,

Toktarovich

2024

MMEP

View full text Add to dashboard Cite

In early works, we presented a new economical and effective method for finding the global optimum of a function of many variables, which was conditionally called the auxiliary function method. The essence of the method is that a multi-extremal and multivariable objective function is transformed into a convex function 𝑔 𝑚 (𝐹, 𝛼) of one variable, which is the Lebesgue integral over a compact where the objective function is considered:, 𝑚 ∈ 𝑁 . The function 𝑔 𝑚 (𝐹, 𝛼) was called the auxiliary function. In early works, the properties of the auxiliary function and the algorithm of the new method were studied, the convergence of the method was proven, and computational experiments were carried out with multiextremal functions in three-dimensional space. Based on these results and in order to demonstrate the advantages of using the auxiliary function method, this paper considers the problem of finding global minima of objective functions in a fourdimensional space constructed on the basis of hyperbolic and exponential potentials and conducts a comparative analysis of the results obtained. In this work, as a result of completed computational experiments on test functions in three-dimensional and fourdimensional space, where auxiliary functions with different values of the degree 𝑚 𝜖 𝑁 were expanded, important conclusions were obtained and proven. As a result, the change in the auxiliary function depending on its degree m is clearly shown. This result provides even more opportunities to improve the efficiency of the constructed method. Next, you can set up first-and second-order methods to find the "oldest " zero auxiliary function.

show abstract

Section: Computational Experimentsmentioning

confidence: 99%