Structure of Filled Functions: Why Gaussian and Cauchy Templates Are Most Efficient

  • Vyacheslav Kalashnikov Central Economics & Mathematics Institute (CEMI)
  • Vladik Kreinovich University of Texas at El Paso (UTEP)
  • José Guadalupe Flores-Muñiz Universidad Autónoma de Nuevo León (UANL)
  • Nataliya Kalashnykova Universidad Autónoma de Nuevo León (UANL)
Keywords: Optimization Algorithms, Filled Function Method, Gaussian and Cauchy Functions

Abstract

One of the main problems of optimization algorithms is that they often end up in a local optimum. It is, therefore, necessary to make sure that the algorithm gets out of the local optimum and eventually reaches the global optimum. One of the promising ways guiding one from the local optimum is prompted by the filled function method. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and Cauchy functions. In this paper, we provide a possible theoretical explanation of this empirical effect.

Published
2016-11-14
How to Cite
Kalashnikov, V., Kreinovich, V., Flores-Muñiz, J., & Kalashnykova, N. (2016). Structure of Filled Functions: Why Gaussian and Cauchy Templates Are Most Efficient. International Journal of Combinatorial Optimization Problems and Informatics, 7(3), 87-93. Retrieved from https://ijcopi.org/index.php/ojs/article/view/30
Section
Articles