Generation of complex nonlinear benchmark functions for optimization using fuzzy sets and classical test functions

Abstract

In this paper, we present a novel methodology to generate complex functionsusing two-dimensional fuzzy sets as weights for combining classical benchmarkfunctions. These new functions have different characteristics from original ones,but the minimum, borders and geometry characteristics of the functions are stillknown. Three different combinations of two functions (Rosenbrock and Bukin’s F4)are used to exemplify the method and its potential to generate specific test functionsto study and improve optimization methods.