Bacterial Foraging-Tabu Search Metaheuristics for Identification of Nonlinear Friction Model

Table 1

Summary of the unconstrained problems used for performance test.

Test functions	Equations	Surfaces in 3D
BF	𝑓(𝑥,𝑦)=𝑥^2+2𝑦^2−0.3cos(3𝜋𝑥)−0.4cos(4𝜋𝑦)+0.7 global minimum of 0 at (0,0), search space: [2 2; −2 −2] and 𝐽min≤1×10^−9.
RF	𝑓(𝑥,𝑦)=𝑥^2+𝑦^2−10cos(2𝜋𝑥)−10cos(2𝜋𝑦)+20 global minimum of 0 at (0,0), search space: [2 2; −2 −2] and 𝐽min≤1×10^−8.
SF	𝑓(𝑥1,𝑥2)=[1/500+∑^25𝑗=1(1/(𝑗+∑^2𝑖=1(𝑥𝑖−𝑎𝑖𝑗)^6))]^−1 when 𝑎𝑖𝑗=^−32−1601632−32⋯01632−32−32−32−32−32−16⋯323232. global minimum of 0.998 at (−32,−32), search space: [40 40; −40 −40] and 𝐽min≤0.9990.
SchF	𝑓(𝑥)=418.9829𝑛−∑^𝑛𝑖=1(𝑥𝑖sin|𝑥𝑖|);𝑛=2 global minimum of 0 at (420.9687, 420.9687), search space: [500 500; −500 −500] and 𝐽min≤1×10^−1.
ShuF	𝑓(𝑥1,𝑥2)=∑^5𝑖=1𝑖cos((𝑖+1)𝑥1+𝑖)∗∑^5𝑖=1𝑖cos((𝑖+1)𝑥2+𝑖) when −10≤𝑥1,𝑥2≤10. global minima of equal values −186.7309 at 18 different locations, search space: [10 10; −10 −10] and 𝐽min≤−186.73.