Multipath Adaptive Tabu Search for a Vehicle Control Problem

Table 1

Summary of the surface optimization problems.

Surface names	Surface functions	Search spaces	Sketches
Bohachevsky	𝐹(𝑥,𝑦)=𝑥^2+2𝑦^2−0.3cos(3𝜋𝑥)−0.4cos(4𝜋𝑦)+0.7,; 𝑓min(0,0)=0	[−2,2]
Rastrigin	𝐹(𝑥,𝑦)=𝑥^2+𝑦^2−10cos(2𝜋𝑥)−10cos(3𝜋𝑦)+20,; 𝑓min(0,0)=0	[−2,2]
Shekel’s foxholes	𝑓(𝑥1,𝑥2)=[1/500+∑^25𝑗=1(1/(𝑗+∑^2𝑖=1(𝑥𝑖−𝑎𝑖𝑗)^6))]^−1	[−40,40]
	Where
	𝑎𝑖𝑗=^−32−1601632−32⋯01632−32−32−32−32−32−16⋯323232
	𝑓min(−32,−32)=1
Shubert	𝑓(𝑥,𝑦)=(∑^5𝑖=1𝑖cos((𝑖+1)𝑥1+𝑖))(∑^5𝑖=1𝑖cos((𝑖+1)𝑦+𝑖))	[−10,10]
	𝑓min(𝑥𝑗,𝑦𝑗)=−186.7309,𝑗∈{1,2,…,17,18}
Schwefel I	𝑓(𝑥1,𝑥2)=418.9829×2−∑^2𝑖=1(𝑥𝑖sin√|𝑥𝑖|),; 𝑓min(421,421)=0	[−500,500]
Schwefel II		[400,500]