Analysis of algorithms

Among 40 functions, 27 are classical functions whereas 13 functions are rotated and/or shifted and hybridized to construct modified functions. Depending on the three basic properties (modality, separability, and scalability) mentioned above, we classify the 27 functions under consideration into six groups (Group I through VI). The rest of the 13 modified functions are categorized into three groups according to their complexities. The definition of the functions under different groups with their corresponding search ranges ([lb, ub]) of solution variable
(X), global optimum (X*) and the function value at global optimum, f(X*) are listed as