Optimization Functions: There are several characteristics of the test functions that feature the complexity of the functions’ landscape like modality, separability, scalability (Dieterich and Hartke 2012). Modality is defined by the number of ambiguous peaks in the function landscape. A function is called separable if the variables of the solution are independent and can be optimized separately. On the other hand, the inseparable class of functions are highly difficult to solve as the variables are interrelated and affect each other. The functions that are extendable to arbitrary dimensionality are known as scalable function, otherwise are called non-scalable. The scalability often introduces high extent of complexity to the search space such as some test function landscapes become multimodal from unimodal when the number of dimensions is scaled up.

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 following:

You are required to implement nature-inspired algorithm to find the optimal value of any 20 optimization functions of your choice from the list given below for your class project.

Group IV: Multimodal, Separable and Scalable

Schwefel 2.26 function

fSchwefel2.6X=418.9829d-i=1d xisinxi

lb, ub=-500, 500d, X*=[420.9687, …, 420.9687]T, fSchwefel2.6X*=0