*Discription of Mathematical Test Function*

Rastrigin is a multimodal function and is challenging to solve because it contains several local minima regions where an optimization algorithm with limited exploratory power is likely to become trapped. The function's lone globally optimal solution, 0, is located within the domain of [−5.12, 5.12] at f (x\*) = [0, 0, . . . , 0].

The step mathematical test function is one of the more complicated and complex problems due to the lack of suitable direction. The minimum value is fixed at zero. The search region of said benchmark problem is [−100, 100], and the shape of the given benchmark problem is flat.

Researchers are using the Quartic function as a benchmark problem due to its unimodal quality. Its global point is zero and the space of its search is mentioned and presented between the values of [−1.28] and [1.28].

The test function, namely "Sphere," is a unimodal and continuous function, and the solution of such types of problems is easy. The search domain should be mentioned in the brackets [−5.12, 5.12]. The zero is the minimum value of the given sphere function where the value is derived by the computational scientist and the research optimization school.

Griewank is the mathematical test function that is used in the field of engineering design for the validation of computational techniques. The mentioned problem is complex and multimodal, and its feasible range of function is [−100, 100]. The scientist has already discovered that the global optimal solution to the aforementioned benchmark problem is zero.

The Alpine 1 function is a mathematical test function used to validate computing strategies in the field of engineering optimization. This function is Multimodal and Continuous with a −10 ≤ xi ≤ 10 constraint. The origin is the location of the global minimum, where x = (0, 0) and f(x) = 0.
