A series of benchmark functions were selected due to their inherent difficulty to find their absolute minimum or maximum numerically because they are either: non-separable, non-differentiable, have a high number of dimensions or have multiple local minima (multimodal). These functions are usually used to test the performance of optimization algorithms (Yang). The selected benchmark functions are:
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Schaffer N1
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Holder-Table
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Cross-in-Tray
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Happy cat
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Schaffer N4
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N-D Sphere
More detalied description of the function is found in the following table
The second column describes the boundaries of the search space that was used for each function. The third column is the number of dimensions. The fourth column gives a description of the function, D: differentiable; ND: non-differentiable; NS: non-separable; U: unimodal; M: multimodal. f(x_{min}) is the minimum of the function and x_{min} is where the minimum can be found in the domain of the function, the |x| symbol means that the value of x can be positive or negative.
In bold are the best results