Rastrigin function

In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed in 1974 by Rastrigin as a 2-dimensional function and has been generalized by Rudolph. The generalized version was popularized by Hoffmeister &; Bäck and Mühlenbein et al. Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima.
On an -dimensional domain it is defined by:
where and. There are many extrema:

The global minimum is at where.
The maximum function value for is located at :

Number of dimensions	Maximum value at
1	40.35329019
2	80.70658039
3	121.0598706
4	161.4131608
5	201.7664509
6	242.1197412
7	282.4730314
8	322.8263216
9	363.1796117

Here are all the values at 0.5 interval listed for the 2D Rastrigin function with :
The abundance of local minima underlines the necessity of a global optimization algorithm when needing to find the global minimum. Local optimization algorithms are likely to get stuck in a local minimum.