Griewank function

In mathematical optimization, the Griewank function is used as a performance test problem for optimization algorithms. For order $n$ it is defined by:^[1]

f(x_{1},x_{2},\ldots ,x_{n}):=1+{\frac {1}{4000}}\sum _{i=1}^{n}x_{i}^{2}-\prod _{i=1}^{n}\cos \left({\frac {x_{i}}{\sqrt {i}}}\right).

The Griewank function has a global minimum at $f(0,0,\ldots ,0)=0$ and multiple local minima^[2]. A typical search area is $x_{i}=[-600,600]$ , for $i=1,\ldots ,n$ ^[1].

References

^ ^a ^b Griewank, A. O. "Generalized Decent for Global Optimization." J. Opt. Th. Appl. 34, 11–39, 1981
^ Locatelli, M. "A Note on the Griewank Test Function." J. Global Opt. 25, 169–174, 2003

[Griewank1981-1] Griewank, A. O. "Generalized Decent for Global Optimization." J. Opt. Th. Appl. 34, 11–39, 1981

[2] Locatelli, M. "A Note on the Griewank Test Function." J. Global Opt. 25, 169–174, 2003

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See also

References