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Ackley Function


The Ackley function is a nonconvex test function used to compare methods of global optimization. In d dimensions, its usual form is

 f(x)=-aexp(-bsqrt(1/dsum_(i=1)^dx_i^2))-exp(1/dsum_(i=1)^dcos(cx_i))+a+e,

where the standard parameter values are a=20, b=0.2, and c=2pi. With these values, the function has global minimum f(0)=0. Its nearly flat outer region, large central depression, and many local minima make it a useful benchmark for testing whether a global optimization method escapes local minima.


See also

Cosine, Exponential Function, Global Minimum, Global Optimization, Local Minimum, Optimization Theory

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References

Ackley, D. H. A Connectionist Machine for Genetic Hillclimbing. Boston, MA: Kluwer Academic Publishers, 1987.

Cite this as:

Weisstein, Eric W. "Ackley Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AckleyFunction.html

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