makeAckleyFunction {smoof}

Ackley Function

Description

Also known as “Ackley's Path Function”. Multimodal test function with its global optimum in the center of the defintion space. The implementation is based on the formula

f(\mathbf{x}) = -a \cdot \exp\left(-b \cdot \sqrt{\left(\frac{1}{n} \sum_{i=1}^{n} \mathbf{x}_i\right)}\right) - \exp\left(\frac{1}{n} \sum_{i=1}^{n} \cos(c \cdot \mathbf{x}_i)\right),

with a = 20, b = 0.2 and c = 2\pi. The feasible region is given by the box constraints \mathbf{x}_i \in [-32.768, 32.768].

Usage

makeAckleyFunction(dimensions)

Arguments

dimensions

[integer(1)]
Size of corresponding parameter space.

Value

[smoof_single_objective_function]

References

Ackley, D. H.: A connectionist machine for genetic hillclimbing. Boston: Kluwer Academic Publishers, 1987.