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 \(\mathbf{x}_i \in [-32.768, 32.768]\).
makeAckleyFunction(dimensions)[integer(1)]
Size of corresponding parameter space.
[smoof_single_objective_function]
Ackley, D. H.: A connectionist machine for genetic hillclimbing. Boston: Kluwer Academic Publishers, 1987.