makeAckleyFunction: Ackley Function

In jakobbossek/smoof: Single and Multi-Objective Optimization Test Functions

Ackley Function

Description

Also known as “Ackley's Path Function”. Multi-modal test function with its global optimum in the center of the definition 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

An object of class SingleObjectiveFunction, representing the Ackley Function.

[smoof_single_objective_function]

References

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

jakobbossek/smoof documentation built on Feb. 17, 2024, 2:23 a.m.