@article {pub4219,
	title = {MF2: A Collection of Multi-Fidelity Benchmark Functions in Python},
	author = {Sander van Rijn AND Sebastian Schmitt},
	year = {2020},
	abstract = {The field of (evolutionary) optimization algorithms often works with expensive
black-box optimization problems. Because of how computationally expensive they
are, real-world problems are not a first choice to test on when developing new
algorithms. Instead, benchmark functions such as Sphere, Rastrigin, and Ackley
are used. These functions are not only fast to compute, but also have known
landscape properties that can be taken into account when examining the
performance of new algorithms.

As the same sets of benchmark functions are typically used in literature, having
it makes sense to simply use a pre-written implementation. This ensures
correctness of the functions, makes any results directly comparable, and simply
saves time from not having to implement the functions yourself. For the
{\textquoteright}regular{\textquoteright} single-fidelity benchmarks, the COCO BBOB
[@nikolaus_hansen:2019] software is such a widely used collection.

As the field of *multi-fidelity* optimization is becoming more popular, a
similar set of common benchmarks is appearing in the literature:

  * Forrester et al. [@forrester:2007] introduced a simple 1D bi-fidelity
    function for mostly illustrative purposes.
  * Dong et al. [@dong_multi-fidelity:2015] introduced bi-fidelity versions of
    the Bohachevsky, Booth, Branin, Himmelblau and Six-hump Camelback functions.
  * Toal [@toal_considerations:2015] introduced correlation-adjustable multi-
    fidelity versions of the Branin, Paciorek, Hartmann3 and Trid functions.
  * Surjanovic and Bingham [@simulationlib:2017] have previously collected a
    small collection of MATLAB/R implementations for the Borehole, Currin and
    Park91 A and B functions.

{\textquoteleft}{\textquoteleft}MF2{\textquoteleft}{\textquoteleft} is a new collection of these commonly used multi-fidelity functions,
implemented in Python. It uses a standard interface that allows for querying
single vectors or multiple row-vectors as a single matrix. It also offers a
simple factory pattern interface for functions with parameters for e.g.
correlation and dimensionality.

This package is currently in use by the authors in their research on multi-
fidelity hierarchical surrogate models.},
	publisher = {The Journal of Open Source Software},
	journal = {Journal of Open Source Software}
}