Title: A literature survey of benchmark functions for global optimisation problems

Authors: Momin Jamil; Xin-She Yang

Addresses: Blekinge Institute of Technology SE-37179, Karlskrona, Sweden; Harman International, Cooperate Division, Becker-Goering Str. 16, D-76307 Karlsbad, Germany ' Middlesex University, School of Science and Technology, Hendon Campus, London NW4 4BT, UK

Abstract: Test functions are important to validate and compare the performance of optimisation algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties to be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimisation problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and it can be expected that this complete set of functions can be used for validation of new optimisation in the future.

Keywords: global optimisation; test functions; unimodal; multimodal; separable; non-separable; benchmark functions; benchmarking; unconstrained optimisation; validation.

DOI: 10.1504/IJMMNO.2013.055204

International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.2, pp.150 - 194

Received: 26 Feb 2013
Accepted: 28 Feb 2013

Published online: 22 Jul 2013 *

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