A literature survey of benchmark functions for global optimisation problems

By Momin Jamil, Xin-She Yang. Int. J. Math. Model. Numer. Optimisation, 2013

1,418 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ae3ebe6c69fdb19e12d3218a5127788fae269c10

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Ebola Optimization Search Algorithm: A New Nature-Inspired Metaheuristic Optimization Algorithm (2022, background): “It has been shown that these test functions work well for situations where the quality of intelligent and resistant optimization algorithms are tested [41], [75]–[79].”
Chaos Game Optimization: a novel metaheuristic algorithm (2020, background): “A total number of 239 mathematical functions categorized into four different groups based on their specific characteristics are utilized (Jamil and Yang 2013; Jamil et al.”
On the exploration and exploitation in popular swarm-based metaheuristic algorithms (2018, background): “In literature, such test functions with diverse properties are vastly used in order to test and validate metaheuristic performances [29].”
A Comprehensive Review of Swarm Optimization Algorithms (2015, background): “The benchmark functions selected and their characteristics are presented in Table 2 [130, 131].”
An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges (2023, background): “175 benchmark functions are collected by Jamil and Yang (2013).”