A Collection of 30 Multidimensional Functions for Global Optimization Benchmarking

Vagelis Plevris and German Solorzano
Additional contact information
Vagelis Plevris: Department of Civil and Architectural Engineering, Qatar University, Doha P.O. Box 2713, Qatar
German Solorzano: Department of Civil Engineering and Energy Technology, OsloMet—Oslo Metropolitan University, Pilestredet 35, 0166 Oslo, Norway

Data, 2022, vol. 7, issue 4, 1-51

Abstract: A collection of thirty mathematical functions that can be used for optimization purposes is presented and investigated in detail. The functions are defined in multiple dimensions, for any number of dimensions, and can be used as benchmark functions for unconstrained multidimensional single-objective optimization problems. The functions feature a wide variability in terms of complexity. We investigate the performance of three optimization algorithms on the functions: two metaheuristic algorithms, namely Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), and one mathematical algorithm, Sequential Quadratic Programming (SQP). All implementations are done in MATLAB, with full source code availability. The focus of the study is both on the objective functions, the optimization algorithms used, and their suitability for solving each problem. We use the three optimization methods to investigate the difficulty and complexity of each problem and to determine whether the problem is better suited for a metaheuristic approach or for a mathematical method, which is based on gradients. We also investigate how increasing the dimensionality affects the difficulty of each problem and the performance of the optimizers. There are functions that are extremely difficult to optimize efficiently, especially for higher dimensions. Such examples are the last two new objective functions, F29 and F30, which are very hard to optimize, although the optimum point is clearly visible, at least in the two-dimensional case.

Keywords: optimization; unconstrained; benchmark functions; objective function; GA; PSO; SQP (search for similar items in EconPapers)
JEL-codes: C8 C80 C81 C82 C83 (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2306-5729/7/4/46/pdf (application/pdf)
https://www.mdpi.com/2306-5729/7/4/46/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jdataj:v:7:y:2022:i:4:p:46-:d:791563

Access Statistics for this article

Data is currently edited by Ms. Cecilia Yang

More articles in Data from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().