DIRECTGOLib - DIRECT Global Optimization test problems Library

With the introduction of DIRECTGOLib (which stands as DIRECT Global Optimization test problems Library), we present a new and an actively growing online collection of the box- and generally-constrained test and engineering problems for DIRECT (DIviding RECTangles)-type global optimization [5].

DIRECTGOLib is a continuation of our previous DIRECTLib library [11], which was widely used in different studies (see, e.g., [6, 7, 8, 9, 10]). However, DIRECTLib was designed as a static library and did not offer the global optimization community comfortable opportunities to contribute to its growth. Therefore, a new DIRECTGOLib is designed as an open-source GitHub repository to which other researchers can easily contribute.

Moreover, all the problems are described using MATLAB programming language and syntax, seeking maximum usability with our recently introduced open-source tool: DIRECTGO: A new DIRECT-type toolbox for derivative-free Global Optimization.

Problems

There already exist various collections of global optimization test problems. The uniqueness of this collection is that it mainly concentrates on problems commonly used to test various DIRECT-type algorithms with at least one reliable source of experimental results. While the problems are gathered from the various sources but below we highlight a few that form an essential part of the current version:

• Global Optimization Test Problems (Hedar list) [1]
• Virtual Library of Simulation Experiments: Test Functions and Datasets [2]
• CEC2006 benchmark set [3]
• Global bound and linear constrained problems [4]
• Parameter estimation in the general non-linear regression model [12]
• Engineering design examples [13]

Classification

Based on the type of constraints, continuous global optimization test problems from DIRECTGOLib are classified into three main categories and the number of test problems within each category of the current version is specified in brackets:

• Box-constrained (55 problems in total)
• Linearly-constrained (35 problems in total)
• Generally-constrained (39 problems in total)

We also separate problems coming from practical applications:

• Engineering problems (11 problems in total).

Newly Added

Eight new box-constrained global optimization test problems:

• Crosslegtable.m
• Damavandi.m
• Deb01.m
• Deb02.m
• Permdb4.m
• Pinter.m
• Trefethen.m
• Vincent.m

Modified

One box-constrained global optimization test problem:

• Trid10.m

Contribution to DIRECTGOLib

We welcome contributions and corrections to this resource either way:

• By email - send us new problems, corrections, or suggestions by email: linas.stripinis@mif.vu.lt or remigijus.paulavicius@mif.vu.lt.
• GitHub way - fork the GitHub repository, add new problems or correct existing ones, then create a pull request, and we gratefully incorporate your contribution!

References

1. A. Hedar. 2005. Test functions for unconstrained global optimization. http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm.
2. S. Surjanovic and D. Bingham. 2013. Virtual Library of Simulation Experiments: Test Functions and Datasets. http://www.sfu.ca/~ssurjano/index.html.
3. Jing Liang, Thomas Runarsson, Efrén Mezura-Montes, M. Clerc, Ponnuthurai Suganthan, Carlos Coello, and Kalyan Deb. 2006. Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Nangyang Technological University, Singapore, Tech. Rep 41 (01 2006), 251–256
4. A.I.F. Vaz and L.N.Vicente, A particle swarm pattern search method for bound constrained global optimization, Journal of Global Optimization, 39 (2007) 197-219.
5. Jones, D.R., Perttunen, C.D. & Stuckman, B.E. Lipschitzian optimization without the Lipschitz constant. J Optim Theory Appl 79, 157–181 (1993). https://doi.org/10.1007/BF00941892.
6. R. Paulavičius, J. Žilinskas. (2014) Simplicial Global Optimization, SpringerBriefs in Optimization, Springer New York, New York, NY. doi:10.1007/978-1-4614-9093-7.
7. Stripinis, L., Paulavičius, R. & Žilinskas, J. Improved scheme for selection of potentially optimal hyper-rectangles in DIRECT. Optim Lett 12, 1699–1712 (2018). https://doi.org/10.1007/s11590-017-1228-4.
8. Stripinis, L., Paulavičius, R. & Žilinskas, J. Penalty functions and two-step selection procedure based DIRECT-type algorithm for constrained global optimization. Struct Multidisc Optim 59, 2155–2175 (2019). https://doi.org/10.1007/s00158-018-2181-2.
9. Stripinis, L., Paulavičius, R. A new DIRECT-GLh algorithm for global optimization with hidden constraints. Optim Lett 15, 1865–1884 (2021). https://doi.org/10.1007/s11590-021-01726-z.
10. Stripinis, L., Žilinskas, J., Casado, L. G., & Paulavičius, R. (2021). On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization. Applied Mathematics and Computation, 390, 125596. https://doi.org/https://doi.org/10.1016/j.amc.2020.125596.
11. Stripinis, L. & Paulavičius, R. 2020. DIRECTLib – a library of global optimization problems for DIRECT-type methods, v1.2. https://doi.org/10.5281/zenodo.3948890.
12. J. Gillard and D. Kvasov. 2017. Lipschitz optimization methods for fitting a sum of damped sinusoids to a series of observations. Statistics and Its Interface 10, 1 (2017), 59–70. https://doi.org/10.4310/SII.2017.v10.n1.a6
13. Tapabrata Ray and Kim Meow Liew. 2003. Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Transactions on Evolutionary Computation 7, 4 (2003), 386–396. https://doi.org/10.1109/TEVC.2003.814902