DIRECTGOLib - DIRECT Global Optimization test problems Library

With the introduction of <strong>DIRECTGOLib</strong> (which stands as <strong>DIRECT</strong> <strong>G</strong>lobal <strong>O</strong>ptimization test problems <strong>Lib</strong>rary), we present a new and an actively growing online collection of the box- and generally-constrained test and engineering problems for <strong>DIRECT</strong> (<strong>DI</strong>viding <strong>RECT</strong>angles)-type global optimization [5]. <strong>DIRECTGOLib</strong> is a continuation of our previous <strong>DIRECTLib</strong> library [11], which was widely used in different studies (see, e.g., [6, 7, 8, 9, 10]). However, <strong>DIRECTLib</strong> was designed as a static library and did not offer the global optimization community comfortable opportunities to contribute to its growth. Therefore, a new <strong>DIRECTGOLib</strong> is designed as an open-source GitHub repository to which other researchers can easily contribute. Moreover, all the problems are described using <code>MATLAB</code> 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. <strong>Problems</strong> 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] <strong>Classification</strong> Based on the type of constraints, continuous global optimization test problems from <strong>DIRECTGOLib</strong> 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). <strong>Newly Added</strong> Eight new box-constrained global optimization test problems: <code>Crosslegtable.m</code> <code>Damavandi.m</code> <code>Deb01.m</code> <code>Deb02.m</code> <code>Permdb4.m</code> <code>Pinter.m</code> <code>Trefethen.m</code> <code>Vincent.m</code> <strong>Modified</strong> One box-constrained global optimization test problem: <code>Trid10.m</code> <strong>Contribution to DIRECTGOLib</strong> We welcome contributions and corrections to this resource either way: <strong>By email</strong> - send us new problems, corrections, or suggestions by email: [e-mail] or [e-mail]. <strong>GitHub way</strong> - fork the GitHub repository, add new problems or correct existing ones, then create a pull request, and we gratefully incorporate your contribution! <strong>References</strong> A. 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(2014) Simplicial Global Optimization, SpringerBriefs in Optimization, Springer New York, New York, NY. doi:10.1007/978-1-4614-9093-7. Stripinis, L., Paulavičius, R. &amp; 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. Stripinis, L., Paulavičius, R. &amp; 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. 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. Stripinis, L., Žilinskas, J., Casado, L. G., &amp; 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. Stripinis, L. &amp; Paulavičius, R. 2020. DIRECTLib – a library of global optimization problems for DIRECT-type methods, v1.2. https://doi.org/10.5281/zenodo.3948890. 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 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