Experimental Data for a modification of the BIRECT (BIsecting RECTangles) algorithm : "Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme"

This data is used as the basis for the following preprint: "Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme". Here we experimentally investigated a modification suggested to the recently introduced BIRECT (BIsection of RECTangles) algorithm (https://doi.org/10.1007/s10898-016-0485-6). A new deterministic approach, named BIRECT-V algorithm (where V stands for vertices), combines bisection with sampling on diagonal vertices. Also, a new variation of the BIRECT-V algorithm, called BIRECT-Vl is also introduced. This data set contains the results of these experiments, the original source codes for the BIRECT-V algorithm used in the experiments, as well as the scripts used for evaluating the results would be available in a future version. First, We applied both algorithms to several well-known test problems using from (http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm), obtaining data1, data4, and data7. Second, we modified the optimization domain for certain functions, and obtained dataset 2, 3, and 5. These results were compared to the original BIRECT, BIRECT-l, DIRECT, and DIRECT-l.

References

Hedar, A.: Test functions for unconstrained global optimization. http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm (2005). Online; last visited:  26/11/22

Stripinis, L., Paulavicius, R.: DIRECTLib – a library of global optimization problems for DIRECT-type methods, v1.2 (2020). DOI 10.5281/zenodo.3948890; accessed : 08/12/22

Paulavicius, R., Sergeyev, Y.D., Kvasov, D.E., Zilinskas, J.: Globally-biased BIRECT algorithm with ˇ local accelerators for expensive global optimization. Expert Systems with Applications 144, 11305 (2020). https://doi.org/10.1016/j.eswa.2019.113052

Paulavicius, R., Chiter, L., Zilinskas, J.: Global optimization based on bisection of rectangles, fu ˇ nction values at diagonals, and a set of Lipschitz constants. Journal of Global Optimization 71(1), 5–20 (2018). https://doi.org/10.1007/s10898-016-0485-6