DOI: 10.5281/zenodo.7416231
title: Experimental Data for a modification of the BIRECT (BIsecting RECTangles) algorithm : "Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme"

description: 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. <strong>References</strong> 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
description: Details of the data are as follows: Data1: experimental results related to BIRECT-V, Data2: experimental results related to BIRECT-V (modified domain), Data3: experimental results for BIRECT-Vl (modified domain), Data4: experimental results for comparison of BIRECT-V vs BIRECT, Data5: experimental results for comparaison of BIRECT-Vl vs BIRECT-l, Data7: experimental results for BIRECT-Vl, birect-v.glob.solution.txt : . Results for BIRECT-V for a set of test problems (from: http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm ) with modified domain and original domain. right side: Global minimizer found x_min, left side: global minimizer from : https://doi.org/10.5281/zenodo.3948890 iter.prog.modified.txt : Iteration progress in solving Ackley 3 (n = 10) test problem (upper: BIRECT-Vl, lower : BIRECT-V) Figure POH.png : Graphic illustration of potentially optimal hyper-rectangles (POHs) on the Branin test problem in eighth iteration; rectangles measure versus minimal function value; Scatter plot.png : Branin test problem, sampling points (red color), and the global minimizer (x_min) in blue color; Convergence plot.png : graph representing the number of function evaluations vs f_min for the Branin test problem. graph.png : graph of the Branin test function. Any questions or suggestions, contact L. Chiter at Department of Mathematics, Ferhat-Abbas University of Sétif1, Sétif 19000, Algeria; via email to lchiter@univ-setif.dz