# Experimental Data for the preprint "Diagonal Partitioning Strategy Using Bisection of Rectangles and a Novel Sampling Scheme"

## Description

This data is used as the basis for the following preprint: N. Guessoum et al. "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. 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 the literature, obtaining data1, data4, and data6. 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.

## Files

## Steps to reproduce

Tests were carried out by L. Chiter. Data 1, 4, and 6 were reverified by Pr. M. Bentobache at Université Amar Telidji Laghouat, Algeria. 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, Data6: experimental results for BIRECT-V when the number of function evaluations exceeded the prescribed limit of 1000000; Iteration progress.txt : . Iteration progress in solving Branin test problem. 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. test function graph.png : graph of the Branin test function. If you have any questions or suggestions, contact Prof. L. Chiter at Department of Mathematics, Ferhat-Abbas University of Sétif1, Sétif 19000, Algeria; or via email to lchiter@univ-setif.dz