Experiment 2D and 5D: Progressive Sample Scaling Algorithm To Solve Many-Affine BBOB Functions.

<b>Summary</b>The Progressive Sample Scaling (PSS) algorithm is a deterministic iterative method with the purpose of solving Many-Affine BBOB type problems provided by the IOHprofiler environment^[1]. The PSS algorithm operates in two stages: Sample and Scaling.In the Sample stage, the algorithm generates a combination of equidistant points within the problem's boundaries, where each point corresponds to a variable array with a fixed dimension size. Subsequently, the points are evaluated, a fitness array is generated, and the best fitness value is recorded. The number of points to generate combinations is specified by the user, if an array of points is provided, these points are evaluated, and the one with the highest fitness is selected.In the Scaling stage, the number of points around the best point identified in the Sample stage is increased, the best point is chosen, the search is refined progressively around it. This process is repeated until the budget is exhausted. Optionally, there is a factor value that can increase or decrease the number of points during execution in the Scaling stage.Once the budget or iterations are exhausted, the best solution is extracted. For this specific experiment^[2]^[3], the average AOCC is calculated.<b>Objectives</b>Solve Many-Affine BBOB Functions using a Deterministic Algorithm.<b>Limitations</b>This algorithm is designed for Many-Affine BBOB problems of 2 and 5 dimensions.<b>Experiment Result</b>2D Experiment: Average AOCC 0.59113570901930215D Experiment: Average AOCC 0.4861510330030686<b>Environment</b>The notebooks are configured for 2 and 5 dimensions.The hardware used was a Lenovo computer (ThinkPad T14s Gen 4), with an AMD Ryzen 7 PRO 7840U w/ Radeon 780M Graphics, 32 GB RAM, running the Microsoft Windows 11 Pro Version 10.0.22631 Build 22631.<b>References</b>[1] IOHprofiler https://iohprofiler.github.io.[2] GECCO 2024 Competition: Anytime Algorithms for Many-affine BBOB Functions https://gecco-2024.sigevo.org/Competitions#id_Anytime Algorithms for Many-affine BBOB Functions.[3] Anytime Algorithms for Many-affine BBOB Functions https://iohprofiler.github.io/competitions/mabbob24.